Researchers find why are some word problems harder than others

[@Eduarodi]

It took me about 1% of the time to turn both problems to mathematical terms: 14-2, another 1% to figure out that the answer is 12, and 98% thinking it couldn't be that easy and where's the trick. 😂

[@Qermaq]

You know, that's probably how we should solve every problem. :)

[@Eduarodi]

@@Qermaq Probably. But it surprises me that so many people get the wrong answer.

[@shanehebert396]

Exactly the same here... spent more time wondering where the trick was and what I was missing.

[@leif1075]

HOW do pll get it wrong..what's the trouble point? O ly thing I can think k lf is they thi k the smurf alone is 14 cm?

[@ericherde1]

Or if “attains” refers only to the height that the smurf gained by stepping onto the table, instead of the total height of table plus smurf.

[@theelk801]

the hardest part of both these questions was making sure I hadn’t missed some obvious trick

[@Sonny_McMacsson]

Basically. They looked like the same problem to me after I was reasonably sure I understood what was being asked. I wonder what sort of thing actually tripped them up.

[@faithhellman402]

@@Sonny_McMacsson Perhaps they over thought the question, expecting it to have been much harder than it actually was or something. 🤷‍♀

[@kunalkashelani585]

I went into this has to be a trick question for experts to fail and hence figured, if the table is tilted, then the data is not sufficient. In the second question however, no such nuanced issue could be found and hence the answer had to be 12 Dollars!

[@burns4246]

@@kunalkashelani585 what tripped me up was what is the notebook cost 14 $ , that makes the ruler 0$. so julie buys the eraser for -2$? i said 12 cus thats the answer i was guessing they wanted. i could see a trick question in there if they wanted

[@goldenwarrior1186]

@@burns4246No it said that the notebook and ruler together cost $14, not that the notebook alone costs $14

[@hailmary7283]

The hardest part about both of these questions was realizing that "Yes it really is that simple."

[@EaglePicking]

Yeah, same here. I'm used to getting hard problems on this channel, and this was just too easy to be true, so I read them both twice to double-check for possible pitfalls.

[@Ultranger]

What’s weird is I struggled more with the first problem… however my problem was whether attaining a certain height meant measuring from the floor to the top of their head, or from the floor to their feet. I guess that would make more sense if it was a trick question though.

[@taekwondoneopets]

Same. When you climb a mountain with another person of different heights, you both attain the same height. In this case, the semantics often refer to height measuring from sole of feet to reference point at sea level. That's where I got the question wrong too.

[@likebot.]

It makes no difference whether the table was included in the Smurfs height. The math question doesn't need the table. The question is effectively: Smurf #1 is 14cm in height, Smurf #2 is 2 cm shorter. How tall is Smurf #2?

[@aaronbredon2948]

Yes, it could be interpreted as 14 being the right answer - they both attained (were standing atop) the same table of height 14cm, so they both attained 14cm.

[@diedoktor]

​@@likebot. It doesn't matter if the table is included or not, since if it is then it's included on both sides.

[@kevinmartin7760]

I was wondering the same thing: Is Grumpy 2cm shorter (on the floor) than slouchy is (on the table)? Re-reading the question, though, I see that at the point the heights of Grumpy and Slouchy are compared, both are on the table, and the interpretation of comparing one's height standing on the floor with the other's height standing on the table would be very unreasonable.

[@keithgoodnight3463]

This surprised me quite a bit. I got the answer to both questions with no problem, but more relevant to the study is that when the second question came up, my immediate first thought was "But that's exactly the same question. There's no difference." The study as described doesn't distinguish between people who see the problems as equivalent, and those who perceive a difference in difficulty but got both answers correct (or incorrect) anyway. That's the distinction that intrigues me most on hearing about this study.

[@faithhellman402]

Yeah, I recognized them as the same problem as well. I thought it kinda messed with the results for us watching the video, cause we saw them one right after the other, after having already seen it in the math format from the thumbnail, so it felt a little biased for me to say: yup, super easy problem. 😂

[@rebeccalynn7795]

thinking this too.

[@gerrya2133]

My guess is the test didn't test the problems back to back with the same person. Either there were a lot of problems and these duplicates were mixed in, or there was a mirrored set of problems that were given to different sets of participants.

[@hbrg9173]

Both of them are x + y =14, what is x + (y - 2)? A bigger confusion was with the first one because usually a height of a person is their own height, not depending on their location. So I had to assume that they meant his head is 14 off the ground, regardless of his actual height.

[@kmbbmj5857]

I think a bigger study is how the expectation of a trick question changes how people answer questions. We've all seen so many trick "gotcha" questions over the years that we no longer trust our answers to the problem; instead, we expect Loki or the Riddler to jump out with a "gotcha."

[@gila168]

I spent more time questioning my instinct because I thought these were trick questions.

[@Goose____]

exactly like me lol, i thought 12 was wayy to obvious so it's wrong

[@jcsjcs2]

Same. I was weighing the odds of "attaining a height of 14 cm" meaning that the smurf climbed a table that is 14 cm high... It was more of an English quiz than a math quiz.

[@JLvatron]

The 1st question had only 3 variables, but the 2nd Question had 5. The trick was that both questions were not as similar as they said.

[@InvaderMixo]

Honestly, I thought the first question had more of a potential trick. Saying that Slouchy "attains the height" is slightly ambiguous. Does it mean his personal height or overall height from the ground?

[@mandolinic]

I found these so easy I was worried that there was a trick I was missing. However, I was completely confused by the ordinal/cardinal rationale. I just can't see and qualitative difference between a height and a price. One height can be larger than another - and ditto for prices. Both are represented by numbers and I can sort any list of numbers into an ascending or descending sequence. Maybe it's because I was a professional programmer for over 40 years?

[@macklyn]

Exactly the same here on trick, ordinal/cardinal difference and programming career. :D

[@danp8321]

Yeah I don't see why height should be an ordinal number; it's a scalar quantity just as price is, it doesn't represent any sorting order or anything like that

[@jrkorman]

I have to totally agree with the observation regarding height/price. To me these are merely values along a number line. The only thing that I had to stop to think about is "What did the author of the question mean by using the word 'attain'". The question in itself is not complete because it does not contain a reference point RE: what point on the Smurf is the highest most datum. We are left to assume that it is the top of the head. We also have to assume that the lowest datum is some surface the table is sat upon.

[@temtempo13]

Also a programmer here. I think the video bobbled the difference between "what kinds of numbers are these" and "what kind of mental representations come most naturally to people manipulating these numbers." It's ridiculous for the video to claim that "cardinal numbers are inherently unordered." It might be the case that we tend to think more about ordinality when it comes to people's heights than cardinality (e.g. "am I shorter than my friend, am I tall enough to reach the high shelf")?

