# Pizza question: which answer is right? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [May 30, 2017, 3:50am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700 "2017-05-30T03:50:10Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![UDS](https://avatars.discourse-cdn.com/v4/letter/u/ecae2f/32.png) [@UDS](https://boards.straightdope.com/u/UDS)\ **Post date:** [May 30, 2017, 8:02am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/41 "2017-05-30T08:02:49Z")
> [@Gray\_Ghost](#): > > Which is great, if we’re in a 400-level course discussing the finer points of mathematical reasoning. These are kids. In an educational system that doesn’t do all that well a job teaching them what fractions are to begin with. > > How about we teach them arithmetic with fractions, _and make sure they understand it,_ before we spend class time showing them that math is just a particular branch of philosophy? Maths is a particular branch of philosophy, but you don’t have to teach kids that explicitly. You do have to teach them the fundamental tools of maths, though, which include deductive reasoning. If the system isn’t doing this, that would explain why it’s not having great outcomes. “If 4/6ths of Marty’s pizza is a more generous serve than 5/6ths of of Luis’s, what does that suggest?” is a way of doing precisely that. When I saw the question, I assumed this was the point that it was intended to convey, and I was (and still am) genuinely baffled as to how the teacher did not see this. Context is everything. I’m accustomed to a convention for discussing mathematics in which facts given in the problem are, well, given. The question explicitly stated that Marty ate more pizza than Luis, and an answer which says “that’s impossible” would look like smart-assery to me, when both common experience and simple deductive reasoning show that it is eminently possible. But maybe the question was included in a test where students were told that some of the information given in the questions was bogus, and they were invited to try and identify it. (Even then, the question was poorly written; the equivalence of the two pizzas should have been specified.) Absent this, though, the student’s answer to the question was correct and reasonable and looks to me like the one the question was designed to elicit; the teacher’s answer was wrong. ---
**Author:** ![Idle\_Thoughts](https://avatars.discourse-cdn.com/v4/letter/i/838e76/32.png) [@Idle\_Thoughts](https://boards.straightdope.com/u/Idle_Thoughts)\ **Post date:** [May 30, 2017, 8:47am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/42 "2017-05-30T08:47:47Z")
There is one single word that was left out that would have made a world of difference, and that word is “their”. The question, AS GIVEN, implies that Marty FACTUALLY (already) ate more pizza than Luis, so therefore any answer along the lines of “Sorry, 5/6th is bigger, so that means Luis ate more” is total bullshit. The question (IMO) automatically implies that the whole thing is over and done with and that Marty is the clear winner in “who ate the most pizza”. So, given that solid premise…there is only way way for Marty to have eaten more, despite only eating 4/6ths and that’s if Luis’ pizza is a little 10 inch one and Marty’s is, like FORTY INCHES across. Yes, Marty ate more pizza. BY FAR. Now had the question been “Who ate more of THEIR pizza?” rather than “Who ate more pizza?”…then yeah, there is no way Marty’s 4/6th beats Luis’ 5/6. No matter how you cut it (heh), Luis ate more of HIS personal pizza, even if it was a really tiny one and Marty’s was the size of a tire. But the question as you put it did not include the word “their”…it wasn’t “who ate more of their pizza?”…it was “who ate more pizza?” and giving the already finished results (I.E. Marty ate more pizza than Luis). At this end, we’re supposed to take the question at its word. There is no reason to doubt the question is lying, after all…or that it’s a trick question. If you ask someone something like “Okay, Ellen ran a mile in four minutes and Peter ran that same mile in 3 minutes and fifty nine seconds, yet Ellen was declared at having ran the mile FASTER than Peter…how is this possible?” you’re not going to be looking for or expecting an answer of “A haw haw…it’s not possible! Because three minutes and fifty nine seconds is FASTER than four minutes, ya numbskill! A haw haw! I got you good!”…what is going to happen is that they’re going to sit down and try to puzzle out how it’s possible, because they figure there’s an aspect that they’re not thinking of yet. It’s like the joke “What did one elephant say to the other?” and the answer is “Nothing. Elephants can’t talk!” A hahaha…you got me. See, now that’s funny… BECAUSE IT’S A JOKE! You expect it to be a joke in that case, though, but here the question was put forth seriously. So…final opinion: The kid is clearly right, the teacher is a moron and can’t seem to admit that he’s wrong, and everyone should always think before making questions like this, just to make sure there’s no loopholes if you’re clearly trying to go for just one answer. ---
