Each child, like each adult, has different motivations in life. Not all children are equally motivated for schoolwork.
> The admission test is not racist per se, but if it results in, say, blacks not being admitted to an institution, it exist in a framework that materially enables racism
No. You need to look at confounding variables, not just race. It could be that a large percentage of black children in this area come from poor families and must therefore work part-time jobs after school instead of studying. That’s just one example of many possibilities. “Correcting” the problem by putting these children into this special school does nothing to change their poverty: they still must work after school and can’t study. And that means they can’t keep up with the other children in this privileged school. Your solution is probably to make the schoolwork easier and force everyone to suffer the same fate. My solution is to give that family money so their high school kid doesn’t have to work to help support his family.
In reality, your solution is the one that gets chosen because of the wokeness movement.