# 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:** 20\ **Page:** 3
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [April 21, 2020, 5:45pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/41 "2020-04-21T17:45:38Z")
> [@Machine\_Elf](#): > > But the standard for computing percentages is to use the amount before the given transaction as the denominator - not the amount from before some previous transaction. > > Stock prices are a good example. If your stock reports a drop of 10% one day, then posts a gain of 10% the next day, then it hasn’t recovered. well yes, clearly. My point is that the those questions, as written, do not have the necessary information in them to lead to one, and one only, correct answer. For both of them there are plausible and reasonable interpretations for several “correct” answers The pencil one contains all the info needed and has no room for interpretation. ---
**Author:** ![Gatopescado](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gatopescado/32/5711_2.png) [@Gatopescado](https://boards.straightdope.com/u/Gatopescado)\ **Post date:** [April 21, 2020, 7:43pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/42 "2020-04-21T19:43:27Z")
The real question is why such a disparity of pencil quality that would adequately justify the price difference. ---
**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 21, 2020, 8:13pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/43 "2020-04-21T20:13:17Z")
> [@Gatopescado](#): > > The real question is why such a disparity of pencil quality that would adequately justify the price difference. [Artisanal pencils](https://www.fendrihan.com/products/blackwing-602-pencil-set-of-12?utm_medium=cpc) But the real money is in the [sharpening](http://www.artisanalpencilsharpening.com/). ---
**Author:** ![Ulfreida](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ulfreida/32/8014_2.png) [@Ulfreida](https://boards.straightdope.com/u/Ulfreida)\ **Post date:** [April 21, 2020, 8:18pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/44 "2020-04-21T20:18:39Z")
So it isn’t a math problem at all. It’s an english problem. ---
**Author:** ![WildaBeast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wildabeast/32/6_2.png) [@WildaBeast](https://boards.straightdope.com/u/WildaBeast)\ **Post date:** [April 21, 2020, 9:12pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/45 "2020-04-21T21:12:37Z")
> [@Machine\_Elf](#): > > But the standard for computing percentages is to use the amount before the given transaction as the denominator - not the amount from before some previous transaction. > > Stock prices are a good example. If your stock reports a drop of 10% one day, then posts a gain of 10% the next day, then it hasn’t recovered. Likewise many people have difficulty understanding that if an item is on sale for 20% off the original price, and you have a coupon for 20% off your entire purchase, that’s not the same as a 40% discount. ---
**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:** [April 21, 2020, 9:28pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/46 "2020-04-21T21:28:54Z")
> [@Telemark](#): > > [Artisanal pencils](https://www.fendrihan.com/products/blackwing-602-pencil-set-of-12?utm_medium=cpc) I’ll take “ART IS ANAL PENCILS” for $200, Alex. ---
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [April 21, 2020, 9:45pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/47 "2020-04-21T21:45:49Z")
> [@Ynnad](#): > > Engineers, accountants, and physicists all get it wrong. They all insist that the cheap pencil costs 10 cents. Even when I show them they are wrong, they still insist that the cheap pencil costs 10 cents. If Engineers, accountants, and physicists all fail to understand this relatively simple algebra word problem after you explain it to them, I have to think that the problem lies in your explanation. Lots of people have pointed out why _initially_ most people get this wrong, but the actual math to solve it is like 7th grade level. I find it really hard to believe that people who had to excel in math at the college level can’t manage to understand this. ---
**Author:** ![AnalogSignal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/analogsignal/32/1085_2.png) [@AnalogSignal](https://boards.straightdope.com/u/AnalogSignal)\ **Post date:** [April 21, 2020, 10:01pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/48 "2020-04-21T22:01:12Z")
> [@penultima\_thule](#): > > An old rural favourite; > If a hen and a half, lays an egg and a half, in a day and a half … so; > How many eggs do four hens lay in six days? I found this trickier than the original problem but it is still solvable with Wolfram Alpha: > **[1.5\*1.5x=1.5,4\*6x=y - Wolfram|Alpha](https://www.wolframalpha.com/input/?i=1.5*1.5x%3D1.5%2C4*6x%3Dy)** > > Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Wolfram finds the number of eggs produced by one hen in a day (x) = 0.666667 and the final answer (y) is 16. ---
**Author:** ![sitchensis](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sitchensis/32/4892_2.png) [@sitchensis](https://boards.straightdope.com/u/sitchensis)\ **Post date:** [April 21, 2020, 10:16pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/49 "2020-04-21T22:16:45Z")
Just about every time a sports based thread pops up someone drops in to tell everyone how sports are stupid. At least with sports we know with certainty that people actually enjoy them. This is a game, like sports, only it’s a game that not many people enjoy. It’s like the 15th time your Grandpa pulls a quarter from your ear. ---
