# Why Does Almost Everyone Get this Question Wrong? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [April 21, 2020, 12:52am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239 "2020-04-21T00:52:17Z")\ **Posts on this page:** 15\ **Page:** 6
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 24, 2020, 3:19pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/101 "2020-04-24T15:19:01Z")
I think I have an answer to my question. A special thanks to **TriPolar**. It all depends on the context in which the question is asked. If I ask the question in the course of some idle chit chat then most people will come up with some quick answer in the hopes that I will shut up, go away, and leave them alone. (Good luck with that.) However, if it is on an IQ test, or part of an important academic exam, or a homework problem where you have plenty of time to think about it, then you might be more likely to give the correct answer. After all, who cares about John’s pencils anyway? ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 24, 2020, 4:06pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/102 "2020-04-24T16:06:21Z")
That’s part of it. However, there’s another part: these questions are similar to optical illusions or magic tricks. They rely on folks’ underlying assumptions and intuitions about the world, and on giving an easy, round-number answer that looks good if you don’t think carefully about it. One of the interesting bits from Andy’s link was that people generally get the question right if you remove the intutive answer. Ask people this question and see what the answer is: > [@](#): > > John buys two pencils, a cheap pencil and an expensive pencil. There is no sales tax. John spends a total of $0.97 for the two pencils. The expensive pencil costs $0.43 more than the cheap pencil. How much did the cheap pencil cost? Suddenly there’s no intuitive answer, and many more people will get the answer right–assuming you can persuade people to bother with the question at all. In any case, you’ll get fewer incorrect answers, and of the incorrect answers you get, there won’t be nearly as large a cluster around a single, incorrect answer. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [April 24, 2020, 4:11pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/103 "2020-04-24T16:11:49Z")
> [@Left\_Hand\_of\_Dorkness](#): > > That’s part of it. However, there’s another part: these questions are similar to optical illusions or magic tricks. They rely on folks’ underlying assumptions and intuitions about the world, and on giving an easy, round-number answer that looks good if you don’t think carefully about it. > > One of the interesting bits from Andy’s link was that people generally get the question right if you remove the intutive answer. Ask people this question and see what the answer is: > Suddenly there’s no intuitive answer, and many more people will get the answer right–assuming you can persuade people to bother with the question at all. In any case, you’ll get fewer incorrect answers, and of the incorrect answers you get, there won’t be nearly as large a cluster around a single, incorrect answer. Which suggests that people don’t get it wrong just because they don’t care (if they didn’t care, they’d get it wrong for the $1.10 version and for the $0.97 version). It’s that when there appears to be an obvious answer, they don’t care to do any further work - but apparently when there isn’t an obvious answer leaping out at them, they have no objection to doing the work to actually find the right answer. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 24, 2020, 4:21pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/104 "2020-04-24T16:21:28Z")
> [@Andy\_L](#): > > Which suggests that people don’t get it wrong just because they don’t care (if they didn’t care, they’d get it wrong for the $1.10 version and for the $0.97 version). It’s that when there appears to be an obvious answer, they don’t care to do any further work - but apparently when there isn’t an obvious answer leaping out at them, they have no objection to doing the work to actually find the right answer. Exactly. I sometimes teach an after-school magic club, and I tell my students that a good magic trick includes a plausible, impossible explanation for what’s happened. If you just show something weird happening with a string, folks will be confused and either have no explanation for what happened, or else they’ll figure it out. But if you tell them that you can make the string pass straight through your neck, then they’ll watch you do the trick and think that’s what they’ve seen: it’s a plausible explanation whose only problem is that it’s clearly incorrect. That’s where the fun of watching good magic comes from, that cognitive dissonance. These questions offer the plausible incorrect solution, like a good magic trick. The difference is that the incorrect solution isn’t clearly incorrect. It’s less like a good magician, and more like a con artist, in that regard. By the way, I think digging in deep to why people miss these questions is a lot more interesting than just saying, “People r dumb”. Thanks for the insights! ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 24, 2020, 4:46pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/105 "2020-04-24T16:46:05Z")
Here’s one that one of my physics professors used to get a lot of grad students with: There is a steel plate affixed to the ceiling, with a bar magnet stuck to the plate and hanging from it. Draw a complete free-body diagram (a diagram showing all of the forces) for the bar magnet. Or, since this is a text-based medium, just list all of the forces. ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 24, 2020, 5:01pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/106 "2020-04-24T17:01:33Z")
> [@Chronos](#): > > Here’s one that one of my physics professors used to get a lot of grad students with: > > There is a steel plate affixed to the ceiling, with a bar magnet stuck to the plate and hanging from it. Draw a complete free-body diagram (a diagram showing all of the forces) for the bar magnet. > > Or, since this is a text-based medium, just list all of the forces. Is the normal force of the steel plate against the magnet one of them? ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [April 24, 2020, 5:09pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/107 "2020-04-24T17:09:12Z")