[@mastick5106]

Guess I should have scrolled down farther to make sure my comment hadn't already been made in some form 🙃. (fellow programmer here, 30 years)

[@jcsjcs2]

Interesting. In my mind I've converted the cardinal numbers "price" into ordinal numbers by imagining a stack of money. For me both questions were identical. However, I did struggle with the meaning of "attain a height of x". I was wondering if this is a trick question and the are actually asking for the height of the smurf table, as in "reaching an altitude of 1000 m", where you wouldn't add you height of 1.80 m onto the altitude.

[@Koshak87]

My thought exactly on both counts.

[@mehrdadjimboudi2891]

Exactly what I thought! Also english isnt my first language, I was asking myself what exactly attain means, then going on to google the difference between attain and obtain😂

[@h2_]

hm, weird. I thought the first one was a lot harder because the way it was saying "attains" felt really awkward and made me second guess what they were asking vs what they were trying to ask

[@flippantelf]

Facinating! Even as a former mathematics teacher, I put a non-trivial amount of thought into these questions. I found each question to be worded poorly from one perspective or another, but the second (cardinal) problem's wording was worse than the first's (ordinal). Granted, these are only two examples of what must have been dozens of questions analyzed for the study. However, I would like to give my two cents on the difference between them, and why I think the second is more difficult even without accounting for the difference between the units of measure. TL;DR: the second problem is worded more ambiguously than the first in ways that have nothing to do with the units of measure; also, both reading and writing word problems is hard. I apologize, brevity is not one of my strengths. As a disclaimer, I was expecting to be tricked by these problems: if I was not expecting to be tricked, I would not have spent nearly as much time or effort dissecting the language of the questions. Also, my opinions are based mostly on my own experience and thought process, which may or may not generalize to any group of people. In the first problem, the wording "...now attains the height of..." is not specific: it could be height above the ground on which the table stands, or it could be height with respect to the surface of the table. The word "now" implies that this is a change from some previous height, and that this is therefore height as measured from the ground, smurf and table combined. However, determining this isn't necessary to correctly solve the problem: because the question is phrased using the same ambiguous language "What height does GS attain...", we can assume with reasonable certainty that the author intended the same interpretation for both smurfs. Therefore, we don't need to know the author's intent: the two smurfs take the same action (climb on the table), and if SS "attains" a height of 14 cm, then GS "attains" a height of 12 cm. We can argue about what that actually means some other time. In contrast, the second problem has semantic ambiguity that cannot be so easily solved. Firstly, we are not told what either Anthony or Julie is actually doing or intending to do: instead, we are told what they "want". One may reasonably assume that if someone "wants" something in a store then they will buy it, but it is very easy to imagine circumstances in which a shopper "wants" something that they do not buy, due to lack of money, availability, or...anything, really. Even though this language is consistent between the two shoppers, that does not guarantee their behavior will be consistent: Anthony could want the ruler and choose to buy it, while Julie may want the eraser but choose not to buy it. While knowing Anthony's "total" implies that he is buying more than one object (both notebook and ruler), no such language clarifies Julie's intent. We must assume that each shopper will buy everything they want for the problem to be solvable, which I believe is a less certain assumption that assuming an author means the same thing when they reuse the same language. Secondly, Julie wants to buy "the same notebook as Anthony": does this mean she wants a notebook that is functionally identical to the one Anthony wants, or does she literally want the exact same notebook? Is the notebook special in some way? Are they going to get into a brawl over the notebook like parents before Christmas, vying for the last copy of that popular toy? If that is the case, only one of them can buy the notebook: without knowing who will buy the notebook, the problem is impossible to solve. Granted, I don't think any reasonable person would assume that this was the author's intent: I have never witnessed or heard about storeroom brawls over a notebook, and I know of neither limited edition notebooks nor collectors that covet them. I think that it is reasonable to assume that they will buy different notebooks of the same make, model, and price. Still, this is a harder assumption to make than before because we must assume that the author does not mean what they actually wrote, and my default for reading comprehension is "assume the author means what they actually write". Also, since we know Anthony's "total" but not Julie's, the author may be implying that Anthony is the one buying the (single) notebook, and that Julie is not. If Julie does not buy the notebook, we cannot know what Julie will pay. To give the author(s) credit, it is hard - very hard - to write a word problem that is simultaneously detailed, succinct, and unambiguous. I also think that these examples point out something else: math "word problems" are more a test of reading comprehension than they are of math ability, and many of these problems are poorly worded. It is only natural that people would fail to arrive at the author's intended conclusion if the author does not clearly state the premise and/or the goal of the problem. If the other problems used for this study were similarly ambiguous, I question the validity of its results. Bonus: anyone may legitimately ask "You're critical of the second problem's wording, but could you have done any better?" Like I said, phrasing problems is hard: while I do think I can do better, I'm sure my attempt will also have flaws. I will therefore give you my version and you can roast me for it; it seems only fair. "Anthony buys a notebook and a ruler from a store, and the store charges him a total of $14 for the two items. Julie buys a notebook and an eraser from the same store. Her notebook costs the same as Anthony's notebook, and her eraser costs $2 less than Anthony's ruler. How much does the store charge Julie?"

[@veralegendi9098]

Thank you for the detailed clarification and your attempt for a better wording. This one is clear cut... I guess the real problem is with the original creators who intentionally or not made two sloppy verbal excercises.

[@faming1144]

We don't know! The store should charge $12, but do they? Maybe the clerk hits a wrong button on the register...

[@nicolaskoroloff3458]

Julie couldn't buy the same notebook as Antony: he had already bought it!!

[@darshraatparsadhraj5583]

*Goods stock has left the chat* I know it’s supposed to be a joke

[@Alphaminx]

The first one was much harder for me solely because of the word attains. I was getting caught on if it was used as " the table gives (said smurf) 14 cm" or if it meant "the smurf becomes 14 cm while on the table". I got to both answers 14 and 12 because of this logic, but decided for 12 because it made a little more sense in the context of the question. The second one was super easy.

[@Metal_Master_YT]

SAME more people need to mention this!

[@mrosskne]

the problems sound like they were written by aliens

[@JLvatron]

There were more differences in the 2 questions. Q1 had 3 objects: Slouchy Smurf, Grouchy Smurf, and the table. Q2 had 5 objects: Anthony, Julie, a ruler, a notebook, and an eraser. So while still easy, this question was more complex than the 1st. It wasn't just about Ordinals & Cardinals.

