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orbitz
02-26-2003, 03:45 PM
I had a math test recently and got it back and one of the questions I got wrong but feel that the question can be interpreted in a few ways that make the answers different. I was hoping to get other peoples opinion on this question (and their answer to see if it is anything like mine).

The question is:
Some cookies are left on a table in a room with 17 unsupervised Math students, and they (the cookies) all disappear. If, with no additional information, I am absolutely certain that atleast one of those students must have taken 5 or more of the cookies, how many cookies atleast, were left on the table?


The possible answers that I can see:
(Please try the problem before hand so your answer is not tainted...if you care)

The first 2 answers rely on how you interpret:



I am absolutely certain that atleast one of those students must have taken 5 or more of the cookies


1) If you interpret the 'must' to say that the student did not have a choice, then the minimum number of cookies is 69. This is to say, if each person takes an equal amount, except for that 1 person, we have the situation where each of the 17 students get 4 cookies, except for the one person who gets 5 so the answer is 4*17+1, 69. This situation uses the second definition of 'must' on dictionary.com saying: To be compelled, as by a physical necessity or requirement.
In order for all cookies to be gone, and in order for 1 person to haev been required to take 5 cookies, the answer would be no less than 69 cookies.

2) If you interprete 'atleast one of those students must have taken 4 or more' to say that as a minimum, 1 student took 5 cookies, then the answer becomes 5 or more cookies. This situation uses dictionary.com's 4th definition of 'must': To be determined to; have as a fixed resolve.
1 student is resolved or determined to take 5 cookies, and they are all gone, meaning that the minimum number of cookies is 5.

The final answer relies on the interpretation of the last part of the last sentence.

This part states:


how many cookies atleast, were left on the table?


3) Under strict grammar, the answer can be 0. How many cookies were left on the table after they disappeared? None.

I think that this question is badly phrased and that because we are using a language that is full of ambiguities, the question must be as explict as possible as to not allow for any misunderstanding in what the question is asking. I do not think this question accomplished this.

Any feed back anyone could offer would be much appreciated.

XSquared
02-26-2003, 04:09 PM
Its a trick question. Get over it.

minesweeper
02-26-2003, 04:10 PM
Initially I went for your answer 3 thinking it was a trick question like the old 'plane crashes on the border between 2 countries, where do they bury the survivors?' type of question.

Then I re-read the question and went for your answer number 2 (assuming a trick question was not possible). It says at least 1 student took 5 cookies, so there must have been at least 5 cookies to take.

I can't see how you would interpret the question as number 1. It only sayd that at minimum, 1 student must have taken 5 cookies, there are no rules stating how many any of the other students took.

Magos
02-26-2003, 04:14 PM
I can't see the math in that question. I believe in #2.

alpha
02-26-2003, 04:20 PM
I would think it is a trick question. It could be six. "at least" one student took "at least" 5. so if it were at least one, it could be two students, one student with 5 cookies, and one student with one. but it could also be 5.

imYoDaddyC++
02-26-2003, 04:20 PM
Originally posted by minesweeper
'plane crashes on the border between 2 countries, where do they bury the survivors?'




In the ground?

and for the OP, I'm gonna go with number 3, i think it's a stupid trick question. what kind of math class was this from?

Eibro
02-26-2003, 04:31 PM
Originally posted by imYoDaddyC++
In the ground?

and for the OP, I'm gonna go with number 3, i think it's a stupid trick question. what kind of math class was this from?
Last time I checked you didn't bury survivors.

MadHatter
02-26-2003, 04:31 PM
>>where do they bury the survivors?

>In the ground?

that's not nice...

//edit: damn you, eibro.. i was there first... almost...

orbitz
02-26-2003, 04:45 PM
Discrete Math 2.

I know have a nasty habit of being a stickler for detail, I know I should just give up, but I think peopel should be made aware of the issue of interpretation especially when it comes to word problems. Another few pointes were made that make this question a trick:
(#math@efnet got these)

1) If you know with certainty that 17 students ate 69 cookies then you know atleast one student ate 5 or more cookies.
But knowing that one student ate 5 or more cookies does not allow you to know there were atelast 69.