> [@Left\_Hand\_of\_Dorkness](#): > > I sometimes teach an after-school magic club, and I tell my students that a good magic trick includes a plausible, impossible explanation for what’s happened. Here’s Penn Jillette speaking on the subject - [https://youtu.be/S3vTld5pNlI?t=114](https://youtu.be/S3vTld5pNlI?t=114) ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [April 24, 2020, 5:20pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/108 "2020-04-24T17:20:40Z")
> [@Chronos](#): > > Here’s one that one of my physics professors used to get a lot of grad students with: > > There is a steel plate affixed to the ceiling, with a bar magnet stuck to the plate and hanging from it. Draw a complete free-body diagram (a diagram showing all of the forces) for the bar magnet. This is going to be really hard for a novice like me. > [@](#): > > Or, since this is a text-based medium, just list all of the forces. Oh! Strong nuclear force, weak nuclear force, gravity, electromagnetism. ---
**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:** [April 24, 2020, 8:09pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/109 "2020-04-24T20:09:24Z")
> [@yarblek](#): > > For my own amusement as a mathematically challenged dummy and for anyone so or otherwise inclined: > > Going up a hill at 30 mi/h and going back down at 60 mi/h, it seems obvious that the distance does not change going up and down the hill. So if you know this, an average speed of 45 mi/h can never be correct even if I really felt like it should have been. It might be easier to see this when assuming a value for the distance but I wanted to solve it without doing so algebraically. > > [ol] > [li] Average speed is total distance/total time. [/li][li] Total distance is up hill + down hill = x mi + x mi = 2x mi.[/li][li]Total time = (distance going up hill / speed going up hill) + (distance going down hill / speed going down hill) [/li]= (x mi / 30 mi/h) + (x mi / 60 mi/h) > = (2x mi / 60 mi/h) + (x mi / 60 mi/h) > = 3x mi / 60mi/h = (3/60)x mi / mi/h = (1/20)x / h.[/ol] > > Therefore, the average speed = 2x mi / (1/20)x h = 2(20) mi/h = 40 mi/h. If you go 1 mile at 30mph it will take you 2 minutes. If you go 1 mile at 60mph it will take you 1 minute. If you travel 2 miles in 3 minutes you are averaging 40mph. So your way of doing it with magical runes turned out to work. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 24, 2020, 8:49pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/110 "2020-04-24T20:49:43Z")
Yup, **Ynnad** , that’s the one that most physics grad students missed. ---
**Author:** ![Noel\_Prosequi](https://avatars.discourse-cdn.com/v4/letter/n/b19c9b/32.png) [@Noel\_Prosequi](https://boards.straightdope.com/u/Noel_Prosequi)\ **Post date:** [April 26, 2020, 9:46am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/111 "2020-04-26T09:46:36Z")
Re the Oz 5c piece - Some old school types used to call a sixpence (which was the imperial equivalent of the 5c piece) a ‘zac’. No idea why. Haven’t heard it for years though since the value in a 5c piece now makes discussions about them pretty much irrelevant. ---
**Author:** ![Acsenray](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/acsenray/32/4519_2.png) [@Acsenray](https://boards.straightdope.com/u/Acsenray)\ **Post date:** [April 26, 2020, 12:02pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/112 "2020-04-26T12:02:09Z")
Short for “Anzac”? Apparently during the war, the Australian sixpence was minted in the United States — [Sixpence (Australian) - Wikipedia](https://en.wikipedia.org/wiki/Sixpence_(Australian)) ---
**Author:** ![Musicat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/musicat/32/20189_2.png) [@Musicat](https://boards.straightdope.com/u/Musicat)\ **Post date:** [April 26, 2020, 12:17pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/113 "2020-04-26T12:17:24Z")
> [@Noel\_Prosequi](#): > > Re the Oz 5c piece - Some old school types used to call a sixpence (which was the imperial equivalent of the 5c piece) a ‘zac’. No idea why. Haven’t heard it for years though since the value in a 5c piece now makes discussions about them pretty much irrelevant. I must continue the hijack, then I’ll stop. I was in Sydney once (1960’s), and wanted to make a phone call. Outside a bank was a booth (remember those?), but phone calls cost 5 cents and I had no change. I went up to a bank teller and asked for nickels for my dollar bill. She had no idea what I meant. I kept thinking, “_Nickels_, you stupid foreigner!” I only hope I wasn’t thinking out loud. I was aware that the currency had recently transitioned from pounds & shillings to a decimal system, but for a bank, this was ridiculous! Then another teller heard us, leaned over, and said, “I think he means 5-cent pieces.” It was my turn to feel foolish. And you certainly don’t want to hear how I couldn’t make the phone work at first. ---
**Author:** ![Carryon](https://avatars.discourse-cdn.com/v4/letter/c/9fc29f/32.png) [@Carryon](https://boards.straightdope.com/u/Carryon)\ **Post date:** [April 26, 2020, 9:41pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/114 "2020-04-26T21:41:51Z")
My thought is people take “a dollar more” to mean “an additional dollar,” which in that case mean ten cents. It’s like the old song, “I was going to St Ives” the traditional answer is one person was going, the rest were going the other way, but nothing in the rhyme says that, two people can meet up from different angles and continue together. ---
**Author:** ![squidfood](https://avatars.discourse-cdn.com/v4/letter/s/a87d85/32.png) [@squidfood](https://boards.straightdope.com/u/squidfood)\ **Post date:** [April 27, 2020, 11:06pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/115 "2020-04-27T23:06:07Z")
The egg one has always been my case study for teaching dimensional analysis, i.e. “watch your units”. If you’re trying to get to eggs per chicken per day, writing out (1.5 eggs)/(1.5 chickens)/(1.5 days) makes it somewhat clear that cancelling two of the 1.5s (i.e. going to 1 egg/1 chicken) leaves an inconvenient extra 1.5 (days) in the denominator. [Previous page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=5)