# Math Test Problem Disagreement

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• 02-26-2003
orbitz
Math Test Problem Disagreement
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:

The first 2 answers rely on how you interpret:

Quote:

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:
Quote:

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.
• 02-26-2003
XSquared
Its a trick question. Get over it.
• 02-26-2003
minesweeper
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.
• 02-26-2003
Magos
I can't see the math in that question. I believe in #2.
• 02-26-2003
alpha
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.
• 02-26-2003
Quote:

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?
• 02-26-2003
Eibro
Quote:

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.
• 02-26-2003
>>where do they bury the survivors?

>In the ground?

that's not nice...

//edit: damn you, eibro.. i was there first... almost...
• 02-26-2003
orbitz
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)
Quote:

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.
• 02-26-2003
Yodiddy
Quote:

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*
• 02-26-2003
Silvercord
that question makes no sense. If all of the cookies disappeared then none were left on the table.

Quote:

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*...
• 02-26-2003