Math Problem

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61

[quote]jbpick86 wrote:
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]

Where is it implied? All it states is there are 96 screws in the jar. It goes on to make further factual statements before asking the question. There is no indication of an element of time here, that is something you are mistakenly assuming and thus leading you down the wrong path. It doesn’t say “first”, or “second”, or “then”, or “before”. It lists a group of facts.

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[quote]tedro wrote:
Kansas. BS in math.[/quote]

When it says “in one”; How are you not deriving that it means “In one Jar” (which we were previously told had only 96 screws)?

Because if you interpret as “in one jar 1/4 are being used” then there are no screws outside of the jar. And for your scenario to work you have to have screws OUT of the jar, of which there is no mention.

IF you want to read it at its most literal level with no implication:

IN Jar A there are 96 screws, and one quarter of them are being used for a job while never being taken out of the jar, Jar B, C, and D would all operate the same way. So by the most literal interpretation 15/32’s of the total volume of screws are not being used.

64

[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]
That there are 96 screws in the jar is quite clear and not disputed. The difference in interpretation revolves around whether those screws that are in use are in the jar and part of the 96 or outside of the jar and a separate part of some total that includes them and the 96.

As to your last sentence, actually, it states that “In one 1/4 is being used in another 5/8, in another 3/4, and the last one 1/2.” That doesn’t mean 1/4 of the screws that belong to the jar (you seem to have added the notion of belonging to a jar based on your interpretation and that is certainly not mentioned in the original question).

[quote]tedro wrote:

[quote]Silyak wrote:
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?
[/quote]

That statement is fairly clear. It’s the next part of the question that gets foggy.

[quote]tedro wrote:
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]

“In one[of the jars]” has multiple meanings? You can argue that “one” refers to types of screws and not jars, but that is my point about weird antecedents. The real problem with this interpretation, though, is that the problem never states that the screws in the 4 jars are different or distinguishable beyond their physical location as inside of one of the jars. There is no indication that screws outside of the jars (which, beyond the assumption that screws in use are not in jars, are not explicitly stated to exist) are definitively tied uniquely to one of the four jars and its constituent screws.

My larger wonder about this question is whether or not the OP faithfully copied the question in the first place. He may have just summarized it from his memory of a test. This seems most likely as beyond the poor wording, the question is definitively improperly punctuated.

65

[quote]tedro wrote:
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.[/quote]

It is necessary if you wish to interpret it in the manner you did.

The sentence either means there are four jars with 96 screws in them, or there are four jars with 96 screws in each of them.

But because the sentence is poorly written, you cannot conclusively arrive at either interpretation.

Simply put- each is used horribly wrong here, and as a result the sentence is confusing.

The rest of the sentence is not that confusing, besides the punctuation errors that I think maverick88 made. Hell, that in itself raises a question- did maverick88 even write the question out right?

66

[quote]jbpick86 wrote:

[quote]tedro wrote:
Kansas. BS in math.[/quote]

When it says “in one”; How are you not deriving that it means “In one Jar” (which we were previously told had only 96 screws)?

Because if you interpret as “in one jar 1/4 are being used” then there are no screws outside of the jar. And for your scenario to work you have to have screws OUT of the jar, of which there is no mention.

IF you want to read it at its most literal level with no implication:

IN Jar A there are 96 screws, and one quarter of them are being used for a job while never being taken out of the jar, Jar B, C, and D would all operate the same way. So by the most literal interpretation 15/32’s of the total volume of screws are not being used. [/quote]

Because I already know each jar has 96 screws, which leaves only one way to interpret the rest of the question and that is “in one” means the total group of screws belonging to that jar.

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[quote]tedro wrote:

[quote]jbpick86 wrote:

[quote]tedro wrote:
Kansas. BS in math.[/quote]

When it says “in one”; How are you not deriving that it means “In one Jar” (which we were previously told had only 96 screws)?

Because if you interpret as “in one jar 1/4 are being used” then there are no screws outside of the jar. And for your scenario to work you have to have screws OUT of the jar, of which there is no mention.

IF you want to read it at its most literal level with no implication:

IN Jar A there are 96 screws, and one quarter of them are being used for a job while never being taken out of the jar, Jar B, C, and D would all operate the same way. So by the most literal interpretation 15/32’s of the total volume of screws are not being used. [/quote]

Because I already know each jar has 96 screws, which leaves only one way to interpret the rest of the question and that is “in one” means the total group of screws belonging to that jar.[/quote]

But it says IN ONE 1/4th are used, it didn’t say they were taken out. So if taken at its most literal, should we not deduce that the no screws ever left the jar?? And then wouldn’t that mean that 96 screws per jar are all that are used??

