Modifiers - Sentence Dissection/Explanation Required

As per the intended meaning of the sentence, the part of the sentence after "that/which" is modifying the clause before "that/which" by presenting the result of the action.
Clause (action)= Larry failed his test
Modifier (presenting result)= he will will be going to summer school

Now, usage of "which" in the above sentence is wrong because "which" can modify only a noun and never a clause. So, as per this sentence "which" is illogically modifying "test".

Furthermore, I think the sentence structure is incorrect because both "that" and "which" can't modify a clause. A correct structure would be "Larry failed his test, so he will be going to summer school" or "Larry failed his test, a situation that implies he will be going to summer school".

I hope you're clear.

Feel free to discuss any doubts.