[@professorsogol5824]

Actually it has two notebooks as well. We need to verify that the first notebook is equivalent to the second notebook before we can get to the math.

[@robertveith6383]

Presh showed no variables or equations in the working of the first problem, but he showed three variables and a couple of equations for the second problem.

[@JLvatron]

@@robertveith6383 Good point. That proves it was more complex.

[@l.w.paradis2108]

But everybody uses money.

[@joefoulger3510]

@@robertveith6383 he showed them, but they aren't necessary to come to the correct conclusion. It's simple logic. If Julie is spending $2 less on her eraser than Anthony is spending on his ruler, then the total cost of her purchase is $2 less. 14-2=12. You don't need any equations at all. He also could have shown 2 different equations for the smurf problem, he just didn't show them

[@handanyldzhan9232]

The key difference between Q1 and Q2 is that the former has a bit of an ambiguity in that the fifth sentence compares Grouchy's height to Slouchy's, but each have two different "heights" thanks to the usage of the phrase "attains the height of...", so being 2 cm shorter could mean more than one thing (if one's initial height is compared to the other's height on the table, it's technically unsolvable because we don't know the table's height). Q2 is a pretty straightforward question with no weird wording.

[@RonnocFroop]

Given what the question's asking it shouldn't really matter whether the table is included in height or not. Either Slouchy+Table=14cm, and Grouchy+Table=12cm, or if the table's height doesn't matter for the obtained height then Slouchy=14cm and Grouchy=12cm.

[@Marc-gj9vx]

Q2 is also a lot ambiguous, i wasn't sure if there was a trick. Why would they use "want to buy" instead of just saying "buys"? Because you can want to buy stuff without actually buying it... So it's extremely poor wording.

[@casualmarkit9969]

Also, saying they want the same notebook can imply the literal physical same book of which only Either could buy it, making it unsolvable from that interpretation.

[@christianbolt5761]

I studied both mathematics and physics. I ran into many math grad students who had difficulty tutoring a word problem based calculus. It was easy for me. This is the same root issue

[@leif1075]

Did you mean turning a word problem into calculus terms?

[@totally_not_a_bot]

​@@leif1075Word problems using calculus, as compared to the two in the video which use arithmetic. Math is ideas and logic before it is symbols and notation.

[@philrobson4287]

The Smurfs one baffled me because there was no indication whether his height he attained was the height of his feet or height of his head.

[@nheather]

I saw the two questions as identical - clearly my mind didn’t think of them as ordinal and cardinal.

[@DanielHarveyDyer]

My problem with this is that the second question requires an extra logical step Q1 gives slouchy+table and asks for grouchy+table Q2 gives ruler+notebook and asks for notebook+eraser So the second question requires you to apply the commutative property of addition. An equivalently hard problem in smurfland would be to say slouchy standing on a box is 14cm, so how tall is grouchy with a box on his head?

[@yurenchu]

You mean: how tall is _the box_ when it is on Grouchy's head?

[@studgerbil9081]

Anyone who couldn't solve this basic grammar-school algebra question cannot be called an "expert" in mathematics.

[@yurenchu]

These are probably not actual questions that appeared in the test; more likely, these two problems were just invented by Presh as simple examples to illustrate the point of the referenced study to a mostly laymen/non-expert audience.

[@ramiel555]

When I took my ACT's in high school (total score of 28, so pretty good), my math scores were worse on the easier types of questions than they were for higher level stuff, so this is something I've experienced directly. Definitely makes you stop and reevaluate what you thought you knew

[@alvinhelms]

I don't appear to suffer from this bias, because the answers to both questions were equally obvious (and frankly, incredibly easy) to me.

[@DanielFSmith]

For the money question in the USA, you have to figure out the local city's sales tax rate, subtract that from the $14, take $2 off, then re-apply the tax rate.

[@Peter.Sky.Walker]

I think Presh throws these type of videos in every once in a while to make people like me feel smarter than I normally would (which I normally wouldn't). Either that, or he's trolling us.

[@artemisfowl7307]

😂

[@jonmccormick6805]

If he isn't trolling us, he could be checking on our intelligence. I'm very pleased with myself when I don't need paper and a pencil (WAIT do they still make pencils?) and figure out the answer before the video is done.

[@piman9280]

"Don't blindly trust experts."

[@rafael_l0321]

lol. like people have said in other comments: instant solve, then thinking "it can't be that easy, I'm missing something"... although previous exposure to the "a baseball and a bat cost $1.10..." problem should also be an important factor to be considered

[@robertworden9810]

Getting 12 as an answer for both was easy, but the way the first question was worded it would be more correct to say there is not enough info to answer correctly since “is” and “attain” are used in inconsistent ways to refer to their heights. If you interpret those words the same way for both smurfs there is not enough info.

[@Metheglyn]

The first question is poorly phrased. It should have been: "Slouchy Smurf is a certain smurf He smurfs onto a smurf. He now smurfs a smurf of 14 smurf Grouchy Smurf smurfs onto the same smurf as Slouchy Smurf. Grouchy Smurf is 2 smurf shorter than Slouchy Smurf. What smurf does Grouchy Smurf smurf when he smurfs on the smurf? Given the smurfs smurfed, is it possible to smurf a smurf? (A) No, there is not enough smurfs to smurf the smurf. (B) Yes, and the correct smurf is _____. That would have solved any ambiguity.

[@thebyzantine241]

I don't think ordinal vs. cardinal has anything to do with it. I think the issue is the cognitive biases of framing and anchoring. Framing and anchoring are cognitive biases that cause the initial impression to be given greater weight than information presented later. When I quickly whipped through these I got the first one wrong and the second one correct, opposite of what the statistics suggest ought to have happened, and I know why. The sequence of the wording is the explanation; the last sentence says "when he climbs on the table" immediately after the statement "Gouchy Smurf is 2cm shorter than Slouchy Smurf". The second question says "Julie wanted to buy the same notebook as Anthony, AND an eraser, and then says the eraser costs 2 dollars less than the ruler. In this case it is the total that gets anchored from the word "and" that frames the solution mentally. I see what the study author is getting at, but there are other plausible explainations, the sequence of the statements causes the total to get anchored in the second case, but the relative value of g=s-2 in the first. The 4th sentence differs between the two examples in that one is a statement of equivalency, and the other contains an 'and" statement. After careful reflection and writing everything down in symbollic form the errors are easily identified but if you quickly step through it in your head you might easily miss the real question.

[@newpgaston6891]

I'm a bit puzzled, to me the questions were the exact same. I'm not sure what the ordinal/cardinal changes for other people! I would also be curious to see what questions they DID failed (assuming it wasn't these questions, because that would be depressing), to see whether the cardinal/ordinal thing can change something for more difficult questions

[@jcsjcs2]

In my case I had converted the cardinal numbers "price" into ordinal numbers by imagining a stack of money, then cross-checking the answer with arithmetic. So both questions were basically the same.

