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Once, in a college class of mine, my teacher defied each of us to elaborate a good question for an IQ test. I proposed the following one.

Is the option C a correct answer for this question? Please select one of the following options.

A - YES
B - YES
C - NO
D - NO

The correct answer is quite simple (I think), but it triggered a huge discussion on the classroom about its validity. Some of my colleagues were saying the question was not a good sentence because it has references to itself. Meanwhile, others (and I) argued that it is, in fact, a good "meta" question.

I really would like to know some opinions about it. And, of course, If you want, you may answer it.

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    $\begingroup$ IMHO, this is a good logic puzzle. But if I'm asked whether this is a good IQ test, I'm not sure. Most IQ tests deal with some abstractions, visuals, or patterns. So perhaps logic questions are a bit out of topic for IQ test. But who knows. $\endgroup$ – athin Jul 8 at 22:58
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    $\begingroup$ I find the question whether this is a good IQ question opinion-based and in general off-topic for puzzleSE. $\endgroup$ – infinitezero Jul 9 at 2:52
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    $\begingroup$ I have no comment on whether it is good for IQ because IQ has criteria beyond the scope of this board. Is it a good riddle? Sure, I got the correct answer but i have a beef with the question. It should be “is C the correct answer...” $\endgroup$ – Damila Jul 9 at 4:15
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    $\begingroup$ How is this even remotely on-topic? One of the fundamental rules across all of Stackexchange is that this is a Q&A site, not a discussion forum. $\endgroup$ – BlueRaja - Danny Pflughoeft Jul 9 at 18:41
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    $\begingroup$ The phrasing of the question could be improved. Answer (D) seems to be the intended correct answer - but the problem is that (D) reads "No", which is the same answer as part (C). Which means that by picking (D) you are LITERALLY picking the same "answer" as had you picked (C). I would change it to say "Is the option C the correct OPTION for this question?" - the difference between option and answer is essential. $\endgroup$ – Dast Jul 10 at 9:40

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I disagree with most of the other answers - I think it is a better question than most actual IQ test questions.

The point is that if you haven't seen something like this before, then whether you're capable of figuring it out is a really good determiner of the ability to think logically. And it's perfectly plausible to do so; you don't need any outside knowledge, and it's pure logic. By contrast, a lot of IQ-style questions of the form "which grid fits the pattern", etc, really do rely on having seen lots of those questions before to have an idea of what type of "patterns" are considered valid, and while they certainly do require intelligence once you know the unstated rules for designing them, they also rely on your knowledge of those rules (somewhat like cryptic crosswords).

Even if a candidate has seen something like your question before, I think actually going through the process and getting the right answer takes intelligence rather than just knowledge. It's really not just a question of turn the handle and the answer comes out - you have to think about the options carefully in a way specific to this question.

However, it's a bad question from an IQ-test writing point of view for the following reason: you can't write lots more questions in the same style. If someone can do this one, they will be able to do all the rest. (The only benefit to having more than one question like this is to detect guessing.)

But actually that drawback is what I like about it - it measures what it measures very well. A lot of questions on IQ tests are about trying to spot what the question writer was thinking, and consequently which candidates will succeed varies a lot from question to question. So these questions do not even measure what they are trying to measure particularly well, which is why you need a lot of them. So if you were getting paid for writing IQ test questions, you might want to stick to the traditional style!

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    $\begingroup$ Thanks! I share the same feeling about this. $\endgroup$ – Pspl Jul 9 at 8:23
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    $\begingroup$ The fact this answer was accepted, especially with that comment, strongly implies that the asker wasn't actually asking a question, but looking for someone who agreed with him. Now, that's okay, but not really what a site like this is for... $\endgroup$ – Jasper Jul 10 at 12:48
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    $\begingroup$ You selected this as "correct" answer when you are not capable nor qualified to make that judgment. $\endgroup$ – IvanP Jul 10 at 20:08
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    $\begingroup$ @IvanP You should see this site called StackOverflow. $\endgroup$ – Kaz Jul 10 at 21:32
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I don't think this is a good question for an IQ test. The problem is that there are some strategies to solve this kind of meta-question and who know one of these strategies can answer in seconds. Also, there is some linguistical knowledge involved (for example a non-native speaker could score less than a native one).

