How much do you understand this math question?

[Forest Cat]

Has anybody noticed that this is much less a math problem, and much more a language problem, in which people fail to apply the literal meaning of the phrase "more than"?

As I mentioned, this is a standard question in certain types of research. It has been asked of math majors in universities. They answer correctly only slightly more often than average.

Yeah the word "more" is very important here. 1 dollar more than.

 

[TBRS1]

Yeah the word "more" is very important here. 1 dollar more than.

Yup.

If the question was phrased as:

The bat costs $1, and the ball costs $0.10, how much more did the bat cost? Most people would answer $0.90. This is first grade math.

The phrasing of the question makes it tricky.

 

[Hypnalis]

Has anybody noticed that this is much less a math problem, and much more a language problem, in which people fail to apply the literal meaning of the phrase "more than"?

As I mentioned, this is a standard question in certain types of research. It has been asked of math majors in universities. They answer correctly only slightly more often than average.

If you're thinking of the trick where people don't convert to proportions (percentages) from Verisatium - that one can fool math majors if they're drunk, otherwise not.

A math guy will not miss simultaneous equations with as many equations as variables - they learn the methods for don't this with multiple dimensions as teenagers.

OTOH math guys aren't necessarily good at mental arithmetic.

 

[stevens]

I just want to know where you can buy a bat for 1 dollar. Mine cost 60 dollars. Can't buy a bat for 1 dollar, or a ball for 10 cents, I say all this is completely wrong. It's a trick question.

Now that's exactly the way my autism kicks in. Somebody would present me the problem, and then I'd hold forth for 15 minutes about the statistical unlikelihood of the transaction being possible citing data from the Bureau of Labor Statistics and the St. Louis Federal Reserve. I'd have to stop after the 15 minutes, because the questioner would either fall asleep or walk away. Now that is the real test for autism.

 

[Misty Avich]

I asked a colleague at work this math question and he answered it the "autistic" way straight away, even though he's 100% NT. He's not very detail orientated at all, yet seemed to know how the question should be answered. But he's in his 70s, so maybe a bit of experience can help too, as he's been on this planet a very long time so has probably heard it all.

 

[Hypnalis]

That's not the equation, though. It's 1.00 + 0.10 = 1.10,...or 1.10 - 1.00 = 0.10.

In your scenario:

A
Ball = 10
Bat + Ball = 110

Clearly possible.. and in this case, Bat = 100.

B
But there's a problem: it does not satisfy the condition:
Bat = Ball + 100
If Ball = 10, and we apply the condition Bat = Ball + 100 ...
then Bat = 110, and Bat + Ball = 120,, which contradicts A.

C
Clearly Ball = 5 works.

IIRC all of the answers that calculated 5 used a valid method.
One of mine goes through the calculation steps in more detail.

The proof that 5 is the unique answer isn't difficult but it's almost always the case (and is so here) that the proof is harder to understand than the problem, so just trust me on this

 

[Neonatal RRT]

Bat ($1.00) + ball ($0.10) = $1.10 with the bat being $1.00 more than the ball. False. If the ball was $0.10 and the bat were a $1.00 more, then the bat would be worth $1.10 and the total would be $1.20.
Bat ($1.05) + ball ($0.05) = $1.10 with the bat being $1.00 more than the ball. Correct.

EDIT: Ahah! OK, the lightbulb just went on.

 

[Hypnalis]

I asked a colleague at work this math question and he answered it the "autistic" way straight away, even though he's 100% NT. He's not very detail orientated at all, yet seemed to know how the question should be answered. But he's in his 70s, so maybe a bit of experience can help too, as he's been on this planet a very long time so has probably heard it all.

This isn't about NT/ND. It's about one minor aspect of abstract thought.

The trick is much less difficult than some of the abstract thinking tools used in language that "Aspies" have but some ASDs do not.

I don't like this question as an NT test, because the wording tempts people to make the wrong choice. Some people (not all) will miss the fact that to resolve the wording you have to switch to a math/logic approach.


Something to think about: when I was studying, the local match company put puzzles on their matchboxes.
I was the guy who could always solve them fast, so I'd get the ones everyone else failed on.
Most were like this: simple, but crafted to require a way of addressing the problem that's not natural to the way our brains work.