[@trollsneedhugs]

I agree. It's hard to be sure, because it's hard to mentally analyse your own cognitive processes, but I think I turn them into algebra in my head, with unit type being an irrelevant label.

[@newpgaston6891]

@@trollsneedhugs same... to me the only minor 'challenge' is that when I saw that both questions were exactly the same, I thought "surely they're not", so I spend a few seconds trying to see why one would be different, thinking perhaps the wording tricked me... but no, there was nothing; They really were the same.

[@quentind1924]

It’s the same because you got both in a raw. If now you have a video with 50 math questions (and the first problem is like question 8 while the same version of this problem but with money is near 35), you won’t recognise that they are the same question, and now you might have more difficulties with one of them

[@HopUpOutDaBed]

the difference is prices can fluctuate based on what you buy. If you buy 2 things in the right combination sometimes you get a discount. Buying a 100 pack of something from costco is not the same price as buying 100 individual candy bars. It's not as simple as adding up each individual item, it's about thinking of the items AS A GROUP. using this logic, the eraser could be $2 less than the ruler individually, but that is irrelevant when comparing the (eraser + notebook) combination is distinct from the (ruler + notebook) combination. So this is why they would say not enough information is there.

[@jesseessej]

Both questions were of course so exceedingly easy I solved them in my head near instantly, however because they were so simple I sat pondering for some time thinking I was missing something obvious. In question 1, I was thinking "maybe slouchy Smurf was slouching, so I don't have enough information"

[@michelecoleman5490]

This was my exact issue with the smurf problem. The missing information was whether Slouchy was standing up straight when he "attained" the given height. The word "attained" is very odd here. I would say that by standing on my tippy toes or wearing tall shoes I can "attain" a height that's greater than the official height listed in my doctor's records. Introducing a character who's specifically known for slouching into a question about non-canonical height measurements felt like a deliberately confusing choice.

[@connor1586]

Second was easy. First confused me a bit because I was trying to figure out how height would be measured. If I stood on a platform 100ft in the air, you would say I was 100ft in the air, not 105.5 ft (I.e measuring height from ground to where their feet are). The correct option in the answer is measuring from the ground to their head. If you get mixed up in this way the answer is either 14 cm (because the smurf's height wouldn't matter) or 12 cm (because it does) and therefore you may say not enough information because you don't know how they are measuring.

[@alykadane7206]

The difficult word here is not Smurf, the difficult word here is "Attain".

[@igrim4777]

There is no " _the_ correct answer" for question one. The terms are poorly defined and ambiguous and the phraseology is itself open to interpretation. The use of "now" is objectionable as that is commonly used to indicate another agent in effect especially with the verb tense and aspect used in the sentence. Often now indicates a new action, as in "He climbs on the table. He now surveys his domain." "This causes him to attain", "By doing so he attains", "He attains", or "and so attains" (note the lack of capital indicating it is not a new sentence)" are all superior phrasings and would indicate that the only causative agent to be considered is the climbing (and standing upright) upon the table. Similarly, the question should state "what height _will_ he attain when he _climbs_ upon" or "what height _does_ he attain _by climbing_ upon", note the changes in verbs and conjugation. A smurf physicist teaching a class up to smurf high school would say that a smurf berry and smurf ball, both approximated by spheres albeit of different radii, have both attained a height of x smurfmetres when placed upon the same level smurf table compared to the datum that is the level smurf floor. That the centre of masses (assuming radially symmetric but not necessarily homogenous mass distributions) and tops of the spheres are different to each other is not important for the questions typically asked (such as time to impact when dropped from height x). Similarly, if I were to ask "what's your height, a huge number of people would answer "x cm" or "y feet z inches" and give the same answer regardless of whether they were at the top of a staircase or its bottom as height is not generally considered a variant. The "attains" indicates some variant feature but does not clearly indicate the manner of the change. While the question appears to indicate that this invariant was not the target, if the question was after height to top of head, the question needed to state that height was being measured to top of head since, as implied, measuring to the bottom of the feet when standing on the table is a valid and very sensible interpretation.

[@RAG981]

As a mathematics teacher for >30 years I am well aware of the problems people have in sorting out the math in worded questions. There was a distinct divide between students who could do arithmetic problems and those who could tackle worded ones. I saw the same problem when having to sit in on classes of different subjects when teachers were away. Many students had difficulty just understanding what they were being asked, for example in comprehension exercises. I think the idea that everyone has an internal dialogue is the problem. One has to be able to explain it to oneself in one's mind, and this is much rarer than recognised. I would normally expect a mathematical mind to have less difficulty.

[@totally_not_a_bot]

The problem with word problems is that you need to have a good grasp on both math and language. Not just English, but English grammar. You need to be able to answer abstract questions about concrete relationships, and that's kinda hard. I'd wager there's a distinct overlap between students who are good at word problems and students who are comfortable in a foreign language learned after childhood.

[@mrosskne]

I've never learned a foreign language and I've never had any issues with word problems

[@Geo25rey]

First problem was harder than the second one. Consider the fact that Slouchy Smurf slouches. Assume he slouches some fixed distance, the problem would then be impossible to solve since we are given Slouchy's height not taking into account how much he slouches. This is because typically when you measure a person's height they are meant to stand up straight and not slouch.

[@ZincAddict]

Unlike 99% of the comments, I did get the second question wrong thinking there wasn't enough info. The difference for me was that I didn't care about the smurfs individual height in the first question, but I definitely cared about the notebook's price for some reason

[@JNCressey]

The video is missing an explaination of how anyone could get either of these questions wrong.

[@simongross3122]

The height of a person could really defined as the distance from the soles of their feet to the top of their head. Thus it would make no difference to my height if I were standing at sea level or on top of a mountain or, indeed, the moon. So why should it make a difference if I were a smurf standing on a smurf table? The first question was very poorly worded as it did not define height as the distance from the floor to the top of the smurf's head. I think there's a strong argument for saying that there was not enough information to answer the first question. Nothing to do with ordinal or cardinal numbers. Just poor construction of the question.

[@karhukivi]

It is usually the wording that causes the problems. For example the famous Monty Hall game show problem is difficult for many people because they don't realise that Monty must know where the key is - he cannot open one of the remaining doors at random, as that might accidentally reveal the prize. But the problem is worded to steer the reader away from that very important fact.