Thus you will be testing the knowledge of the participants rather than their IQ.

The same reasoning holds for chess puzzles, grid-deduction, logical-deduction...

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    $\begingroup$ IQ is completely arbitrary anyway $\endgroup$ – Quintec Jul 8 at 17:11
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    $\begingroup$ A lot of the questions from my old 'Know Your Own IQ' book are language- or culture- based. For example: "Underline the odd-man-out: Alexander, Napoleon, Wellington, Nelson, Hannibal". Or: "Underline which of these towns is not in the USA. GICOHAC, SHENAT, TONSOB, GOTHNINSAW". And even the ones that aren't require you to parse sentences like, "Underline which of the five numbered figures fits into the empty space." The amount of language understanding required for this one seems fairly low in comparison. So it's a 'fair' question by historic standards, if not by modern standards. $\endgroup$ – user3153372 Jul 9 at 6:01
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    $\begingroup$ @user3153372 that sounds like an illegitimate IQ test $\endgroup$ – PyRulez Jul 9 at 23:25
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    $\begingroup$ @user3153372 ... the joke being that all of the names are actually (once you unscramble them) towns in the USA. Athens Ohio, Athens Georgia, Athens Alabama, Athens Texas ... $\endgroup$ – Prime Mover Jul 10 at 21:26
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    $\begingroup$ @user3153372 There are a lot of things historically that billed themselves as 'IQ' tests but did not actually test anything other than some basic pattern recognition combined with knowledge that was quite often highly prevalent in a specific group of people but almost nonexistent outside of that group. Those aren't 'IQ' tests though, they're elitist propaganda designed to make that specific group of people feel smarter. $\endgroup$ – Austin Hemmelgarn Jul 11 at 2:09
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Bad question.

I would imagine a person who is familiar with the idea of paradoxes and self-referentiality would immediately go "aha, I get what this is" and answer D. Another person may have never seen something like this before and may think "what in the world are they even asking? Is C the right answer to the question? But what question? I see no question here?". Such a person may rather assume that the test-maker made a mistake and may decide, especially if the test is timed and with multiple questions, to just skip it.

Another way to see that this is a bad question is that if you know how to solve it, then the solution is obvious (D). You state so yourself. So what exactly are you measuring here? The people that already know, get the right answer immediately. The people that don't know, might or might not figure it out, but either way, it's clear that you are testing whether people know what sort of question it is, rather than their ability to figure something out.

I think a better intelligence question would be to ask why in the world college professors and their students are wasting their time on this sort of useless stuff. It's going to take a real genius to figure that one out.

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    $\begingroup$ I agree with you on some level. However, doesn't your first point of view is valid for any other kind of question? Just imagine a person who is familiar with the idea of sequences and patterns would immediately go "aha, I get what this is"... $\endgroup$ – Pspl Jul 9 at 8:20
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    $\begingroup$ OP asks if this is a good for an IQ test. IQ is not what you wish it to be. It is not what you think intelligence is or should be. It is a number that can be measured - the factor of variance behind performance in different mental-ability related questions. A better question is one that better correlates with that factor, that's it. The question proposed in your final paragraph might be an "intelligence question", but it wouldn't be measurable and usable in an IQ test and would not be a useful "IQ question". $\endgroup$ – Džuris Jul 9 at 9:45
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    $\begingroup$ Indeed, everything is obvious once you know the answer. I don't see how it's specific to this question, though. $\endgroup$ – Eric Duminil Jul 9 at 20:33
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I assume the answer is meant to be

D-NO

Reasoning:

It's the only option that's completely consistent with the semantic conditions. A and B are out because they imply YES, which means choosing either would contradict C being the correct choice and choosing C itself would mean C wasn't the correct answer, another contradiction. That leaves only D.

It's not a bad question, but it's best to avoid self-referential questions in my view.

