Does it show more intelligence to ask questions or to answer them?
Put that way, it seems perfectly obvious to me it's the latter, though in thinking about a complex subject like intelligence that's overly simplistic. It doesn't take any particular intelligence to just ask questions, any damn fool can generate endless lists of questions, and lots of damn fools do. Finding answers, assuming the questions are both answerable and worth answering, is the hard part. But I also think it often takes a fair bit of intelligence to figure out which questions are answerable and/or worth answering. And of course it takes intelligence to ask an intelligent question.
I'm inclined to the view that intelligence is probably not measurable, in the sense that you can't meaningfully reduce it to a single number like an IQ. IQ scores are based on a rather complex mathematical technique called factor analysis that attempts to extract measures of one's skill at verbal, spatial, and mathematical tasks from a fairly large set of answers you provide to carefully crafted questions, then tries to combine them into a single number. I score well on IQ tests because I'm pretty good at certain tasks this culture, or at least the people in it who make up IQ tests, thinks are valuable. I outscore my wife by 20 points, mostly because she has no aptitude for mathematics, though it's clear to me from living with her for almost 30 years that her verbal and spatial skills are at least as good as mine. And her colour sense is infinitely superior. Our home would look, at best, boring, if I picked the paint and wallpaper. Needless to say, I don't, she does that, I just put the stuff on the walls.
Or put her in a room with a dozen strangers. She'll do much better than I will. In 3 hours she'll have the family history of everyone in the room and everybody will think she's a charming and delightful conversationalist, which of course she is, and she'll remember everything. Put her in a room with the same people a year later and she'll remember everyone's name, their spouses' names, their children's names, and will ask knowledgeable and pertinent questions about the events in their lives since she last spoke to them. I've seen her do it multiple times at staff Christmas parties. She knew more about the people I worked with than I did, and I saw them 5 days a week, she saw them once a year. No intelligence test I've ever seen can measure that skill, and for the kind of work she does it's extraordinarily valuable. There have been attempts lately to incorporate that kind of thing into intelligence testing, with the appearance of an idea called emotional intelligence, though I have no idea how successful it's been.
Intelligence seems to me to be one of those things about which people say things like, "I have no idea how to define it but I know it when I see it." Similarly, I'm sure most of us are pretty confident we can spot someone who lacks it very quickly. But it's far from clear precisely what it is we're detecting. Certainly verbal skills are part of it, as are the ability to understand complex issues, to absorb new information, but that list is potentially endless, and strongly affected by the nature of the information. I can absorb new information about mathematical subjects almost instantly in most cases, for instance, and remember it, while my wife will never get it, but she can absorb new information about people and remember it forever, while for me that kind of information rapidly disappears from my memory unless there's some particular reason for me to keep it. People I don't know well and rarely see are to me like mathematics is to her.
Am I more intelligent than she is? According to IQ tests, I am, in fact according to the standards I'm more intelligent than 97% of people, but she has useful skills and knowledge I can't hope to match, so I don't believe it. What I believe is that all the measures of intelligence I've ever seen are nonsense.