But even if you’re coming up with new questions all the time, a child who has experience solving this kind of problem will be at an advantage over a child who has never tried it.
Not only that, but questions can include a lot of implicit assumptions. One example I saw from a test was something along the lines of, "You go to a store. The sign says it's closed for lunch. It's currently 12:55, and you have an appointment at 1:30. What do you do?"
The correct answer was "Wait 10 minutes, then leave if it's not open." But people with lower incomes were disproportionately likely to say you should just walk away and come back some other time. This is because people in low-income neighborhoods have been taught that loitering in an empty lot leads to bad things.
I don't know about IQ tests, but this is certainly not true for the SAT. SAT prep only raises scores by about 30 pts (on the old 1600 pt test), at least according to studies not funded by Kaplan.