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> ...the researchers note that the sister raised in the US had suffered three previous concussions...
And this, too:

> ...the twin raised in Korea described growing up in a loving and harmonious family home, the adopted sister reported a harsher upbringing, colored by regular conflict and the divorce of her adopted parents.

So much this is how the world turns.
It's been decades since I bothered with an IQ test...but several of the tests I recall were very obviously the sort of thing that you could both cram for, and improve your score by practicing their narrow style of questions/problems.

But, alas - "twin K got a higher test score than twin A, after twin K went to test-prep school" is not a headline to get many clicks.

I’ve taken several in my life and have received scores differing by as much as 20 points.

“Psychometrics is a soft science with poor replicability except IQ which is as diamond hard as physics and is reliable enough to make broad generalizations about people and explain away just about any difference in outcome.” - the HBD or whatever it’s called this week crowd.

Oof. I'd never heard of HBD ("human biodiversity") before. That's an impressive bit of euphemism: racism dressed up in eco language.
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.