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    $\begingroup$ I disagree with your logic for A and B. The question asks if C is "a correct answer" not if it is "the correct answer". It would not be contradictory for example if A, B, and C were somehow all correct answers (e.g. if they all contained "yes"). Your conclusion about A and B are correct, but the reasoning is not. The reason they are wrong is because those answers are themselves incorrect. $\endgroup$ – JBentley Jul 9 at 8:43
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    $\begingroup$ @JBentley: But then : "Please select one of the following options". To me, it meant that since there's no reason to prefer A over B, the answer had to be either C or D. It cannot be C, so... $\endgroup$ – Eric Duminil Jul 9 at 20:35
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    $\begingroup$ @EricDuminil That you can only select one doesn’t mean only one is correct. $\endgroup$ – 11684 Jul 9 at 23:23
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    $\begingroup$ @JBentley Well, C can't be a correct answer for obvious reasons. Note that it does not ask "is NO a correct answer to this question?" $\endgroup$ – user253751 Jul 10 at 11:33
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    $\begingroup$ @JBentley A can't be the correct answer (obviously). B can't be the correct answer (obviously). C can't be the correct answer. D can be the correct answer. Therefore the correct answer is D. $\endgroup$ – user253751 Jul 11 at 13:52
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Is this a good question?

No it isn't. The reason is that due to the broken way self-reference is worked into it, it has no answer.

Here is why.

Firstly, the answer to the question is a value from the domain { "Yes", "No" }, not one from the domain { A, B, C, D }. Those letters are just labels for the answer. That's how multiple choice testing works. The label is not the answer, the labeled answer is the answer.

Because both C and D are labels for "No", those two choices are equivalent: they constitute the same answer. It cannot be the case that C is a correct answer, but D isn't.

Because C is a label for "No", the question "is option C a correct answer?", means exactly the same thing as "is 'No' a correct answer?"

Thus, let us entertain the possibility that "No" is the correct answer, i.e. C is not correct. If "No" is the correct answer, that is equally represented either by C or D; it means that C is a valid choice, just like D. But that cannot be because "No" means "C is not a valid choice".

Thus, "Yes" must be the correct answer. But then, only the choices A and B are tied to that answer. That "Yes" answer, however, means that C is correct (and also D), and not A or B.

So the situation is not well-formed; though it may not be the intent, the question reduces to the Liar Paradox.

It may have been the intent that D must be the answer; but that can only be the case if we consider C and D to be distinct from each other, even though they both map to the same "No" answer, which is not a valid concept.

It cannot be that the "D flavored 'No'" is correct but the "C flavored 'No'" isn't; 'No' is just 'No'. The specific alphabetic labels do not contribute anything to the semantics of the "Yes" or "No".

The multiple choice test is just a format for easier grading: the correct answer is given away along with several distractors, and for the sake of simplicity, these items are all given symbolic labels, which otherwise don't mean anything.

A well-formed multiple choice question has a correct answer even if we take away the choices and ask for the answer to be stated.

In this regard, our question runs aground already: it contains a reference to one of the labels, which makes it impossible to remove the choices such that the question still makes sense.

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    $\begingroup$ Exactly right. There is no correct answer. And D is not the correct answer. $\endgroup$ – gnasher729 Jul 10 at 9:04
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    $\begingroup$ Could the question be improved if it asked "Is C the correct answer?" and the choices were "A-YES B-Yes C-NO D-No, where the correct answer was "No", in mixed-case italics. $\endgroup$ – supercat Jul 10 at 16:13
  • $\begingroup$ @supercat, If the question is "Is C the correct answer?", then it's still a yes-or-no-question. Since "D-No" is neither "yes", nor "no", it's not a plausible answer. $\endgroup$ – Kaz Jul 10 at 16:17
  • $\begingroup$ Great answer, upvoted. As to the "IQ question" in the OP, I'd have answered "E". $\endgroup$ – bobflux Jul 10 at 23:57
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    $\begingroup$ @anregen My answer doesn't revolve around any distinction between "answer" or "response" at all; I didn't even mention the latter word. Let them be synonyms; it's clear that the question is a yes-or-no question: if it has a correct response/answer, it is either "yes" or "no". D is just the name of the response/answer, which is also known by the name C. "Is C a correct answer" means the same thing as "Is C the name of an answer which is correct?" not literally that the letter "C" is the answer. Just like "I will have combo C" doesn't mean you will be eating the third letter of the alphabet. $\endgroup$ – Kaz Jul 11 at 1:41
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The aim of an IQ test is to measure (some form of) intelligence. Therefore a good question is any question that requires this intelligence. If you consider that being comfortable with this kind of self-referential questions counts as "intelligence", then it is a good question. I personally think id does.

