Sure. But 96% of people missing that? Seems high.
How many people work with square feet and square yards on a regular basis? I’d bet for a lot of people, the last time was in a math class in highschool.
Does it really seem high? Think of the percentage of people in this thread who missed the fact that 4% refers to the number of people who got this problem and another problem correct.
It’s really easy to miss things like that, even for people who are very, very good at reading.
Personally I doubt the correlation between intelligence and literacy. For thousands of years, most people couldn’t read. I think most intelligent people are literate simply because most people are literate. If you have an intelligence test that requires or relies on literacy, the test is fundamentally flawed.
~Max
I work with lots of people who have engineering degrees. Yet it wouldn’t surprise me if many of them couldn’t pass the “carpet cost” test. And I have no idea why. Like me, they had to have taken algebra, trig, calculus, statistics, etc. Yet many I work with wouldn’t be able to calculate the slope of a line given two points on the line. I can’t explain it.
I was pretty confident that ChatGPT would get the carpet problem right, and it did:
To compute the total cost of carpeting your living room floor, you’ll first need to determine the total square footage of the room and then convert it to square yards to match the pricing unit.
Calculate the square footage of your living room:
Living room dimensions: 9 feet by 12 feet
Total square footage = 9 feet * 12 feet = 108 square feetConvert square footage to square yards (1 square yard = 9 square feet):
Total square yards = 108 square feet / 9 square feet/square yard = 12 square yardsNow, you know you need 12 square yards of carpet.
The price per square yard of Dupont Stainmaster carpet is $9.49.
Calculate the total cost:
Total cost = Price per square yard * Total square yards
Total cost = $9.49/square yard * 12 square yards = $113.88So, the total cost of exactly enough carpet to cover your living room floor is $113.88.
It immediately saw the need to convert the floor size to square yards. I wish I knew what the credit card problem was, as I’m pretty sure it would get that, too. Which, according the claim cited in the OP, would put it within the 96th percentile of human capabilities on those questions.
Very cute. The answer is “5” only if you express the appropriate surprise: 5! 
ChatGPT bristles at the joke and finds it unfunny. I accused it of being humourless and nitpicky: 
5! (5 factorial) is equal to 5 × 4 × 3 × 2 × 1, which equals 120.
As we calculated earlier, the result of the expression “230 - 220 ÷ 2” is also 120. So, in this particular case, they happen to be the same value, but it’s important to note that the result of the expression is 120, not 5!.
In other places, the book makes a lot of qualified correlations between language skills and general intelligence. After discussing various definitions (and problems and debates with such), it quotes many recent studies using functional imaging, such as fMRIs, which measure very quick changes in blood flow, as a proxy for brain activity. More brain activity often is not a positive; though highly dependent on area, efficient brains using less glucose often seem to solve problems better.
In any case, some good studies suggest actively reading to children under four may significantly boost intelligence, and smart women (more than smart men) often have relatively larger amounts of blood going to areas involved in language processing. Though nothing in brain science is easy or straightforward, a link between literacy and intelligence is very reasonable though intelligence does take a multitude of other forms. (Listening to Mozart or playing computer games do not show much benefit when testing aspects of intelligence not closely related to the specific training.)
I agree with you, though, that many good tests do not involve literacy as such.
You can find them here: National Assessment of Adult Literacy (NAAL) - Sample Questions Search: 1985, 1992 & 2003
The credit card question is probably N110901 (34.9% answered correctly) and the earlier carpet question is N091001 (17.6% answered correctly). At least, those questions match the descriptions provided and the combined success rate is around 4%-ish.
Thanks for the link. It’s interesting to see the actual questions, and also the percentage who got them right, and how that 4% was arrived at. The very low 17.6% who answered the trivial carpet question correctly is rather incredible. I suspect most that got it wrong were tripped up.
Here’s a direct link:
https://nces.ed.gov/NAAL/sample_question.asp
The credit card question was a challenge in terms of how to present it to ChatGPT because of the big tables involved, whose formatting got very messy. Yet, amazingly, ChatGPT was able to sort out the badly formatted mess and make sense of it and answer the question. So it’s now confirmed to be in the 96th percentile of humans, according to the criteria in the OP.