**Author:** ![penultima\_thule](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/penultima_thule/32/3833_2.png) [@penultima\_thule](https://boards.straightdope.com/u/penultima_thule)\ **Post date:** [April 21, 2020, 10:28pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/50 "2020-04-21T22:28:08Z")
> [@TriPolar](#): > > How did you and they buy things in the old days when everything used to cost a nickel?. Well in Australia, way back in those days the coin we would have used was called a shilling. If you got a good deal you might have got tuppence or thripenny bit as change. Australia made the change to decimal currency on 14th February 1966 and we never have used nickels… ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [April 22, 2020, 1:16am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/51 "2020-04-22T01:16:23Z")
OP here. I think I have gained a little insight. \*\*TriPolar \*\*said, “_… That’s what pops into people’s minds and they don’t think any further through because who cares about John and his pencils anyway?_” People that know me well respond this way: they look silently in another direction without saying anything hoping that I will leave soon because “who cares about John and his pencils anyway.” Several posters have suggested that the math problem is deliberately contrived so as to be misleading. Maybe it is a bit contrived. It doesn’t seem to follow the expected order of statements and questions for most ordinary discussions about pencil purchases. A more normal discussion might be as follows: ZEKE: How much did you spend for those two pencils? SUSAN: $1.10. ZEKE: That one is really pretty. How much did that one cost? SUSAN: The pretty one cost $1.05. ZEKE: So I guess the plain one only cost a nickel then, right? SUSAN: Yes. [ZEKE AND SUSAN HAVE SEXUAL INTERCOURSE IN THE BACK ROOM] However, consider the following (somewhat contrived) discussion between Alice, Bob, and Charles, who are partners in a small accounting firm: ALICE: We’re almost bankrupt. The only cash we have left is $1.10. BOB: What do we need the most that costs $1.10 or less. CHARLES: We are out of pencils. We can’t do accounting without pencils. ALICE: Bob, go to the store and buy some pencils. [ALICE AND CHARLES HAVE SEXUAL INTERCOURSE IN THE BACK ROOM WHILE WAITING FOR BOB TO COME BACK WITH THE PENCILS] [LATER] BOB: I’m back. CHARLES: How many pencils did you buy? BOB: Two. Check out this one pencil. Its really cool. It’s what they call an artisanal pencil. CHARLES: Did you bring back any change. BOB: No. I spent all of our money. CHARLES: Dammit Bob, how much more did you have to spend just to get that stupid artisanal pencil. BOB: It only costs one dollar more than the regular pencil. Excuse me, I have to take this call. [BOB EXITS ROOM] ALICE: Bob is such an idiot. We don’t need fancy pencils. If he had just bought regular pencils we would have 22 pencils now. So, I guess it would be an unusual situation and non-ordinary conversation that set up this math problem. But it could happen. And I still say that it is not a “trick question.” ---
**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 22, 2020, 1:48am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/52 "2020-04-22T01:48:48Z")
In Kahneman’s book Thinking Fast and Slow, the question is “A bat and a ball cost $1.10. The bat costs $1 more than the ball. What does the ball cost?” - so there’s no confusion about artisanal pencils. ---
**Author:** ![jtur88](https://avatars.discourse-cdn.com/v4/letter/j/e9c0ed/32.png) [@jtur88](https://boards.straightdope.com/u/jtur88)\ **Post date:** [April 22, 2020, 2:52am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/53 "2020-04-22T02:52:41Z")
> [@CookingWithGas](#): > > More precise wording would have been “Go up a hill 30 MPH and back down the same hill at 60MPH.” Which I think everybody would assume anyway. “_Back_ down” implies, in plain language, “return to the starting point”. It is redundant to add “the same hill”.’ ---
**Author:** ![Tim\_R.Mortiss](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim_r.mortiss/32/142_2.png) [@Tim\_R.Mortiss](https://boards.straightdope.com/u/Tim_R.Mortiss)\ **Post date:** [April 22, 2020, 6:06am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/54 "2020-04-22T06:06:50Z")
Well, for the record, I’m an engineer, and I got the correct answer on the first try. I really doubt any engineer would get it wrong. We are trained to approach math problems logically, not casually. ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [April 22, 2020, 6:21am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/55 "2020-04-22T06:21:28Z")
> [@MichaelEmouse](#): > > Like what? Obsessive or compulsive attention to detail, mild paranoia or excessive nitpicking, inability to let go and enjoy the moment, a generally reductive worldview or over analytical attitude. Related example, it’s a popular wish to have a photographic memory, but the few individuals who actually come close often report it kind of makes them miserable because they cannot recall something bad without reexperiencing the emotional impact. ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [April 22, 2020, 6:36am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/56 "2020-04-22T06:36:48Z")