Or you could read it that in each of the 4 Jars there is a total of 96 screws rendering the problem unsolvable, so technically you saying that you know that 96 screws are in each jar is also incorrect.

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[quote]magick wrote:

[quote]tedro wrote:
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.[/quote]

It is necessary if you wish to interpret it in the manner you did.

The sentence either means there are four jars with 96 screws in them, or there are four jars with 96 screws in each of them.

But because the sentence is poorly written, you cannot conclusively arrive at either interpretation.

Simply put- each is used horribly wrong here, and as a result the sentence is confusing.

The rest of the sentence is not that confusing, besides the punctuation errors that I think maverick88 made. Hell, that in itself raises a question- did maverick88 even write the question out right?
[/quote]
You’re right that the sentence needs a comma to be grammatically correct. That said, the usage of the word "each’ indicates that each jar has 96 screws. If it was intended for the total number of screws in all the jars to be 96, “each” would not be used.

69

[quote]Silyak wrote:
You’re right that the sentence needs a comma to be grammatically correct. That said, the usage of the word "each’ indicates that each jar has 96 screws. If it was intended for the total number of screws in all the jars to be 96, “each” would not be used. [/quote]

Right, which is why I said that a simple assumption that there must have been a comma there fixes it.

But, as it stands, the sentence is horribly written and confusing. The word “each” obviously demands that you interpret it in that manner, but you can’t actually interpret it in that manner unless you assume that a comma must be there as well.

Therefore… it’s a horribly written sentence.

70

[quote]Silyak wrote:
That there are 96 screws in the jar is quite clear and not disputed. The difference in interpretation revolves around whether those screws that are in use are in the jar and part of the 96 or outside of the jar and a separate part of some total that includes them and the 96.
[/quote]
As far as I can tell that is the fact that is being disputed by everyone except yourself, however your interpretation requires that a jar used for storing screws can have all of its screws inside the jar and that some of those screws are in use while others are not, even though every screw is sitting in the same jar. I claim the two different meanings of “in” in this question lead to no alternative interpretations. You claim a screw can somehow be “being used” and in the jar at the same time, while the “not being used” screws sit in the exact same jar at the exact same time. So again, while your interpretation does rely on a grammatically correct reading, it requires a semantically incorrect interpretation.

A: (Takes jar)
B: Hey, I’m using those!
A: No your not, they’re just sitting in the jar.
B: Well I’m going to use them.

But the question clearly states they are being used, not about to be used.

It doesn’t need to be mentioned, and that is obviously what makes the question a difficult test of logic.

Why would the screws need to be different other than the fact that they belong to different jars? The question itself ties them to their particular jar and that is all of the information that is necessary to answering the question.

[quote]
My larger wonder about this question is whether or not the OP faithfully copied the question in the first place. He may have just summarized it from his memory of a test. This seems most likely as beyond the poor wording, the question is definitively improperly punctuated. [/quote]
I do wonder the same thing, but I think I like it this way.

71

[quote]magick wrote:

[quote]tedro wrote:
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.[/quote]

It is necessary if you wish to interpret it in the manner you did.

The sentence either means there are four jars with 96 screws in them, or there are four jars with 96 screws in each of them.
[/quote]

No, the sentence can only mean that each jar has 96 screws. Just because a comma adds clarity does not mean it is necessary or grammatically correct without one.

72

[quote]tedro wrote:

[quote]magick wrote:

[quote]tedro wrote:
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.[/quote]

It is necessary if you wish to interpret it in the manner you did.

The sentence either means there are four jars with 96 screws in them, or there are four jars with 96 screws in each of them.
[/quote]

No, the sentence can only mean that each jar has 96 screws. Just because a comma adds clarity does not mean it is necessary or grammatically correct without one.
[/quote]

Actually that is incorrect. Because of placement of “each” the problem could literally be unsolvable and mean that each jar contains some portion of a total of 96 screws.

73

[quote]jbpick86 wrote:
Actually that is incorrect. Because of placement of “each” the problem could literally be unsolvable and mean that each jar contains some portion of a total of 96 screws.
[/quote]
Sorry, but it is. Each is an adjective and has to reference something, in this case the jars. Under your interpretation, you imply that some other group of entities that is not mentioned must each posses four jars. This would not be correct as there is nothing else in the sentence for each to relate except for the jars.

74

[quote]tedro wrote:

[quote]jbpick86 wrote:
Actually that is incorrect. Because of placement of “each” the problem could literally be unsolvable and mean that each jar contains some portion of a total of 96 screws.
[/quote]
Sorry, but it is. Each is an adjective and has to reference something, in this case the jars. Under your interpretation, you imply that some other group of entities that is not mentioned must each posses four jars. This would not be correct as there is nothing else in the sentence for each to relate except for the jars.[/quote]

The more I think about it, the more I think you are right.

