What is wrong with my reasoning on this ACT English question [duplicate]

Solution 1:

The answer "no change" is correct.

You can find the applicable grammar "rules" here, on Grammarbook.

This is a summary of the information on that site, which provides a number of examples:

• When "like" is a preposition (as it is here), it means "similar to" and is followed by a noun. It is not used with a verb.
• "As" in this context means "in the same manner that", and is followed by a comparison that uses a subject and verb.

Because "like" can be used as a preposition, you didn't need to rearrange the sentence.

Since prepositions take objects, the preposition following it would have to be in the objective case -- hence "me". "I", on the other hand, is the nominative case of the first person pronoun, and would be used only as the subject of a sentence.

So the correct phrase here is "Like me".

Solution 2:

"Like me" is correct because "me" is the object of the preposition.

"As I do" changes it to a clause with "I" as the subject.

"Like I do" is using the preposition as a subordinating conjunction and is technically incorrect, though common in informal English.