"Like" is used for Nouns or for Hypothetical situations. "As" is used to compare clauses, etc

Matt drives fast cars like his sister does???

The Black Bold part is not a Noun but a clause. So we need "AS"

Let's be clear: the GMAT does NOT expressly test the usage of "like" versus "as." That is NOT one of the diction errors. These words are used to form Comparisons, and "Comparisons" IS a topic the GMAT tests.

Here's the #1 rule of Comparisons: we must compare similar things.

When you say, "Matt drives fast cars like his sister does," your comparison is INCORRECT, because while you are intending to compare Matt to his sister, you are in fact comparing Matt to what his sister 'does.' No go.

Matt is LIKE his sister.

That's a logical comparison. He is not LIKE his sister "does."

For comparisons, don't ever forget to pay attention to the MEANING.

MEANING IS MASSIVE. You can see more SC examples that relate to meaning here: https://gmatrockstar.com/category/gmat/