"Intelligence" is like obscenity, or art - you know it when you see it. It's such a fluid quality that any attempts to define and measure intelligence tend to deviate from their stated goal.
Take Mensa, for example. Mensa is, famously, a club for people with high intelligence. Mensa tests (and thus, inadvertently, defines) your intelligence with a series of puzzles that assess your skill with wordplay, spatial reasoning, math and logic.
Of course, once you've seen enough of these puzzles in the same context written by the same people, you start to get a feeling for what sort of answer they're looking for. You gain the specialized skill of puzzle solving.
Mensa may contain a large number of intelligent people, but it is, in fact, Puzzle Club.
(Tuesday morning, INT: MH's apartment)
EB: I never thought I'd see the day when I'd have to accuse you of snobbery.
MH: Okay, perhaps I'm being a little harsh there. I'm just saying, like with any other species, we have to worry about overpopulation and the quality and viability of the next generation.
MH: The luxuries of civilization necessarily remove the Darwinian tie between genetic fitness and reproductive success. We really need to find a way to reassociate intelligence with how many kids you're allowed to have.
JH: What you're talking about is essentially eugenics, though. Decide some arbitrary set of conditions, and kill off the family line of everyone who doesn't fit the mold.
MH: Well, not kill them, but... maybe just disadvantage them somehow, for the benefit of society. Like, the government gives you a simple test on math, reading, and logic, and if you fail that, you have to pay a little extra on your taxes or something.
EB: They have that. It's called the lottery.
MH: ...I play the lottery some times.
JH (patronizing): And society thanks you for your contribution.