> [@Telemark](#): > > I’m not sure how that relates to the portion of my post that you quoted. The problem as stated is mathematically correct, if misleading to the casual observer. When you say _“a hen and a half lays an egg and a half in a day and a half”_ a casually observer is going to cancel out all the "a half"s and reduce the statement to _“a hen lays an egg in a day”_. But the whole point of the riddle’s misdirection is that you can’t reduce like that. You can only remove the first two, leaving “a hen lays an egg in a day and a half”, the time period doesn’t change. Most folks miss that and therein lies the magic of the riddle. > > It’s the same type of misdirection in the OP’s riddle. This doesn’t make any sense. Even if you assume that the half chicken is an actual dead half chicken, and not a real statistical one (which is stupid, a riddle which relies on common reading errors to encourage you to make a real mistake is fundamentally in a different category than one which has more than one legitimate interpretation) it still explicitly says the half eggs are being laid. ---
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [April 22, 2020, 7:39am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/57 "2020-04-22T07:39:32Z")
> [@jtur88](#): > > “_Back_ down” implies, in plain language, “return to the starting point”. It is redundant to add “the same hill”.’ But you didn’t use plain language, you didn’t specify the same hill and you said nothing about returning to the starting point. Your question _can_ be interpreted in that way but it can also be correctly interpreted in other ways. The uphill and downhill comments might be thought of as an irrelevant factor just like the old “ton of lead or ton of feathers” and dismissed as such. After all, what effect does uphill or downhill have on an average speed you’ve already recorded? Your question was far too loosely worded to be in the same category as the pencil one and if you asked it to me in it’s orginal form I wouldn’t even try to solve it. I’d have to ask you for addtional information to be able to answer it precisely. ---
**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 22, 2020, 8:12am UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/58 "2020-04-22T08:12:00Z")
> [@Novelty\_Bobble](#): > > But you didn’t use plain language, you didn’t specify the same hill and you said nothing about returning to the starting point. > > Your question _can_ be interpreted in that way but it can also be correctly interpreted in other ways. > The uphill and downhill comments might be thought of as an irrelevant factor just like the old “ton of lead or ton of feathers” and dismissed as such. After all, what effect does uphill or downhill have on an average speed you’ve already recorded? > > Your question was far too loosely worded to be in the same category as the pencil one and if you asked it to me in it’s orginal form I wouldn’t even try to solve it. I’d have to ask you for addtional information to be able to answer it precisely. [Are you guys talking about this problem:](https://fs.blog/2014/06/einstein-wertheimer-car-problem/) > [@](#): > > An old clattery auto is to drive a stretch of 2 miles, up and down a hill, /. Because it is so old, it cannot drive the first mile— the ascent —faster than with an average speed of 15 miles per hour. Question: How fast does it have to drive the second mile— on going down, it can, of course, go faster—in order to obtain an average speed (for the whole distance) of 30 miles an hour? ---
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [April 22, 2020, 1:05pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/59 "2020-04-22T13:05:15Z")
> [@TriPolar](#): > > [Are you guys talking about this problem:](https://fs.blog/2014/06/einstein-wertheimer-car-problem/) No, your question fills in the details that the original one leaves out. The original one merely says > [@](#): > > Go uphill 30 MPH and back down 60MPH. Your average speed is not 45 That is all it says and it is ambiguous with alternative potentially “correct” answers ---
**Author:** ![Calavera](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calavera/32/70_2.png) [@Calavera](https://boards.straightdope.com/u/Calavera)\ **Post date:** [April 22, 2020, 1:15pm UTC](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239/60 "2020-04-22T13:15:43Z")
> [@jackdavinci](#): > > This doesn’t make any sense. Even if you assume that the half chicken is an actual dead half chicken, and not a real statistical one (which is stupid, a riddle which relies on common reading errors to encourage you to make a real mistake is fundamentally in a different category than one which has more than one legitimate interpretation) it still explicitly says the half eggs are being laid. **Telemark** is right. He’s not removing the half chicken, just realizing that x chickens laying x eggs in y days will always take y days regardless of what x you use, so you can simplify it by changing x to 1, but y remains the same. [Previous page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=2) [Next page](https://boards.straightdope.com/t/why-does-almost-everyone-get-this-question-wrong/852239.md?page=4)