2)


If, with no additional information, I am absolutely certain that atleast one of those students must have taken 5 or more of the cookies


There is no way you can be sure that atleast one student ate 5 or more cookies with no additional information because in order to know one student ate 5 or more cookies you have to know how many cookies there were to begin with, so this implication does not hold.

It is funny, the author of the question wrote it thinking that the answer was very straight forward, but it is anything but.

Yodiddy
02-26-2003, 04:50 PM
Originally posted by Eibro
Last time I checked you didn't bury survivors.


Um..yeah...I knew that... i was..ummm....kidding....*walks out slowly*

Silvercord
02-26-2003, 04:55 PM
that question makes no sense. If all of the cookies disappeared then none were left on the table.



and they (the cookies) all disappear
...
how many cookies atleast, were left on the table?


I would just say none, because they all disappeared. Either that or I would've gone into school with a lot of ketchup and gasoline, and then with my magical slippers and cape... oh boy... *drools*...

MadHatter
02-26-2003, 05:00 PM
so did you get the answer to the question back with the test results?

MethodMan
02-26-2003, 05:06 PM
When I first read it, it sounds like there is 5 or more cookies, if she is certain at least one took 5 or more, it doesnt have to be more than 5 cookies.. Thanks how I see it.

beege31337
02-26-2003, 05:37 PM
it is definately (4*17)+1
your comment about the zero cookies being "left" is kinda funny, but it's obvious that that was not the intended meaning of the question.

orbitz
02-26-2003, 05:47 PM
I do not feel that oen shoudl be forced into answering a question how it was 'intended' but rather 'what it is asking'.

Govtcheez
02-26-2003, 05:49 PM
"At least" how many cookies are left if " they (the cookies) all disappear"? If all the cookies are gone? The answer's 0. If the cookies are "all" gone, there aren't any left.

What a stupid question...

Mister C
02-26-2003, 05:50 PM
orbitz... Wait until you take higher math like abstract algebra... You will probably be all over your instructor then...

Agree trick question..

salvelinus
02-26-2003, 06:08 PM
5. Since "at least one" student took "at least" 5 cookies, 5 is the minimum for that student, and there's no requirement that any other student took any.
0 would only be correct if "left on the table" at the end of the problem statement meant "left after they were all taken". However, "left on the table" is stated at the beginning of the problem, giving greater weight to the probability that that's what is meant by "left on the table". This is the only ambiguity.

orbitz
02-26-2003, 06:58 PM
Ironically, the reason my teacher is sticking to the answer being 69 is because of the 'must'. He says if atleast one person MUST take 5, then that means we are in a situation where everyone else MUST take 4. BUT, unless he provides a solid definition of 'must', then we cannot be sure what definition he is using, and 'must' has a few definitions, which chagne the result of the answer.

This is ironic because my teacher is hanging onto a grammatical point, and completely ignoring all the other grammatical mistakes in the answer.

I think the question was made with good intentions, but is a horrible question, and a trick.

By the way, this question is taken forma Discrete Math 2 test. I mostly enjoy the class because it seems like alot of the questions try to make you think in a more logical way than other math classes I have had. The problem comes into play with questions where the teacher is askign a question in a vague way because they are afraid they are going to give away too much of the answer, but pay the price in the end because their question is actually to vague to answer. And then they cannot see the other interpretation because they are so focused on what they said. It happens to all of us at some time or another.

dP munky
02-26-2003, 07:51 PM
how the hell do you get everyone else HAS to eat 4 cookies? im not seeing it?

this is the absolute worst question, any answer (technically) would be correct because you have to assume on everything

SourceCode
02-26-2003, 08:59 PM
I gotta go with 3. It sounds like a trick question, the first part says.

Some cookies are left on a table in a room with 17 unsupervised Math students, and they (the cookies) all disappear.

