You're talking about Raven's Progressive Matrices and variations thereof.
RPM only measures a very small subset of what we normally thing of as general intelligence, and they correlate with general intelligence less strongly than vocabulary. They definitely aren't nearly as good at predicting future college performance as the current SAT is.
>You can teach how to solve it to a schoolkid and it is still really hard to practice for.
It's actually not, you can definitely practice for them. And they are very sensitive to repeated testing.
Here's a cited Psychology Stack Exchange answer with a good summary: https://psychology.stackexchange.com/questions/20177/does-pr...
RPM was developed to be free from cultural bias, but we now know that this isn't the case, they can actually be more biased than verbal tests depending on the culture.