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?