They all disappear, so wether one student must take 5 or not is irrelevant imo. There are no cookies left because they all disappear.

salvelinus
02-26-2003, 10:29 PM
Your teacher is wrong. "..at least one student..." means only one student is required in the problem.

*ClownPimp*
02-26-2003, 10:37 PM
This is a basic Pigeonhole Principle problem. There is no trick in this question. The only ambiguity is if "how many cookies were left" meant after they were eaten or before they were eaten. Considering this is a discrete math class and Im sure you guys recently studied the Pigeonhole Principle, it makes the most sense that the question meant before the cookies were eaten.

The correct answer is #1. The question states that the instructor was "absolutely certain that atleast one of those students must have taken 5 or more of the cookies", the only way he could be absolutely certain is if there were enough cookies such that in every possible distribution of the cookies, someone would have at least 5 of them. The amount of cookies required is 4*17+1 to be sure of this.


Think about it this way, say there were 10 cookies. Can you be sure that at least one person had 5 cookies? Of course not. 10 ppl could have had 1. Now consider 20. Still no, since 14 ppl could have had 1 and 3 could have had 2. Continuing on in this pattern you get to 69 and see that no matter how the cookies are arranged, someone MUST have 5.

dP munky
02-26-2003, 10:48 PM
>>"..at least one student..."

i think that says it all, 5 dude, 5

69 doesnt make sense, what if every kid only had 3? how do you know? you dont, NO FURTHER INFORMATION

nvoigt
02-26-2003, 11:46 PM
69 doesnt make sense, what if every kid only had 3? how do you know? you dont, NO FURTHER INFORMATION


If every kid took 3 the instructor could not have been sure. To be sure that one kid took 5 minimum, there must have been 4 for each kid plus one. So even if each kid took only four, to completely disappear it takes one kid to take five ( or more if someone else takes less ).

dP munky
02-26-2003, 11:52 PM
>>one kid took 5 minimum, there must have been 4 for each kid plus one

this is i guess what i dont get then if one kid took 5 minimum, why do any of the other kids have to take any at all

orbitz
02-26-2003, 11:55 PM
I am not debating the Pigeon Hole Principle thinking, I am debating the grammar of the question and the possible interpretations.

Yes we had recently discussed PHP, but I do not think that recent discussion of the PHP is any excuse for asking a badly phrased question. As mathematictions we cannot assume any prior knowledge as to what the question might be asking but need to answer what the question is asking. What a question is asking is based on how it can be interpreted. With a word problem, we are forced to either A) Be as explicit as possible, leaving as little room for other interpretations as possible, or B) Understand that other interpretations rae possible and make room to allow these other interpreations to be correct answers.

I do not see how the asker of this question did A, the question is somewhat ambigious in it's meaning.

If the asker does B, they have to understand that the language is full of these ambiguities. Also, in a college environment, some people are not as familiar with the language due to diversity, and these interpretations should be taken in to consideration. I understand how the PHP thinking process comes about and what quesitont hat is being answered, but what if we take the sentence:

atleast one student must have taken 5 or more cookies.

If we use one possible definition of te word must: To be determined to; have as a fixed resolve.

Does the question not read:

atleast one student had determined to take 5 more cookies.

Does this meaning not give the answer of 5?

Perhaps I am over analysing this whole thing. But I just think the wording of the question ist oo lose and other interpretations need to be acknowledged as correct.

SMurf
02-27-2003, 08:17 AM
(4 * 17) + 1

Perhaps the students were a bunch of nice people and split the last cookie between them?

Mmm, 1/17th of a cookie :p

*ClownPimp*
02-27-2003, 10:00 AM
>Also, in a college environment, some people are not as familiar with the language due to diversity, and these interpretations should be taken in to consideration

I totally agree. Me saying that #2 didnt make sense was based on my understanding of the word "must" in that context. Of course, someone else with less (or more) experience with English may not have seen it the way I did, and the professor should definitely take that into consideration.

dp munky: read my previous post again, I think my explanation is pretty clear.

Silvercord
02-28-2003, 04:27 PM
punch your teacher in the face

EDIT:
and then POOP all over him (or her)