A decade or so back my son applied for one of the few remaining state selective schools in London. About 2000 applied for 100 places. Admission was by similar tests, including verbal and non-verbal reasoning. Despite the claims you can't game these tests, many people use tutors. We didn't, but I bought him all the non-verbal reasoning papers I could find online. He practised a lot, and over six months progressively raised his mark from around 70% (not high enough to get in) to 100% on the final practice paper he did a couple of days before the entrance exam. I'm sure you need some native aptitude, but it's not at all clear to me these really help remove selection bias.

My son told me that when a new teacher gives them a word-search or visual puzzle, they kids will have finished before the teacher has finishing handing them out. On the other hand, he also tells me common sense isn't so common there, so things do tend to balance out in strange ways.