On the other hand, there might be an expectation of "fairness" in the sense that the questions should be clear, only solving it should be difficult. There is another example in a closed question on this site where the correct answer can only be found by understanding there ia a typo in the question. That requires intelligence and "out of tne box" thinking to solve. But that would not be a "fair" question if made intentionally, in my opinion.

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Yes - it is a good question, but is is not as good as this (very old) question http://faculty.uml.edu/jpropp/srat-Q.txt

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    $\begingroup$ This is a neat link, but generally the community likes to have answers that are more than just a link. Can you expand your answer to include some relevant details from the link? No need to reproduce the whole thing. $\endgroup$ – Jeremy Dover Jul 9 at 21:03
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    $\begingroup$ Very interesting link. Thanks for sharing. $\endgroup$ – Pspl Jul 9 at 22:46
  • $\begingroup$ Came here to post this. The SRAT is my favorite puzzle ever. $\endgroup$ – par Jul 10 at 4:20
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I also think it's a bad question.

The purpose of any IQ question is to distinguish intelligent people from the other ones. So obviously: the more intelligent the person is, the clearer they should see that one of the answers is correct and the others are not. In particular: every sufficiently intelligent person must be convinced that the question is well posed.

The puzzle at hand does not meet this criterium. It is well known by logicians that self-reference (or generally: non-wellfoundedness of reference) leads to nonsense. Even if such a question appears to be valid in the sense that there is exactly one answer from which it is impossible to derive a logical contradiction, it is still insufficient for the question to make sense, as illustrated by the following example:

Which of the following is true?

(a) Both sentences are false.
(b) The Earth has the shape of a banana.

Therefore if every person in the world was to answer the said question, the results would include:

- a dummy: "I don't know" - FAIL
- a smarty: "D" - PASS
- a professional logician: "The question is not well-posed" - FAIL

Ergo: the dividing line that question draws between people is not "the intelligent" vs "the unintelligent", but rather "the intelligent but logically uneducated" and "the rest", which is not what an IQ question should do.

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    $\begingroup$ @user253751 Self-reference doesn't have to lead to a contradiction, but even if it doesn't, it's still nonsense. I think that's what Adayah is getting at, though the example is flawed. "This sentence is true" is "self-referentially-stable" in the sense that if we regard it as true, there is no contradiction, and if we regard it as false, there is also no contradiction. But ... that's a bit of a problem, isn't it. $\endgroup$ – Kaz Jul 11 at 0:19
  • $\begingroup$ @Kaz How is the example flawed? $\endgroup$ – Adayah Jul 11 at 11:46
  • $\begingroup$ @user253751 To clarify: by a self-referential statement I mean one for which determining the truthfullness eventually requires knowing it in advance. I claim any such statement is nonsensical. If you disagree (after the clarification), I would like to see a counterexample. $\endgroup$ – Adayah Jul 11 at 11:58
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    $\begingroup$ @Kaz "This sentence is the correct answer" can be a correct answer for a similar question. "This sentence is not the correct answer." can never be the correct answer, because that leads to a logical contradiction. The fact that it's not the correct answer, however, doesn't imply that it's false. It can be true, and also not be the correct answer. (Example: "What colour is the sky?" "A: It's red" "B: It's green" "C: It's blue" "D: Hydrogen has an atomic number of 1") $\endgroup$ – user253751 Jul 11 at 12:32
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I think this is a bad multiple choice question. Not just a bad (MC) question for IQ tests, but in general a bad (MC) question.

Let's start by defining three categories of multiple choice questions:

  1. Good questions: exactly one answer* is right, and getting the answer right conveys a high likelihood the answerer understands the matter at hand well enough
  2. Passable questions: exactly one answer* is right
  3. Bad questions: a good case can be made for multiple answers being right

This is definitely not a good question:

If I consider the fact that A and B are in no way distinguishable and you can only pick one answer, neither can be the right answer. That leaves C and D. C is clearly a contradiction, so the answer must be D. Using the fact that there is only one correct question allowed me to get to the right answer without fully understanding why it is the right answer, so this is not a good question.

