If we go back far enough in time, all humans were in Africa, and that is where the human species was born. It was about 100,000 years ago, a short time on the evolutionary time scale, when some humans emigrated out of Africa and others remained. Geographical divergence means genetic divergence, and the populations adapted to their respective environments. Part of these adaptations entailed differences in IQ, and the most probable explanation in my opinion is provided by J. Phillipe Rushton in his book
Race, Evolution and Behavior. I can explain the theory in more detail if you happen to be interested.
You are right that IQ tests are all about logic and problem solving, and the other aspects of intelligence are overlooked by IQ tests. Logic and problem solving, however, are the skills central to an industrial economy, required especially for engineering, science, law, medicine, teaching, and industrial entrepreneurialism. If there are inequalities between populations with respect to these skills, then it serves to explain economic inequalities. It is still possible that the lower-IQ populations tend to have greater other important skills that contribute to a happier life. If the question is merely about intelligence as measured by IQ, then the data is dispassionately unfair. Even more depressing is that differences in IQ in are largely genetic, as strongly indicated by those studies of identical twins reared apart I mentioned before.
There are many steps the ladder leading to the conclusion that makes one a racist. If you take out only one rung, you never it make it to the step that says, "I am a racist."
1) Intelligence is measurable.
2) Intelligence is largely genetic.
3) Races are genetically distinct.
4) Races have unequal average intelligence.
5) I am a racist.
All steps on the ladder leading up to the last step are scientifically challenged, one way or the other, and I have stepped on them all. I do NOT suggest you do the same.