Grammar rule: any pronoun that follows a preposition must be an object pronoun (me, her, him, us, them NOT I, she, he, we, they).
I realize, however, that most people do not want to think about prepositions and subject and object pronouns, especially while they’re taking the SAT, so now I’m going to give you the shortcut:
Pretty much everyone employs this rule naturally when using singular subject and objects: you just wouldn’t say, “me is going to the store,” or “the cashier gave the change back to he.”
When subject and objects are plural, however, people tend to get confused. But here’s the thing: there’s no difference between using pronouns with singular and plural subjects and objects. In fact: Whatever goes for singular also goes for plural.
The SAT almost always pairs pronouns with a proper names (e.g. Jesse and I; she and Maria), so if you cross out the proper name, you’ll virtually always be able to hear whether there’s an error.
Let’s look at a couple of examples
Incorrect: After nearly a month, the teacher finally returned the report to Sarah and I.
The first thing that we can notice is that we have a name (Sarah) paired with a pronoun (I).
If we cross out the words “Sarah and,” we are left with:
Incorrect: After nearly a month, the teacher finally returned the report to I.
Would you say that? Of course not. You’d say, “The teacher finally returned the report to me.”
So you’d also say:
Correct: After nearly a month, the teacher finally returned the report to Sarah and me.
Or:
Incorrect: Tom and me went to the baseball game yesterday after school. Cross out: [Tom and] me went to the baseball game yesterday after school. If you wouldn’t say “Me went to the baseball game,” you wouldn’t say, “Tom and me went to the baseball game” either. The sentence should therefore read:
Correct: Tom and I went to the baseball game yesterday after school.