[@krzysztofmazurkiewicz5270]

Honestly i found those question similar. In both cases i just quickly made a calculation in my head. Didn't bother much. I did sort of imagine the height problem similarly to what was shown but that didn't affect the overall "equation" in my head. In the second one i just double checked which item was changing so that i was certain about the constant. What i did find puzzling that in both cases the answer was the same value, so when the vide progressed to talk more about it i started to doubt my answers thinking there is some sort of catch. So in my case it would be "don't over think the problem, just make the equations and calculate. It should work." ;)

[@Viel_Glueck]

As the same for me, quickly got both answers but was very unsure whether I made a mistake as they were the same

[@lukeskywalker2255]

just a quick digression it's spelled "equation"

[@krzysztofmazurkiewicz5270]

@@lukeskywalker2255 sorry bout that, had a quick read and corrected, my bad. Should be fine now.

[@lukeskywalker2255]

@@krzysztofmazurkiewicz5270 don't be so formal. I didn't mean to point it out as mistake but rather make you remember the correct spelling. Też jestem Polakiem btw

[@krzysztofmazurkiewicz5270]

@@lukeskywalker2255 still better not to make them in the first place ;) Pozdro ;)

[@pneumatasaur]

A smurf is 3 apples tall. Both apples and cars can be red. How many smurfs do you need to catch to power a car?

[@galacticlava1475]

17 chairs. Please give a harder question next time.

[@s888r]

Imagining Presh saying "Thanks for making us one of the best communities on KZbin" after answering the 2nd question.

[@erikziak1249]

The hardest part for me was to find out the meaning of the word "attain". But both questions were easy and I got both answers, assuming that "attain" means the final height.

[@liamswedberg2827]

Yeah, when I read it I input it as a synonym for "gain", while a more accurate synonym would be "reach" or "achieve"

[@cigmorfil4101]

What does "attain a height of 14 cm" mean? If it means the first smurf is now 14cm off the ground (like throwing a ball up attains a height of 5m means it reaches 5m above the ground), then the second smurf will also attain a height of 14 cm when it climbs on the table, as the table top is 14 cm above the ground.

[@ccmplayer87]

Since English is my second language (not my primary language), I interpreted "attains" as "receive" or more like "additional" instead of "total weight". Therefore, my answer for the first question was "also 14 cm". 😅

[@cigmorfil4101]

@@ccmplayer87 For a mathematician, English is also only a second language...

[@Sonny_McMacsson]

Sometimes slight wording changes actually make a different problem. Probability questions' interpretations seem particularly sensitive to wording. More careful reading doesn't always help.

[@BIueCat]

I’m so bad at math that I thought these were the same type of problem. Equally easy.

[@Vertraic]

Both questions took about 2-5 seconds to answer... Then a minute thinking about them:D The first one was a LITTLE vague, as 'attaining a height' when climbing something frequently refers to the height you are STANDING at rather than how high the top of your head is. (Think mountain climbing) So I thought the issue could be that the first one meant they attained the same height. That is the only reason I doubted my immediate answer.

[@TheDaemonis]

May be it depends on order, but I found the 2nd question easier. Money is what we counting every day :) Not a native speaker though, so word choice may also affect this,

[@gimlarquinn3622]

Yes specially for the words Gain and attain. The one excludes the person's height the other one adds to it.

[@jcsjcs2]

@@gimlarquinn3622 I was struggling with this, so the first question felt more like an English quiz than a math quiz. Luckily my language intuition intuition passed the test.

[@CAPAE]

I answered both questions correctly, but I notably paused on the specific verbiage used in the first question, because, "Attained the height of 14cm," is not the clearest language that can be used and could be reinterpreted as, "Gained the height of the table that stands at 14cm." I caution that some who answered wrong might have answered 14cm, or expressed there was not enough information, because I can imagine some misinterpretations there.

[@ceulgai2817]

I work in adult education, and one thing we're trying to get our instructors to adopt is contextualized instruction (especially in math). In the span of a month, you have given me not one, but two, videos I can show them as to the importance of contextualizing!

[@angelhelp]

As a lifetime struggler with word problems of just about any variety, I will say that solving these might well have taken me an hour. From hours of discussion with friends who are/were (retired now) math teachers, I have finally realized that my particular issues begin with the fact that I simply “don’t speak math”, meaning that I have no idea how to translate a sentence or phrase into an equation or a part thereof. During my school years, I always felt that every math teacher pulled numbers out of the air at lightning speed by creating equations that made no sense to me. While I was occupied trying to determine the source of these numbers and/or equations, the teacher would finish the problem at a similar pace and continue to the next one. I suspect that my slow translation speed was my biggest hindrance, but here’s another. When introduced to the idea of having a letter represent a number, usually the letter was n. When there were no other variables, I could accept that n could be used, but include another variable and I immediately needed to convert everything to x, y, and z. Even now, I will still convert variables to x, y, and z if I see a problem using other letters. Height wouldn’t ever be expressed as h; instead, I’d call it x, y, or z and write the word “height” to the side. Throughout my school years, teachers’ penmanship often required that I rename variables, and my own penmanship becomes more difficult to decipher when I must write rapidly. Lastly, the individual sentences providing information in both problems here were physically so close together that I found it difficult to consider each sentence separately. I would need to doublespace them in order to avoid accidentally misreading something, as well as to give me time to process each sentence. Reading each sentence s-l-o-w-l-y and drawing/updating a diagram would have helped. My problem isn’t with reading per se, given that I could read both words and music well before I was school age. Barring careless errors, I could work the equations that encountered in school and obtain the correct answer(s). Setting up an equation was far more difficult. Given the two problems in the video, I instinctively knew that the first one contained sufficient information to be solved. I suspected that the second one could also be solved, yet it indeed seemed more vague than the first. As a side note, I taught preK - 8 music in school for eighteen years. My own difficulties with word problems turned me into a math diagnostician for the students having their own math issues. Occasionally I’d encounter a student whose math skills were well beyond grade level but the classroom teacher hadn’t yet discovered this.

[@michaelzumpano7318]

Oh, that was just wonderful! Thanks again, Presh.

[@cmilkau]

In German math exams, they're still using the term "2 times more". Idk why it's not used in every day language anymore and it's not obvious whether it means "twice as much" or "three times as much". Also neither is actually "more" if the amount is negative.

[@RockOfLions]

The first problem took slightly longer than it did for PT to read the problem because of the odd phrasing of 'attains a height'. But the second problem took a little bit longer since it involved not only 14-2 but 14-r+r-2. They were not strictly isomorphic even though they both come down to 14-2=12.

[@twinturbostang]

Context is important. When given the questions in this scenario, it's easy for someone to think they are trick questions, or somehow more difficult than they really are. That can fool people into thinking the answer they arrived at is not correct.