This is not a passable question either:

There is definitely a case to be made that there is no good answer here. Other answers have gone into more details about this, but the brief version is that C and D are both "no", so if one is right, the other is too. That means that D is not the right answer, and neither are A, B or C. At this point, answering the question is more about trying to figure out what the asker meant to be the answer than what is actually the right answer, and that's a pretty big sign of a bad question. Surely, trying to figure out what the asker meant is always a part of (multiple choice) questions, but it really shouldn't be more important than answering the question itself.

(The "please select one answer" is a strong hint towards what the asker what answer the asker wanted to hear here, and even the implicit version of it where you expect one answer per multiple choice question unless stated otherwise is enough of a hint that many people would be able to guess it. But how do you select one answer if none of them are correct? On the other hand, if you are trying to test people's ability to make the correct assumptions when there is ambiguity then it's not a bad question.)

Moreover, once you acknowledge that filling out none of the answer is as - if not more - correct as D, you can no longer distinguish between those who skipped the question and those who answered it correctly. And if you consider "nothing" to be a good answer here, you are valuing those who skipped the question (or didn't get to it) over those who got it wrong and that feels rather off to me. So, you cannot even fix the question by allowing "both" answers. So, the best thing would be to disregard the question all together, which makes it worse than just a "bad question" in my opinion.

*: in the case you are doing "select any number of answers", consider the one answer to be a single correct set of letters.

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    $\begingroup$ You could fix the indistinguishability thing by making the answers YES/NO/NO. Bonus: Then, if you just assume it can't be B or C because it can't be both, you're wrong. $\endgroup$ – user253751 Jul 10 at 11:37
  • $\begingroup$ @user253751 Good point. I didn't add it because it wouldn't solve the bigger problem, though. $\endgroup$ – Jasper Jul 10 at 12:39
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This is not a good question, because experience with similar problems makes it easily solvable or very difficult. If IQ is a measure of raw mental power, regardless of experience, then a good question should not be affected by experience on similar questions.

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    $\begingroup$ Isn't that argument also valid for the other typical IQ questions??? $\endgroup$ – Pspl Jul 9 at 10:11
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    $\begingroup$ @Pspl Yes, and this is why I consider every IQ I have ever taken to be very biased. $\endgroup$ – RockPaperLz- Mask it or Casket Jul 10 at 4:38
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I’ll just answer the question itself: Since it is highly debatable, and actually debated, whether D is the correct answer or not, it is not a good question for an IQ test. Any question asked in an IQ test must have a correct answer that is not debated.

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This is an interesting question and might be a fun riddle / logic puzzle. I don't think it'd be a good IQ test question, though, because it's solvability (and maybe also its solution, if any) depends heavily on the axioms being assumed.

As no set of axioms is explicitly stated, several axiom choices can be considered appropriate. For example, it wouldn't be too strange an axiom to assume that if two answers have the same content, they have the same truth value (are either both correct, both incorrect or both undecidable), irrespective of their order or numbering. However, your question becomes undecidable under that assumption / axiom.

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  • $\begingroup$ Q: "The answer to this question is C." (A) 123 (B) 123 (C) 123 (D) 123 <- axiom violated $\endgroup$ – user253751 Jul 13 at 11:21
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Here's why only D is correct, using reductio ad absurdum arguments.

Assume A is a correct answer. Then "the option C a correct answer for this question", but C is not a correct answer, since it contradicts A. So the assumption that A is a correct answer has lead to a contradiction, therefore A is not a correct answer. Same for B.

Assume C is a correct answer. Then it is not the case that "the option C a correct answer for this question", again leading to a contradiction.

So none of A, B, or C is a correct answer.

And since C is not a correct answer, the answer to "Is the option C a correct answer for this question?" is NO, and so D is a correct answer.

