I don't think the single number really means anything specific, not even if you know exactly what sub-tests were run, and whether the number was obtained from something like the RAPM, which essentially is a different kind of test.
In some cases, questions on IQ tests are there simply because when the test was normed, a particular answer resulted in a higher correlation with academic success (as I understand it), and is therefore regarded as the 'correct' answer (whether it is 'strictly' correct, or not). This has nothing to do with the reality of mental processes.
Your understanding of the meaning of the IQ number seems rather like what I understood it to be in 1970, when I worshiped at the altar of IQ, wished I could have been at Akademgorodok, where the most IQish children in the USSR had gone to study.
I have found that the ability to solve a large number of relatively simple questions in a short time (which many IQ tests more or less test for) bears little relationship to the ability to handle a large, complex, deep problem over a period of months or years. Of course, this _can't_ be tested for in a short session, and so simply isn't. The IQ number is meant to be a proxy measure for the ability to do this, and it clearly fails - viz. Mensa and the preoccupation with tricky trivialities.
In any case, these days it's not so simple... maybe you can squint a bit and say that a bigger number sort of predicts academic success. It definitely isn't an indicator of specific abilities that have cut-off points.
I'd meant to stop here, however I should point to Nobel Prize winner Richard Feynman, who, perhaps through lack of interest or preparation for the content some subtests, scored 124. His abilities were apparently not measured by the test, and he was clearly a genius in the sense that his results in Physics were undeniably super-human.
He was a dominantly visual thinker who formulated the complex symbolism of mathematical physics in terms of visual representations, and was able to derive results in Quantum Field Theory (using his invention 'Feynman Diagrams') without resorting to normal mathematical script. In truth, it seems that he only needed the normal way of writing mathematics in order to communicate to others. There is a video on YouTube in which he floundered as he tried to explain in words how his visual thinking process worked.