[@Macieks300]

The first problem is ambiguous and there is no clear answer. The problem is that it's unclear if attaining some height includes your own height or not. I could see it going both ways depending on a definition. For example if I say I jumped up from the ground for 20 cm I don't include my own height.

[@tmhchacham]

Same. I automatically assumed "attains" meant he grew, which was confirmed by saying he was a "certain" height beforehand. Considering we do not know how much he grew, or whether the extra height was added, multiplied, or whatever magic was in play, the question is unsolvable. The second question was simple math, considering they bought the same notebook, and we know one item cost 2 less than the other.

[@quentind1924]

Well both gives the same result so no phrasing problems here

[@Macieks300]

@@quentind1924 They give different answers though. One gives you the answer 14 and the other 12.

[@quentind1924]

@@Macieks300 Oh yeah true i missunderstood your message

[@MezzoForteAural]

I agree. Context matters a lot in word problems. In the context of asking these questions as is, it would be safe to assume they are trick questions and you should view them as such. With that in mind HUGE red flags pop out. For example does Slouchy slouch? Another is that the exact wording is "He" climbs onto the table, but you are asked the height of Grouchy relative to Slouchy, so you would have no accurate height reference. Etc...

[@WRSomsky]

I don't see how one is cardinal and the other is ordinal. I'm trained as a physicist. Both are quantities, ie a dimensionless measure x a unit. Either can be ordered (is taller, costs more). In *theory* heights are usually considered continuous (no, we're not quantizing at the plank scale), while prices usually don't use fractional cents so are discrete, but that doesn't seem to be a significant difference in my mind.

[@tookitogo]

100% agree. I would in no way consider quantities to be “ordinal”. To me, cardinal means “1, 2, 3, …” while ordinal means “first, second, third, …”. I certainly don’t think the Smurf’s head was at “the 14th centimeter”!

[@TCTGFAM]

I thought in the description of the second problem that "the same notebook" was the exact same notebook, so if the other person bought it first, it would be impossible for her to buy it 😂

[@danielderoudilhes4413]

You'r right.

[@jcsjcs2]

That probably explains why very intelligent people failed so often. They recognized that this must be a trick question...

[@HeavyMetalMouse]

For reference: Maths 'expert' here (professional tutor of Maths at levels up to college levels) When presented with the issues, the only hesitation I felt was wondering if there was some sort of 'trick question' going on that made such a straight-forward appearing question not as it would appear. I was more likely to second-guess this with the first question than the second: the language of 'attaining a height' might have been ambiguous, for example; I ultimately concluded there was no apparent wordplay or trickery involved. I was surprised to find that the results showed people having more trouble with the second problem. The second problem's wording, to my mind, lent itself most readily to a strict algebraic translation, leading to a straightforward solution, while the first problem's wording invited a drawn diagram to translate the statements into mathematical language. This, the video then confirms this natural connection... but then, counterintuitively, implies that more errors were made in the version of the problem with a straightforward algebraic translation. The ordinality/cardinality issue was not the primary distinction in my mind, but rather the 'visualization' of the problem as translated into mathematical objects (diagrams and equations). For typical adults, I suppose I can see how problems with a direct algebraic translation would be missed more often - there are a lot of people who have difficulty with symbolic manipulation and such, to the point of some even taking pride in 'never needing to use algebra in daily life'. However, I would have expected experts to have the opposite bias, as experts work extremely often with algebraic manipulation and wouldn't find it unnatural or foreign. Very strange results indeed.

[@RealNaine]

There are more reasons these problems may seem trickier to some people, and they're all related to the wording. Personally I was on the fence about the second one possibly having a "not enough information" answer, but not because of the cardinal number distinction. For the first problem, the question line might be interpreted as "how much is added to Grouchy's height". I found the wording a bit strange and wondered if it could have been intended to mean that. However, comparing the wording in the question to the third line makes it clear that is not the case, and that to attain a height of X means that the total height becomes X. For the second problem, the meaning of "the same notebook" is not obvious. This could mean the same type of notebook at the same price, in which case the answer is $12, or it could mean the exact notebook that Anthony already bought (or wants to buy), which may now be unavailable. Note the question also only states that she WANTS TO buy the notebook, not that she WILL buy the notebook, but it asks how much she WILL have to pay. Depending on whether or not she is able to get the notebook, she may have to pay $12, or may have to pay an unknown lesser amount (since we don't know the notebook price), so there is not enough information to answer with this interpretation of the question.

[@professorsogol5824]

Your right. In the first statement, the semantics is consistent but in the second it is not.

[@yurenchu]

​@@professorsogol5824 "the semantics is consistent" -- O, the irony. My left.

[@aaronbredon2948]

I think of both height and price as real numbers (price is rational numbers, which is a subset). Both are numbers that are not integers - they may contain intermediate values. I also separate out units if everything is in the same unit. And thus I see 2 homologous problems. Both have an unknown value (table, notebook) in all parts of the equation. This unknown value can be ignored as it has no effect on the answer. This is part of solving word problems - convert to equation with variables and units, then solve normally.

[@wj11jam78]

I think about all numbers on a number line, of sorts. I don't really know how to explain it, but when I'm counting, I sort of "fill up a bar". The bar fills up at 9, and so when I count past 9 I make a new bar which stores the next place (so the new bar is filled by 1, the first bar is filled by 0, to make 10). When I need to use binary, my mental model adjusts to that base. And hex, too. So in hex, my first bar fills up until its at F, and then I start a new bar. Then that bar fills until both bars are at FF, then I start a new one again. This is just how I naturally count. I don't intentionally imagine actual bars filling up, I just kinda... see it? And feel it?

[@scarletevans4474]

First problem (ordinals) was actually MORE DIFFICULT for me :D Like you said, semantics matters and some people (especially non-native speakers) can mistake "attain" with "gain", resulting in there being not enough information. For example, if Grouchy's height was to be 3 cm and he stood on 9cm table, he would attain height of 12 cm. But, the same can be true for 4cm+8cm, Xcm and (12-X)cm, etc. So, we know what height he attained, but don't know how much of that height he gained, which without reading the question carefully one can misunderstand what the question is about. So, I think it's more about what we are asked to do, instead of using Smurfs and other entities 🙂Do we know, if the results of the research weren't manipulated by some cheesy wordings like these?

[@Metal_Master_YT]

same issue here xD

[@mrosskne]

It's not even any being a native speaker, the problems are worded in a way that no human speaks. Nobody says "attain a height". It should say, "grouchy's height plus the table's height is 14 cm".

