I have the same experience as you, drossbucket: my rapid answer to (1) was the common incorrect answer, but for (2) and (3) my intuition is well-honed.
A possible reason for this is that the intuitive but incorrect answer in (1) is a decent approximation to the correct answer, whereas the common incorrect answers in (2) and (3) are wildly off the correct answer. For (1) I have to explicitly do a calculation to verify the incorrectness of the rapid answer, whereas in (2) and (3) my understanding of the situation immediately rules out the incorrect answers.
Here are questions which might be similar to (I):
(4a) I booked seats J23 to J29 in a cinema. How many seats have I booked?
(4b) There is a 20m fence in which the fence posts are 2m apart. How many fence posts are there?
(4c) How many numbers are there in this list: 200,201,202,203,204,...,300.
(5) In 24 hours, how many times do the hour-hand and minute-hand of a standard clock overlap?
(6) You are in a race and you just overtake second place. What is your new position in the race?
A possible reason for this is that the intuitive but incorrect answer in (1) is a decent approximation to the correct answer, whereas the common incorrect answers in (2) and (3) are wildly off the correct answer. For (1) I have to explicitly do a calculation to verify the incorrectness of the rapid answer, whereas in (2) and (3) my understanding of the situation immediately rules out the incorrect answers.
I must have missed this comment before, sorry. This is a really interesting point. Just to write it out explicitly,
Now, for both (1) and (3) the wrong answer is off by roughly a factor of two. But I also share your sense that the answer to (3) is ‘wildly off’, whereas the answer to (1) is ‘close enough’.
There are a couple of possible reasons for this. One is that 5 cents and 10 cents both just register as ‘some small change’, whereas 24 days and 47 days feel meaningfully different.
But also, it could be to do with relative size compared to the other numbers that appear in the problem setup. In (1), 5 and 10 are both similarly small compared to 100 and 110. In (3), 24 is small compared to 48, but 47 isn’t.
Or something else. I haven’t thought about this much.
> A Ferrari and a Ford together cost $190,000. The Ferrari costs $100,000 more than the Ford. How much does the Ford cost?
So here we have correct answer: 45000, incorrect answer: 90000
Here the incorrect answer feels somewhat wrong, as the Ford is improbably close in price to the Ferrari. People appeared to do better on this modified problem than the bat and ball, but I haven’t looked into the details.
No need to apologise! I missed your response by even more time...
My instinct is that it is because of the relative size of the numbers, not the absolute size.
It might be an interesting experiment to see how the intuition varies based on the ratio of the total amount to the difference in amounts: “You have two items whose total cost is £1100 and the difference in price is £X. What is the price of the more expensive item?”, where X can be 10p or £1 or £10 or £100 or £500 or £1000.
With X=10p, one possible instinct is ’that means they are basically the same price, so the more expensive item is £550 + 10p = £550.10.
I have the same experience as you, drossbucket: my rapid answer to (1) was the common incorrect answer, but for (2) and (3) my intuition is well-honed.
A possible reason for this is that the intuitive but incorrect answer in (1) is a decent approximation to the correct answer, whereas the common incorrect answers in (2) and (3) are wildly off the correct answer. For (1) I have to explicitly do a calculation to verify the incorrectness of the rapid answer, whereas in (2) and (3) my understanding of the situation immediately rules out the incorrect answers.
Here are questions which might be similar to (I):
(4a) I booked seats J23 to J29 in a cinema. How many seats have I booked?
(4b) There is a 20m fence in which the fence posts are 2m apart. How many fence posts are there?
(4c) How many numbers are there in this list: 200,201,202,203,204,...,300.
(5) In 24 hours, how many times do the hour-hand and minute-hand of a standard clock overlap?
(6) You are in a race and you just overtake second place. What is your new position in the race?
I must have missed this comment before, sorry. This is a really interesting point. Just to write it out explicitly,
(1) correct answer: 5, incorrect answer: 10
(2) correct answer: 5, incorrect answer: 100
(3) correct answer: 47, incorrect answers: 24
Now, for both (1) and (3) the wrong answer is off by roughly a factor of two. But I also share your sense that the answer to (3) is ‘wildly off’, whereas the answer to (1) is ‘close enough’.
There are a couple of possible reasons for this. One is that 5 cents and 10 cents both just register as ‘some small change’, whereas 24 days and 47 days feel meaningfully different.
But also, it could be to do with relative size compared to the other numbers that appear in the problem setup. In (1), 5 and 10 are both similarly small compared to 100 and 110. In (3), 24 is small compared to 48, but 47 isn’t.
Or something else. I haven’t thought about this much.
There’s a variant ‘Ford and Ferrari’ problem that is somewhat related:
> A Ferrari and a Ford together cost $190,000. The Ferrari costs $100,000 more than the Ford. How much does the Ford cost?
So here we have correct answer: 45000, incorrect answer: 90000
Here the incorrect answer feels somewhat wrong, as the Ford is improbably close in price to the Ferrari. People appeared to do better on this modified problem than the bat and ball, but I haven’t looked into the details.
No need to apologise! I missed your response by even more time...
My instinct is that it is because of the relative size of the numbers, not the absolute size.
It might be an interesting experiment to see how the intuition varies based on the ratio of the total amount to the difference in amounts: “You have two items whose total cost is £1100 and the difference in price is £X. What is the price of the more expensive item?”, where X can be 10p or £1 or £10 or £100 or £500 or £1000.
With X=10p, one possible instinct is ’that means they are basically the same price, so the more expensive item is £550 + 10p = £550.10.