So the only ASD in the group was both fastest and best with difficult puzzles.
The math question does test something, but it's not an NT/ND difference.

 

[Hypnalis]

Bat ($1.00) + ball ($0.10) = $1.10 with the bat being $1.00 more than the ball. False. If the ball was $0.10 and the bat were a $1.00 more, then the bat would be worth $1.10 and the total would be $1.20.
Bat ($1.05) + ball ($0.05) = $1.10 with the bat being $1.00 more than the ball. Correct.

EDIT: Ahah! OK, the lightbulb just went on.

You'll be happy to hear that you won't have to learn this twice.

Just think "The problem sets two conditions that must both be true". That makes it easy to unwrap the wording, and easy to check your answers if it "seemed too simple".

 

[TBRS1]

I just read the question, recognize it's a trick, answer incorrectly, check the math and catch the trick, then provide the correct answer.

In IQ tests, this makes me look smart. And it's faster than actually thinking.

 

[Misty Avich]

When I first read the question I immediately answered 10, not really thinking of any reason the question might mean anything else. I thought it was one of those stupid questions like you get on Facebook that says if you answer a question correctly it means your IQ is really high even though anyone who can read and are over the age of 10 can get it. But then I read the article and got frustrated because I was like "but how can it have any other answers?" and I began thinking "so maybe math has been a lie my whole life, or am I getting dementia?"
Then I created this thread, and when Cutesie emphasized the word "more" it began making a bit more sense, though I was still baffled. Then I got it in the end.
My mind doesn't like numbers, it only likes words and letters (unless it's algebra, then my mind interprets it as math and shuts down).

 

[Hypnalis]

There's another math question that a lot of math students get wrong: it's called the "Monty Hall Problem".

When I first saw it, I assumed that the decision maker ("Monty Hall") would deliberately choose in the way that would be worse for the contestant. This is because as an Aspie, I'm very aware of how frequently people act in a way that benefits them at the expense of others, then "sell" it as being in their targets' best interests.

That assumption makes the problem impossible to solve. It took me a long time to realize that there was an unstated assumption of "fair play" in the problem /lol.

(BTW even with the correct assumptions, a lot of people get it wrong. I can explain how it works, but ask at your own risk

 

[Cryptid]

If a bat and ball cost $1.10 in total, and the bat is $1 more than the ball, how much would the ball cost?

Five cents.

$1.10 = ($1.00 + x) +x
$1.10 = $1.00 + 2x
$1.10 - $1.00 = 2x
$0.10 = 2x
$0.05 = x

The only thing I find surprising about this is that a baseball and bat would cost ONLY $1.10 -- the creators of this "test" might want to update their numbers to comply with 21st century economics.

 

[Hypnalis]

I just read the question, recognize it's a trick, answer incorrectly, check the math and catch the trick, then provide the correct answer.

In IQ tests, this makes me look smart. And it's faster than actually thinking.

I do this too, and not just in tests. It's very time-efficient.

I suspect (but can't support with data) that successive approximation, starting with a simple one, is an evolved behavior - i.e. was used long before writing and mathematics were discovered.

Not quite synchronized with pre-literate societies, but imagine someone learning how to shoot a moving target from a moving horse - it's difficult, but many people who couldn't read or calculate have learned to do it.

The math is fairly simple ... if you have a calculator with a Sine function. It's very difficult to do it mentally though, and anyway you need to know how fast both objects are moving, and their relative directions.

Yet for someone with the right skills and experience, doing it "by eye" is possible in a few seconds .
And almost anyone can learn to do that kind of thing (it comes up in many situations that don't require moving animals

So my theory nets out to: we have an innate capability to do rapid approximations that usually produce "good enough" results, and that capability includes improving the approximation process through practical experience.

So my theory implies that we have a natural cognitive bias to prefer that approach to the way mathematics does things. And OFC that bias can be (and is) used to trick people via sneaky wording /sigh.

Back on point: IMO it's a shame that schools don't generally teach the "guess and test first" approach you described, because it's never wrong to do it, and you can do it fast.

 

[Crossbreed]

I just want to know where you can buy a bat for 1 dollar. Mine cost 60 dollars. Can't buy a bat for 1 dollar, or a ball for 10 cents, I say all this is completely wrong...

Maybe, it is wiffle ball...?
Wiffle ball - Wikipedia