**Author:** ![Kamino\_Neko](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kamino_neko/32/34_2.png) [@Kamino\_Neko](https://boards.straightdope.com/u/Kamino_Neko)\ **Post date:** [May 30, 2017, 9:11am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/43 "2017-05-30T09:11:22Z")
> [@Little\_Nemo](#): > > There’s the principle that when you hear hoofbeats, you should assume it’s a horse not a zebra. Yes, and in this case, the horse is that the pizzas are two different sizes. Pizzas coming in different sizes is an everyday thing. Math questions where the answer is ‘the question is actually impossible’ are not. I remember getting questions worded similarly to this one when I was in elementary school, and the kid’s answer was the expected one - we were expected to demonstrate knowledge that fractions weren’t just absolutes in a void; it’s 4/6 or 5/6 of SOMETHING, and that depending on what that something is, 4/6 can be bigger than 5/6 of something else. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [May 30, 2017, 11:12am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/44 "2017-05-30T11:12:02Z")
Meanwhile, **kayaker** finishes Marty and Luis’ pies while everyone else pushes around abacus beads. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [May 30, 2017, 11:27am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/45 "2017-05-30T11:27:29Z")
> [@Isamu](#): > > The kid was right. He/she can reason. > [@MichaelEmouse](#): > > Teacher made a mistake when designing the test. Student’s answer pointed out the mistake (either in good faith or by being a smartass). Teacher punished the student for pointing out the mistake. > > The question does ask how it’s possible. The student’s answer explains how it’s possible. > [@needscoffee](#): > > The premise: “Marty ate 4/6 of his pizza and Luis ate 5/6 of his pizza.” > Nowhere does it state that their pizzas must be the same size. > > The question asked was “\*\*\*How \*\*\*is that possible?” The student responded with the only possible correct answer to the question that was asked, based on the premise. The student is correct, and the teacher is a dunce. > [@UDS](#): > > The teacher is absolutely wrong. It’s clearly possible for 4/6ths of one pizza to contain more pizza by weight, volume or other metric than 5/6ths of another, different pizza. The question stipulates that that is the case in this instance, and asks what circumstances must prevail for this to be so. The correct answer is that Marty’s pizza must be larger than Luis’s. (An honours student might have added that Marty’s pizza had to be more than 20% larger than Luis’s, but the question doesn’t explicitly require this level of detail in the answer.) > > The teacher’s answer that “this is not possible” because it is possible, and common experience tells us so. Has this teacher never been to a pizzeria? > [@Biotop](#): > > The question was not: > > Who ate more pizza? > > The question was: > > How is that possible? > > The second question actually invites lateral thinking. The first does not. > [@Thudlow\_Boink](#): > > To me, the student’s answer was the obvious one, the one which I would have sworn the test’s creator intended. I’ve been a teacher for 27 years and have designed successful exam questions. I agree with all the above posters - the student answered the question correctly (and cleverly) whilst the teacher was wrong on several counts: - shouldn’t have designed the question that way if if the idea was to simply to test if students knew that 4/6 was less than 5/6 - shouldn’t have included the phrase ‘Marty ate more pizza than Luis’ as a statement of fact if it was a lie - should have congratulated the student for an excellent answer ---
**Author:** ![John\_DiFool](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_difool/32/19543_2.png) [@John\_DiFool](https://boards.straightdope.com/u/John_DiFool)\ **Post date:** [May 30, 2017, 11:59am UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/46 "2017-05-30T11:59:36Z")
> [@Alessan](#): > > Math is not zoology. There are no assumptions in math. A Messr. Gödel would disagree with you. ---
**Author:** ![TokyoBayer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tokyobayer/32/13989_2.png) [@TokyoBayer](https://boards.straightdope.com/u/TokyoBayer)\ **Post date:** [May 30, 2017, 12:26pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/47 "2017-05-30T12:26:25Z")
> [@kayaker](#): > > Meanwhile, **kayaker** finishes Marty and Luis’ pies while everyone else pushes around abacus beads. I hope you brought the beer. ---
**Author:** ![Jackmannii](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackmannii/32/311_2.png) [@Jackmannii](https://boards.straightdope.com/u/Jackmannii)\ **Post date:** [May 30, 2017, 12:31pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/48 "2017-05-30T12:31:40Z")
> [@snfaulkner](#): > > Are the pizzas poisoned with pineapple? Weirdly, that was my first thought too. The student was right; the teacher should be sanctioned for dumbbidity. ---
