I used to think standardized tests were the way to go, but...
My kid recently went through another testing gauntlet, which is the 11+ test. For those who aren't in the Southeast corner of the UK, this is a multiple choice type test that looks a lot like an IQ test in some ways. It's a single sitting and determines whether you are allowed into something called a Grammar School, which is just a selective school, and the test is taken the year the kid turns 11.
So the thing about this test is that nobody will admit to it, but everyone in the middle class will hire tutors to help their kids pass the test. Furthermore, private primary schools will spend a lot of time prepping for this test in the two years before the kids take the test. Plenty of people do both: send their kids to a fee-paying primary school, and pay for tutors.
Guess what, the pass rate for fee-paying (aka independent) schools is way higher than for state schools. It's hard to break down which parents went for state + tutoring, but it's not exactly a stretch to suppose those kids did better than state school kids with no tutoring. Furthermore state schools that do well tend to be in certain wealthy areas.
If you have a look at one of these tests, it's pretty clear you benefit from practicing. Like just about any test, if you've done it before you are at an advantage, the more the better.
I don't see how this isn't gaming the test. The idea with a test is to uncover which kids will get the most out of the selective school, but how is that going to work when a select few are prepped for the test?
Now just for the record I did the SAT back when I was a kid. It's pretty much the same as the 11+, for a slightly older age group. Again, it doesn't make any sense to say it's hard to game. People are gaming it as we speak.
I think what might actually be hard to game is teacher recommendations. After all these people have been with the kid for a long time and know what they can do. They also tend to be distanced enough that they don't have to say good things about every kid.