Citation needed - this seems to disagree, and, more generally, I would expect the ability to learn to go hand in hand with the ability to teach.
That seems to suggest that teaching is rare among chimpanzees near the end. Regardless, I'm not a zoologist, and my model of chimps is fuzzy. It may be that someone was commenting just about male chimps and I extended that to all chimps, or that most chimps don't teach except for this variety, or a number of other options.
In their 2011 chapter for the Cambridge Handbook of Intelligence, Stanovich et al. review the evidence suggesting that intelligence and rationality are not the same thing and that rationality is often more important than intelligence. They then lament the fact that there are no standard tests for measuring one's "Rationality Quotient." Then they take a few steps toward such a thing by suggesting some important rationality skills (actively open-minded thinking, fine-grained emotional regulation, tendency to seek information and fully process it, etc.) and rationality 'mindware' (probability theory, scientific process, economic thinking, etc.).
Here are those pages in particular: first a graphic of some important rationality skills and mindware, and then a table of the components of rational thought: rationality components, relevant literature citations, and example word problems that would test for each rationality component.