No, they’re mutually exclusive. The teacher’s answer is that “it’s impossible.” The student’s answer points out a way it is possible. Either it’s impossible or it isn’t.
To make this a good metaphor, you’d have to change it so that the question on the test was “Tommy hears hoofbeats, but there are no horses. How is this possible?”
Tommy answered that they could be zebras, and the teacher said “no, it’s impossible.”
I think the kid gave the only correct answer, and the teacher’s answer is wrong wrong wrong.
Generally, yes, unless you’re told they’re not. Such is the case in the question at hand.
Yes!
Teacher is completely wrong. Their questioned asked for a how it is possible and the student correctly showed how it could be possible.
By the way, I also want some pizza now. 
The test being about ‘reasonableness’ only reinforces that the student is correct. The only reasonable conclusion is that one pizza is bigger than the other.
And for the teacher - :smack::rolleyes:
Was it the teacher’s question, or a question on a test that the teacher administered? Some teachers don’t care what the truth is, just what the answer key says is correct.
(But yeah, the kid’s answer was correct.)
You go to the superintendent of the building and you say, “If you tell me how tall this building is, I will give you this fine barometer.”
And when he heads for the roof, you eat his pizza.
The teacher’s question and answer reminds me of a lame cartoon question drawn by some schoolkids in Taiwan to irritate others:
(Draws picture of bald stick-man): “If the wind blows left, which way does his hair blow?”
Audience: “Left.”
Teller: “Wrong, he’s bald!”
Anyway, the teacher shouldn’t be fired, but he/she should certainly be required to apologize and give the student full credit for that question, and also maybe some extra academic credit points for the test overall.
Because if you don’t accept some basic assumptions then any answer is possible.
For example, why assume that these are the only two pizzas Luis and Marty have ever eaten? The question doesn’t say that. Maybe in the course of his lifetime Luis has eaten five thousand pizzas and Marty’s only eaten five hundred. So Luis ate more pizza than Marty and the student’s answer was wrong.
When you start allowing any possible assumptions into the question, no mathematical problem is solvable.
That doesn’t answer my question. I wasn’t asking why you should have some basic assumptions, but why “the pizzas are equivalent” should be one of them.
If the third statement, that “Marty ate more pizza than Luis” cannot be assumed to be true, then it is equally valid to consider that the first two statements may not be true. IOW, the teacher needs to go back to school.
I’m willing to concede that equal sized pizzas is a reasonable assumption, and if the question were phrased like guizot suggests:
***Marty ate 4/6 of a pizza and Luis ate 5/6 of a pizza. Marty says, "I ate more than you." What's wrong with his statement?***
And a student responded with “Nothing’s wrong with it, Marty’s pizza could have been bigger,” that’s a bit of a cheeky answer. I might still give the student credit but a better answer would be, “5/6 is more than 4/6,” because that’s what Marty actually got wrong.
The problem isn’t that equal sized pizzas is a bad assumption, the problem is that it’s a trick question. “How is that possible?” “It’s not.” That’s a cheeky answer. Yet, apparently, it’s what the teacher wanted? Nonsense.
eta: That’s a good point, Nars. A student could answer, “Luis actually only ate 3/6 of his pizza.”
When the teacher asks “how is this possible?” the student is tasked with trying to think outside the box and come up with a possible solution. The student did that by stating one pizza was bigger. So, yes, we need “assumptions,” but this question was apparently designed to get students to question their assumptions. Too bad the teacher didn’t understand that.
“…and the surgeon said, ‘I can’t operate on this boy; he’s my son!’ Explain.”
“Uh, is it that the surgeon was that boy’s mother?”
“What? No, that can’t be right.”
Yeah, I want one that is
If we accept the teacher’s answer, then the same method can be applied to any other math problem that teacher ever assigns. “Mary has three apples. She gave away two of them. How many does she have now?” “None, because she didn’t have three apples, she only had two”. “Two cities are 100 miles apart. A train leaves one at noon, traveling at 50 MPH. When does it reach the other city?” “Never, because the train doesn’t exist.”. Once you’re allowed to answer a math problem by contradicting the givens, there’s no such thing as a wrong answer any more.
Not to mention, the question only makes sense if we assume that the test-taker already knows that 5/6 is greater than 4/6. If the teacher had asked “Luis ate 4/5 of his pizza, and Marty ate 5/6 of his pizza. Marty ate more pizza than Luis. How is this possible?”, then everyone would go “What do you mean, how is it possible? What’s wrong with that?”. So the question can’t be meant to test the knowledge that 5/6 > 4/6.
Now, what this question could be used for, and (assuming that the teacher was not the one who wrote the question) likely what it was intended for, is teaching the importance of standard units. A pizza is not a standard unit, and so the given statement is possible, as the student realized.
I swear my kid had this same question for homework this year. (Funny enough we live in the same area where the pizza chain in the article is located).
My son also answered with the “Marty’s pizza was larger” answer and he got it corrrect.
I think the poor kid in the article got a bum teacher this year.