The question was “Banks that issue credit cards are organized into two categories in the table below. List the two categories. Using the information given in the table, describe two differences between these two categories.”
ChatGPT response:
The two categories of banks that issue credit cards in the table are:
- BEST DEALS FOR PEOPLE WHO CARRY BALANCES
- BEST DEALS FOR PEOPLE WHO PAY OFF ENTIRE BALANCE MONTHLY
Two key differences between these two categories are:
- Interest Rates:
- In the “BEST DEALS FOR PEOPLE WHO CARRY BALANCES” category, the interest rates range from 10.92% to 13.75%. These interest rates are relatively lower, which can be advantageous for individuals who tend to carry a balance on their credit cards and accrue interest charges.
- In the “BEST DEALS FOR PEOPLE WHO PAY OFF ENTIRE BALANCE MONTHLY” category, the interest rates are higher, ranging from 17.90% to 19.80%. These rates are less relevant to individuals who pay off their credit card balances in full each month because they don’t carry a balance and therefore don’t incur interest charges.
- Annual Fees and Interest-Free Days:
- In the “BEST DEALS FOR PEOPLE WHO CARRY BALANCES” category, the annual fees range from $15 to $30. However, there are no interest-free days provided, meaning that interest begins accruing immediately on new purchases.
- In the “BEST DEALS FOR PEOPLE WHO PAY OFF ENTIRE BALANCE MONTHLY” category, the credit cards generally have no annual fees, which is an advantage for those who pay off their entire balance each month. Additionally, these cards offer interest-free days, ranging from 25 days to 30 days, giving cardholders more time to pay off their balances without incurring interest charges.
These differences reflect the pricing and features of credit cards designed for individuals with different financial behaviors and preferences. Those who carry a balance may prioritize lower interest rates, while those who pay off their balances monthly may prioritize no annual fees and interest-free days.
I bet ChatGPT can’t manage this one, despite 99% of humans succeeding:
This is a good point (only 1/3 of people getting the credit card question is very significant), but incomplete, assuming independent variables. In practice the same people who correctly answer the perceived hardest question are also more likely to get the perceived second hardest question. If 1/3 of people get one question and 1/6 of people another one, up to 1/6 of people might get them both. If both questions were chess puzzles, a grandmaster would be likelier to get them both than I would. Research suggests pretty high correlations (often 0.76 - 0.93) between different purported factors of general intelligence.
Oh, right. Independent variables. The combined success rate isn’t that 6%~ but likely close to that 17%.
At least I managed to sign my SIN card.
Likewise, ChatGPT also can’t pull your finger, but 99% of people may deem this a good idea.
Allow me a cynical counter-point.
An important component of one’s intelligence/literacy is The BS Meter. Which allows us to say “I’ll be paying the carpet company to figure out exactly how many yards/meters they need to charge me for.” and “My insurance broker will be able to show me the differences between benefits.”
The top 4% will also say “I don’t care what Un Neuroscientifique Français says about numerical cognition…”
Well, even the things you mention don’t necessarily require literacy. Maybe the specific tests they use involve literacy but language does not require literacy. For thousands of years, people spoke without writing. I mean, reading stories to children boosting intelligence, that just throws a big red flag. That’s claiming not only correlation but causation. Why would it matter if the story is read, as opposed to just told?
~Max
Here’s how I got there, no calculator.
My room is 9ft x 12ft, or 3 yards x 4 yards which equals 12 square yards.
If the carpet had cost $10 per square yard, the cost would be $120.
But the carpet is .51 per square yard less than that. If I knock .50 each off 12 yards, that’s $6 off the total, which brings me to $114. Then I knock off the extra penny per yard, or .12 , which brings it to 113.88.
I found this pretty easy. I can do most practical math like this without a calculator, I just have to find the right approach.
Apropos of nothing, I just watched an episode of Colombo where he had to convert from square feet to square yards.
~Max
Knowing how to solve the problem – recognizing the form of the solution process in the problem as presented – is the true mathematical literacy.