[@tcfonts]

I'm a bit confused. Grouchy Smurf's height doesn't change by climbing on a table. He would be the same height no matter how high up he was.

[@Macieks300]

Yeah, the wording in that problem is ambiguous on many levels.

[@Draddar]

How does that change the answer?

[@thomaspickin9376]

When they say "What height does Grouchy smuf attain", 'attain' is just another way of saying 'reach' or 'get to', for example if you were climbing a mountain and said "We got to a height of 10,000ft" you wouldn't mean everyone in the party grew to 10,000ft, you'd just be describing how high up you were.

[@Draddar]

@@thomaspickin9376 Clearly not what the original post is unclear about

[@likebot.]

@tcfonts That's exactly how I saw the question. I didn't assume they meant the top of their heads were 14 and 12 cm above the floor after climbing the table, but that is how tall they were from scalp to heel. I saw no question other than what is 14-2. But apparently this question infers that Smurfs are not actually three apples, but only 1 apple tall!

[@joshuakb2]

The first question was intuitive to me. I didn't recognize that the second question was equivalent to the first, so I had to write it down and evaluate it algebraically, and then it became clear

[@JohnR31415]

What if smurfs stand on the underside of tables… (Certain assumptions have to be made in word problems)

[@NorfolkCatKickers]

The only problem was when the said climbs on a table and attains a height of 14cm, this height could mean how tall he is(which doesnt change) or how high up he is measuring from feet, or high up the top of his head is.

[@tszheileung4410]

Me overthinking the question and got the question wrong because I thought it’s a trick question

[@jasonpatterson9821]

The first problem took me more time, but honestly, it was mostly spent going over it again and again because the answers seemed so obvious that I thought I had missed some sort of trick phrasing.

[@piguy314159]

For Q1 there’s not enough information: how do we know Smurf tables are level with the ground?

[@Yusso]

By that logic you can also argue that we don't know that the store did not change their prices.

[@cheweh842]

I did not understand that "attains" meant an operation of "+x cm" in the context of climbing on a table. I thought it meant an operation which transformed height Slouchy into 14cm, with no indication if it is a constant function, so not enough information to determine the result of this operation on height (Slouchy - 2 cm). i.e. I interpreted that Slouchy's body changed due to some magical property of the table.

[@zzstoner]

Honestly, for the first question, it was confusing to understand the frame of reference of "height" as he climbs up onto the table. In other words, was the 14cm relative to the "top of his head", or was it "the amount of elevation gained"

[@Qermaq]

I found the first one marginally harder. So there you go. Welcome to Outlier Land, population me.

[@MatthewMorris6148]

I’m here too! Mainly due to the fact that I was overthinking it. And wondering if the “attained height” included their own height or not.

[@trajectoryunown]

It helps to remove all the unnecessary words first, leaving only pertinent data points. When rephrased, question 1 is: "Slouchy with table is 14cm tall. Grouchy is 2cm shorter. Both are on the same table." You can't logically remove the table as the only defined number is tied to that variable. So simple that converting it to an equation would only complicate the matter. Though, for this particular problem, it doesn't matter. Question 2 is: "A notebook with a ruler costs $14. The same notebook with eraser cost $2 less." Once again, the only seemingly complicated part can be cancelled out which only makes the problem that much easier to solve as it requires less thought. Question 1: Table's height + Slouchy's height = 14cm Table height + Slouchy's height -2cm = Grouchy's height Question 2: cost of notebook + cost of ruler = $14 cost notebook - cost of eraser = $2 (Typing out the equations took about 2-3x the amount of time that typing the explanation did. >.>) Edit: Skipped ahead, and holy crap y'all over-complicate numbers so much. A number is a number, a unit of logic. Why are you associating the data with objects? Who does that? These are almost exactly the same problem. Only difference is the first question subtracts from the total and the latter subtracts from one of the variables.

[@Kay-ql2wl]

The first question was rather confusing because height could mean - distance from ground measured at top of object - distance from ground measured at bottom of object -distance from bottom of object to top of object All options have good arguments to be made for them

[@davidgagen9856]

Table + Slouchy = 14 Table + Grouchy = 12 No different to Notebook + ruler = 14 Notebook + eraser = 12 The concept is the same even if you want to use different mathematical descriptors.

[@Metheglyn]

The problem is, that even though the problems are congruent, their representation in peoples' mind might be affected by a difference in perceived abstractness. In the first case, the difference in height might be represented as "Slouchy is 14 cm. Grouchy is 2 shorter. That is 14, and then we take 2 away. That's the top one, and the next one. 14 - 1 -1. That's 12", while the other one might be more like "Book plus ruler is 14. Book plus eraser is 2 less. So we take 2 away... Hmm which one to pick first ... this one? No, wait, what if that one is for the notebook, no, wait, that doesn't make sense, it doesn't matter, if it's from the book or the ruler, you pay them together. So, let's just take this one. And then another one. Wait, is this one from the, no, wait, we already cleared this; just pick one. And now there are ... a bunch of coins. 1...2...3... Wait, this takes too long. But we know there were 14, and now there are 2 less, so that must be 14-2=12. But if you instead imagined the coins as stacked, it would make it easier. That would be equivalent to converting the cardinals into ordinals.

[@toomanyhobbies2011]

I met a lot of experts that struggled with word problems, and some of them were engineers. The main problem was memorization, they'd been taught to memorize certain patterns and language, so couldn't go beyond that. They really couldn't abstract well at all. And, as in your first example, they couldn't extract the meaningful information.

[@Hikarizu]

I read "What height does Grouchy Smurf attain when he climbs on the table" as "How much height he gains by climbing on the table" not "what is his total height". When I read the second question I noticed it's the same and went back to check the exact wording.

[@ObviousSchism]

The hardest part about both of these problems is understanding the title of the video.

[@josephcarland]

I like the fact that he calls these word problem and not maths problem. I seen to many people calling these maths problem.

[@Marc-gj9vx]

I dont think it has anything to do with ordinal or cardinal. I think its just extremely poor wording of the questions. In the first one it's unclear what "attained a height" meant. Was it from up to their feet or to their head? On the second question it's unclear if the first person actually bought all the items he wanted, or if he just wanted items but didn't purchase them. Other than the poor wording, i didn't find any of the question more complicated than the other and could get to 12 for both..

