Yes doing an SAT test with the answer key isn't intelligent because that's in your "database" and is just a matter of copying over the answers. LLMs don't do this though, it doesn't do a lookup of past SAT questions it's seen and answer it, it uses some process of "reasoning" to do it.
You've now reduced the "process of reasoning" to hitting the autocomplete button until your keyboard spits out an answer from a database of prior conversations. It might be cleverly designed, but generative models are no more intelligent than an answer key or a library's card catalog. Any "intelligence" they appear to encode actually comes from the people who did the work to assemble the training database.