[daquisu]

To be fair, there is some research about IQ having a genetic component, which one can do by comparing twins with the same DNA and twins without the same DNA [citation needed]. People who are curious and have the drive to keep learning are going to have a higher IQ, and personality has a genetic trait.

Just like you, I think IQ is very trainable. It is very common to have questions about logic, which may be represented as Venn Diagrams, or visual questions with multiple parts, each one following a logic...

<appeal to authority> I say that as someone who "started" with 110 QI according to a Orkut online test, and grinded my way to 145 according to different online tests. </appeal to authority>

For that reason people who learned how to prove things in math are naturally going to have a higher IQ: they learned how to solve some questions in the test.