However, still doesn’t solve the fact that while you have an issue with other peoples assumptions about the problem, you have no problem with your own that the screws are actually taken out of the jar. OR that there are screws out of the jar. You are making just as many, if not more, assumptions to get to the 2/5ths answer as everyone who came to 15/32’s.

As I said, if you want to use it as a riddle, because it never said the screws were taken out of the jar, and actually quite clearly said that in the jar the screws were being used, then 15/32’s would be the correct answer.

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[quote]jbpick86 wrote:
The more I think about it, the more I think you are right.

However, still doesn’t solve the fact that while you have an issue with other peoples assumptions about the problem, you have no problem with your own that the screws are actually taken out of the jar. OR that there are screws out of the jar. You are making just as many, if not more, assumptions to get to the 2/5ths answer as everyone who came to 15/32’s.

As I said, if you want to use it as a riddle, because it never said the screws were taken out of the jar, and actually quite clearly said that in the jar the screws were being used, then 15/32’s would be the correct answer.
[/quote]

It doesn’t say taken out, but it says being used. I see no logical explanation for which screws can both remain in a jar that holds screws and be used at the same time.

76

[quote]tedro wrote:

[quote]jbpick86 wrote:
The more I think about it, the more I think you are right.

However, still doesn’t solve the fact that while you have an issue with other peoples assumptions about the problem, you have no problem with your own that the screws are actually taken out of the jar. OR that there are screws out of the jar. You are making just as many, if not more, assumptions to get to the 2/5ths answer as everyone who came to 15/32’s.

As I said, if you want to use it as a riddle, because it never said the screws were taken out of the jar, and actually quite clearly said that in the jar the screws were being used, then 15/32’s would be the correct answer.
[/quote]

It doesn’t say taken out, but it says being used. I see no logical explanation for which screws can both remain in a jar that holds screws and be used at the same time.[/quote]

That’s true. I don’t see the logic of it, but that’s what it says. Logic tells me that when it says that the screws are being used, the person is taking those screws out of the jar of 96 and using them. For you, logic is telling you that someone has already taken the screws out of the jar and left 96 in there. Both of us had to make an assumption based off of what thought the most likely intent was.

77

[quote]tedro wrote:

[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]
I am pretty sure that the usage of “in” to indicate that A belongs to B, but A is not necessarily physically inside of B, is not correct if B is a concrete physical object that would ordinarily hold objects similar to A physically inside of it. The usage of “in” in the belonging sense would be for more abstract entities – a person is “in” a political party.

78

[quote]jbpick86 wrote:

[quote]tedro wrote:
Kansas. BS in math.[/quote]

When it says “in one”; How are you not deriving that it means “In one Jar” (which we were previously told had only 96 screws)?
[/quote]
He found a dictionary reference that says “in” can mean “belongs to”, and does not recognize that usage only applies to more abstract things. e.g. (#1) You can be “in” a political party without being physically surrounded by the other party members. (#2) A screw cannot be “in” a jar without being physically inside the jar.

But he thinks the usage of “in” in #1 is also properly applicable to #2.

If we assume for the sake of argument that he is right about that (which I don’t think he is), then he would be right that 2/5 would be the clear-cut answer.

79

[quote]undoredo wrote:
I am pretty sure that the usage of “in” to indicate that A belongs to B, but A is not necessarily physically inside of B, is not correct if B is a concrete physical object that would ordinarily hold objects similar to A physically inside of it. The usage of “in” in the belonging sense would be for more abstract entities – a person is “in” a political party.
[/quote]
A screw is “in” a group of screws, part of that group is in a jar and part of it is being used.

80

[quote]jbpick86 wrote:
That’s true. I don’t see the logic of it, but that’s what it says. Logic tells me that when it says that the screws are being used, the person is taking those screws out of the jar of 96 and using them. For you, logic is telling you that someone has already taken the screws out of the jar and left 96 in there. Both of us had to make an assumption based off of what thought the most likely intent was.
[/quote]
But again, your assumption makes the initial statement untrue.

81

[quote]tedro wrote:

[quote]jbpick86 wrote:
That’s true. I don’t see the logic of it, but that’s what it says. Logic tells me that when it says that the screws are being used, the person is taking those screws out of the jar of 96 and using them. For you, logic is telling you that someone has already taken the screws out of the jar and left 96 in there. Both of us had to make an assumption based off of what thought the most likely intent was.
[/quote]
But again, your assumption makes the initial statement untrue.[/quote]

No more than yours does.