[@RedsoxNets5]

I got an 800 on the math portion of the SAT. First question was very easy, and second question seemed to pretty clearly be unanswerable. Rather than write variables down to confirm this, I felt confident enough to say "it doesn't matter what other info I'm given, we don't have the value of any of these 3 items except for how they relate to each other." It's definitely possible that my belief in my ability led me to be overconfident with saying the second problem was unsolvable! I also might just suck at math now given I took the SAT 14 years ago 😂

[@kmbbmj5857]

Basically the study confirmed my belief that the trouble with word problems is the word and not the math. Mathematically I had no problem with either. These are really grammar and composition problems more than math problems. Add in the fact that most of us have been subjected to so many trick questions over the years, we suspect any word problem of being a trick question and look for the "trick." In this case I, like many others, wondered if "attain" meant how tall the individual Smurfs were OR the height they were above the ground. I was actually expecting the big "GOTCHA" reveal to say they attained the same height -- that of the table.

[@joeldoxtator9804]

The biggest problem i have found with higher education levels is that it can make you overthink simple problems. For example, with the cardinal number problem, my immediate reaction was to go to algebra and find the values of the ruler and textbook in expressions of ruler cost. So, ruler cost + total cost - ruler cost = total cost. Unfortunately you very quickly realize that there is not enough info to do this forcing you to step back, take a breath and simplify. Then you see it is just the general totals with a difference of two. I think over training can make us see equations in simple arithmetic that are not there.

[@Jenesuispasungeek]

Surprisingly, it was the otherway around for me. I am French. The second question was easy, the first, I had some difficulties to understand the problem. Maybe I should here that in French. And As I understood, you are mentionning Ecole Normal Supérieur, wich is a French scool. Thank you for sharing.

[@ArabianShark]

I'm absolutely flabbergasted. I'm ready to throw the validity of that paper into question. I'm no manner of expert (I mean, I'm an engineer; it's not like I'm mathematically illiterate, but I'm not a mathematician), and I solved those problems with equal ease in my head.

[@hans-joergwahmkow2621]

Both were extremly simple and easy to solve. Couldn't say one was more difficult than the other.

[@s888r]

Option A for both. 1. Question too easy, so the table's legs are cut by an unknown amount before Grouchy Smurf climbs it. 2. Question too easy, so seller charges different for different customers for the same thing.

[@33LB]

i found the question about the notebook and ruler to be the easiest, but that's probably because it was worded using sensible every-day objects. the issue i had with the smurf question was that the wording about a smurf attaining a height after standing on a table threw me off just a little bit... your height is the same regardless of whether or not you are standing on a table.

[@programaths]

We also classify questions in narrative and non-narrative, in how they present chronology and the action verb. In the later years, non-narrative questions are more present, and narrative questions have red herring. So, in the first years, the question tells you what to do. In the later years, the question tells you to do the wrong thing. ^^ First year: Mary has two marbles and gives one to Joe. Joe adds this new marble to his collection of 15 marbles. How many marbles does Joe have ? Last year,: Joe received 2 marbles from Mary and 3 marbles from Jane. Mary had 4 marbles, and Jane had 5 marbles. Now Joe has 6 marbles. How many marbles did Joe have at the beginning? You can see that the second question is much harder.

[@jaybingham3711]

Maybe in part, but it wasn't really about ordinals. I think the bulk of the issue with P2 was confused language. Worse, the word problem was (likely) carefully and deliberately constructed to confuse. This was less about mathematics and more about how problematic nonspecific and/or leading assertions of "facts" can be used to obfuscate and/or avoid responsibility. P2 leveraged a misdirect involving Julie's purchase. The strategic placement regarding her buying an eraser (rather than a ruler) is immediately followed by "How much will Julie have to pay?" And there's the misdirect. A linguistic slight of hand if you will. Pay for what exactly? It's both valid and reasonable that the question asked was with respect to just the cost of the eraser. Especially upon reviewing key missing words in the closing question: "in total." Since those words were used earlier for Anthony's purchase of the same notebook and a ruler, their absence can be relied upon to assert that the question was specifically designed to see if you could suss out that detail and realize it could only be the price of the eraser that was being asked about. Barring that, the question is decidedly ambiguous. There simply are no valid grounds upon which to assume the question meant to inquire about the total price.

[@Electronics4Guitar]

These examples are fairly trivial word problems that anyone that has passed algebra I should solve easily.

[@jeremiahedwards2073]

This is engaging! The question, "What height does Grouchy Smurf attain?" is utterly ambiguous! It could mean either, "How tall is Grouchy Smurf?" Or, it could mean, "How tall is Grouchy Smurf and the table when added together?" This is precisely why so many do poorly in math and why so many hate it. Mathematicians don't understand the English language. Shame on whoever created and wrote this problem. They should take a basic philosophy/critical thinking course. Shame. Sad. The world is worse off and we will all suffer more for this.

[@Erlewyn]

So math has a very specific definition of ordinal/cardinal, different than the common meaning? Because the first question is asking for cardinal numbers, there's no ordering here, it's a quantity of cm.

[@qwerftseattle]

When one climbs 14 units the distance climbed is generally measured between as the distance between their ground levels, not ground levels plus climber height, so I think Q1 is B 14

[@yatharthsikaria5931]

July in total will need to pay ₹26.

[@budgetarms]

The smurfs question was harder for me to answer to be sure because of the attain height was vague to me. The money question was weird because it said, "He also wants a notebook. In total, that will cost him 14 dollars.", "that" was confusing since it did not say he would buy the notebook too, since I would expect it to be "these". The word choices are indeed very important, because some people really want to be sure they understand everything correctly.

[@alexanderklimke6508]

Surprising! I am not a native english speaker. Question 2 does not contain any difficulty, the solution is obvious without eben calculating. Question 1 was hard for me. I neither knew the words "slouchy", nor "smurf" nor "grouchy", could not imagine what a "smurf table" could be, was not sure of the meaning of "attain" in this sense and therfore did not know, wether this was a real math problem or a joke question I had not understood. I just saw the 14 and the "2cm shorter" and thought "14-2 is 12", but I was unsure if I even understood the problem correctly.

[@jackulousb6336]

At first i Thought that the smurf's height was a fixed constant and that the table was an addition to that constant. since the table's height was not given I wasn't able to solve it. but I was easily able to solve the next one because of the sentence "In total, THAT will cost him" the THAT indicates grammatically that it is one thing he is purchasing, where as "attain" in the first problem can be defined as gaining, hence an addition to a constant value. on top of that it states that slouchy smurf has a certain height at the beginning of the question, one assumed to be different to the height + the table.

[@adventureboy444]

I didn't able to solve the second problem because I read it as "The eraser costs 2 dollars less than the notebook"

[@deerh2o]

This really is not all that surprising, but I think there is a fourth takeaway: How many mathematical concepts are taught is that they are taught in isolation. For those of us who enjoy math and do enough math problems, we start creating these connections between what have heretofore been isolated concepts. Even some "experts" don't always make those connections.