**Author:** ![guizot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guizot/32/3636_2.png) [@guizot](https://boards.straightdope.com/u/guizot)\ **Post date:** [May 30, 2017, 12:32pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/49 "2017-05-30T12:32:50Z")
> [@Little\_Nemo](#): > > All I’ve been able to find out about the overall test was that it was supposed to help the students learn to determine if an answer they had come up with was reasonabl or not. An example given was that if you were adding two numbers together and the sum you came up with was smaller than the two numbers you were adding, you should be able to spot that this is not a reasonable answer. So the test was apparently supposed to help students learn to spot obvious mistakes in their math - for example thinking 4/6 of something is bigger than 5/6 of something. Yes. This is a certain genre of question, and it probably appeared as part of a whole section of questions, all of which are phrased in this way:\*\*\*REASONABLENESS: [circumstance] + [proposition that is prima facie not possible] \*\*\*The idea, as you say, is to train students to avoid making obvious mistakes out of sloppiness, without having to go through lengthy proofs. HOWEVER, the language pragmatics of this particular test item themselves are sloppy; it probably was written by a mathematician, and not someone well-trained in test writing. The test item should have been phrased something like this:\*\*\*Martiy 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? \*\*\*That doesn’t avoid the presupposition that both pizzas are the same, but it more clearly portrays the proposition as an assertion to be questioned, rather than a given circumstance. ---
**Author:** ![guizot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guizot/32/3636_2.png) [@guizot](https://boards.straightdope.com/u/guizot)\ **Post date:** [May 30, 2017, 12:47pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/50 "2017-05-30T12:47:37Z")
> [@guizot](#): > > \*\*\*Martiy 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? > > * * * Or perhaps this: _ **Martiy ate 4/6 of a pizza and Luis ate 5/6 of a pizza. Marty says, “I ate more than you.” Is his statement reasonable?** _ ---
**Author:** ![steronz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steronz/32/11765_2.png) [@steronz](https://boards.straightdope.com/u/steronz)\ **Post date:** [May 30, 2017, 12:54pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/51 "2017-05-30T12:54:25Z")
> [@Little\_Nemo](#): > > All I’ve been able to find out about the overall test was that it was supposed to help the students learn to determine if an answer they had come up with was reasonable or not. I’ve helped my 4th grader with a number of these lessons that are designed to get kids to be able to check their work quickly by applying a “reasonableness” test. In all cases that I remember, the questions were worded with a 3rd party. For instance, “Marty ate 4/6 of his pizza and Luis ate 5/6 of his pizza. Sally says that Marty ate more pizza than Luis. Is Sally correct? Why or why not?” Or a more abstract version, “Marty ate 4/6 of his pizza. Luis ate 1/6 more of his pizza than Marty. Sally has calculated that Luis at 5/6 of his pizza. Is Sally’s answer reasonable? Why or why not?” Although in that 2nd example, the arithmetic is usually much more challenging to discourage the kids from simply checking it in their heads. Still, it’s easily possible to word these types of questions in a way that makes it clear what the student is supposed to be doing. I agree with **glee** that including a blatant lie as a statement of fact is… bizarre at best. Also, on preview, ninja’d by **guizot**. ---
**Author:** ![Jophiel](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jophiel/32/66_2.png) [@Jophiel](https://boards.straightdope.com/u/Jophiel)\ **Post date:** [May 30, 2017, 2:39pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/52 "2017-05-30T14:39:37Z")
> [@Little\_Nemo](#): > > There’s the principle that when you hear hoofbeats, you should assume it’s a horse not a zebra. Why assume the pizzas were different sizes if you weren’t told that? The premise there is that zebras as (presumably) rare in your neighborhood whereas pizza coming in different sizes is incredibly common. I would assume that the pizzas were different sizes because that’s the most logical answer (more so than “trick question!” in my book). In fact, if given the question, I would have given the same answer (different sizes) and assumed that the point of the question was demonstrating that percentages are useless without establishing “percentage of _what_?” ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [May 30, 2017, 2:45pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/53 "2017-05-30T14:45:26Z")
The student was right. Nothing about the question indicates that the pizzas were the same size. It’s the same as saying Marty went on a diet and lost 15 lbs, Luis went on a diet and lost 20 lbs, but Luis still weighs more than Marty. A pizza is not an absolute amount of food. ---
**Author:** ![Johnny\_Bravo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_bravo/32/493_2.png) [@Johnny\_Bravo](https://boards.straightdope.com/u/Johnny_Bravo)\ **Post date:** [May 30, 2017, 2:51pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/54 "2017-05-30T14:51:27Z")
I once asked the following question, after a lesson about Abraham Lincoln’s politics leading up to the 1860 election. Q: If Abraham Lincoln were to run for President today, do you think he could be elected? Explain. A student answered, “No, because Abraham Lincoln was assassinated on April 14, 1865.” Kid got full credit and I followed up later to make sure he knew the ‘right’ answer. You always reward cleverness. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [May 30, 2017, 2:58pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/55 "2017-05-30T14:58:38Z")