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  • $\begingroup$ I know this post is a week old by now, but that sort of logic fails if there is no correct answer, e.g. "What is 4+6? (A) 1, (B) 7, (C) 12, (D) 24". It is a very useful tool if you are guaranteed a correct answer, but in the asker's question I don't think you can assume that. $\endgroup$ – Helen Jul 18 at 20:29
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    $\begingroup$ I don’t believe I assumed that there were any correct answers. Once you establish that none of A,B, C is a correct answer by reductio, then you can evaluate the whether D is a correct answer. And it turns out to be correct. The method would also work to show that no answer is correct in your example, as each of them would lead to a contradiction on the form 1=0. $\endgroup$ – David Browne - Microsoft Jul 18 at 21:08
  • $\begingroup$ Ah misread on my part, that's embarrassing. I skimmed the last paragraph too hard and I read it as "Since C is not a correct answer, .... so D is a correct answer". $\endgroup$ – Helen Jul 18 at 21:31
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The question does not specify what qualifies as a "correct" option, and is therefore ambiguous and subject to interpretation.

Although IQ tests seem to often favor such questions, this type of question is not suitable for a multiple choice format if trying to guesstimate intelligence.

A descriptive answer will more likely yield a possible glimpse into intelligence.

That said, I consider every IQ I have ever taken to be very biased. If you go by IQ tests, I'm an extraordinary genius. I see no real-world evidence of that being true.

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  • $\begingroup$ There’s a problem. An “extraordinary” genius is one whose thought processes cannot be followed by others. In other words, your answers are not the ones expected by the test author. If you go by the IQ test, you are just wrong. $\endgroup$ – gnasher729 Jul 10 at 8:57
  • $\begingroup$ @gnasher729 If you are going to publicly tell someone they are wrong, you need to provide references for all your claims. Do you have sources for your claims? They appear to likely be fabricated and not based in science. $\endgroup$ – RockPaperLz- Mask it or Casket Jul 10 at 18:07
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Jordan Peterson in this video tells how IQ questions are selected and which questions are "bad". According to him a "good" IQ test question is one that people with higher IQ get correct more often that people with lower IQ.

So it's not a matter of opinion, it can actually be measured. And you can also measure if the question is biased. This might be slightly language biased, but maybe not as the terms are rather simple.

The objections (self-referrencing, having seen similar things before) can be said about many of IQ test questions but the fact is that ability to answer such questions usually correlates with IQ. Even trivia questions are (mostly and on average) answered better by people of higher IQ. So even those are at least fine or decent for measuring IQ.

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    $\begingroup$ Your definition is circular. If you use an already established IQ test to determine what subquestion is best correlated with a high IQ score, then you are assuming your original IQ test is accurate, but determining the accuracy of an IQ test is the very problem you started off with. But apart from the circularity, the correlation approach is just dumb anyways. Just because something is most-highly correlated, doesn't mean it is justified as a sole indicator, unless you can show that your parameter captures most of the volatility. $\endgroup$ – Jaood Jul 8 at 23:02
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    $\begingroup$ @Jaood it's not my definition, it's an actual method used in psychometry en.wikipedia.org/wiki/Item-total_correlation I am just an enthusiast in this field, but as far as I am aware, one could start with whatever questions and iterating this process will always lead to similar kind of "IQ test questions". $\endgroup$ – Džuris Jul 8 at 23:17
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    $\begingroup$ Your own wikipedia article disagrees with you. It states that it filters out low-correlated questions, i.e. questions that seem to measure something completely different than what what the other questions are measuring. It does not state that it is justified to pick one question that is "most-highly correlated" and use that as a sole-indicator. This is what you seemed to argue in favour for, or at least Peterson did in the link you posted. He says that the way to create IQ tests is to repeatedly pick out the SINGLE best indicator. This is not the approach your wiki-link outlines. $\endgroup$ – Jaood Jul 8 at 23:53
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    $\begingroup$ Also note that the item-total correlation approach is NOT circular, since it does not assign any judgement on its conclusions. It does not state that the resulting items are all great measures of whatever they're supposed to be measuring. It only concludes that they are consistent measures of roughly the same thing. So again, even if you apply this approach properly (which Jordan Peterson doesn't), you don't get "good" IQ-tests out of it ... you only get "consistent IQ-tests" out of it. $\endgroup$ – Jaood Jul 8 at 23:57
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    $\begingroup$ Also, please do provide evidence that if one starts with "whatever questions", it always leads to the same IQ test questions. This is a very strong statement, and I'd be surprised if it were true. Where's your evidence? $\endgroup$ – Jaood Jul 8 at 23:59

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