Also, uniformed officers disproportionately come from uniformed officer families. One way they can give their kin a structural advantage is to design the tests to have certain recurring types of logical problems which can be relentlessly practiced. So, year after year, you'll see the same kinds of exam questions, with the details switched around. That license question or a close logical variant may have been on the test for generations.
I don't know how plates work in the US but in the UK quite often you'll find similar cars with similar plates because they were registered at the dealer in a block. A great example is how about 14 years ago nearly all the police cars in Scotland were silver Ford Focuses with plates that started "SF58" and then had more-or-less sequential runs of three letters. "SF" means it was registered in Edinburgh, "58" means September 2008, and the three letter group is serially assigned. Of course, this applied to all their *unmarked* cars, too...