> [@Johnny\_Bravo](#): > > I once asked the following question, after a lesson about Abraham Lincoln’s politics leading up to the 1860 election. > > Q: If Abraham Lincoln were to run for President today, do you think he could be elected? Explain. > > A student answered, “No, because Abraham Lincoln was assassinated on April 14, 1865.” > > Kid got full credit and I followed up later to make sure he knew the ‘right’ answer. You always reward cleverness. Perfectly reasonable answer because he explained the logic of it. It’s not a question that has a single correct and best answer. What if the question was “What do George Washington, Thomas Jefferson, James Madison, James Monroe, William Henry Harrison, John Tyler, Zachary Taylor and Woodrow Wilson have in common?” and the student answered “They’re all dead”. ---
**Author:** ![Jophiel](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jophiel/32/66_2.png) [@Jophiel](https://boards.straightdope.com/u/Jophiel)\ **Post date:** [May 30, 2017, 3:14pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/56 "2017-05-30T15:14:51Z")
> [@TriPolar](#): > > What if the question was “What do George Washington, Thomas Jefferson, James Madison, James Monroe, William Henry Harrison, John Tyler, Zachary Taylor and Woodrow Wilson have in common?” and the student answered “They’re all dead”. Eight presidents who have never been in my kitchen! ---
**Author:** ![Johnny\_Bravo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_bravo/32/493_2.png) [@Johnny\_Bravo](https://boards.straightdope.com/u/Johnny_Bravo)\ **Post date:** [May 30, 2017, 3:23pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/57 "2017-05-30T15:23:30Z")
Context is also important here. My Lincoln question was following up on a lesson about his politics, so most students understood what I was driving at. If your "eight presidents"question came at the end of a unit entitled “Presidential Facial Hair,” then the expected and reasonable answer would be “none of them had beards.” If the question was on a cumulative exam for a “Survey of US History” course, then it’s too vague to be useful except, perhaps, as a very open writing prompt. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [May 30, 2017, 4:09pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/58 "2017-05-30T16:09:40Z")
> [@Jophiel](#): > > Eight presidents who have never been in my kitchen! This is of course the correct answer. If you lost points for it on Jeopardy then Alex Trebek would come apologize to you personally. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [May 30, 2017, 4:39pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/59 "2017-05-30T16:39:37Z")
> [@guizot](#): > > Yes. This is a certain genre of question, and it probably appeared as part of a whole section of questions, all of which are phrased in this way:\*\*\*REASONABLENESS: [circumstance] + [proposition that is prima facie not possible] > \*\*\*The idea, as you say, is to train students to avoid making obvious mistakes out of sloppiness, without having to go through lengthy proofs. > > HOWEVER, the language pragmatics of this particular test item themselves are sloppy; it probably was written by a mathematician, and not someone well-trained in test writing. > > The test item should have been phrased something like this:\*\*\*Martiy 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? > \*\*\*That doesn’t avoid the presupposition that both pizzas are the same, but it more clearly portrays the proposition as an assertion to be questioned, rather than a given circumstance. I agree that the question was poorly written. That’s why I feel seeing the overall test is important before judging this one question. That said, I’m sticking with the zebras metaphor. When two people sit down to eat pizza in a math problem, your base assumption should be that the pizzas are equivalent. Somebody who ate 5/6 of a pizza generally ate more than somebody who ate 4/6 of a pizza just as somebody who ate three cheeseburgers generally ate more than somebody who ate two cheeseburgers. I’ll also note I didn’t say the student’s answer was wrong. I said both the student’s answer and the teacher’s answers were correct. To use my hoofbeats metaphor, I said hoofbeats could be coming from horses or zebras. Saying horses are more common than zebras and therefore the hoofbeats must be coming from horses is wrong. But saying zebras are possible so the hoofbeats must be coming from zebras is even more wrong. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [May 30, 2017, 5:12pm UTC](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700/60 "2017-05-30T17:12:05Z")
> [@Little\_Nemo](#): > > When two people sit down to eat pizza in a math problem, your base assumption should be that the pizzas are equivalent. Why? [Previous page](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700.md?page=2) [Next page](https://boards.straightdope.com/t/pizza-question-which-answer-is-right/787700.md?page=4)