Sentence Correction

I would have liked to have gone swimming yesterday.

A. to have gone swimming
B. to go swimming
C. to had gone swimming
D. to go to swim
E. to of gone swimming

I think A is correct but the answer is given as B correct. which one is?

Also, do they check Capitals and words like "schooldays/school days" in the gmat? Btw, which one of the 2 is correct?

Check this out: https://www.eslcafe.com/grammar/verbs_other_verbs08.html

I find A and B correct by having different meanings. In any case, the action in the first clause takes place at a moment in the past. But the action in the 2nd clause takes place before or after this past moment.

so A conveys the meaning that at 2pm yesterday I would have liked to have gone swimming at 10am that day.
and B conveys the meaning that at 2pm yesterday I would have liked to go swimming at 4pm that day.

correct me if I'm wrong.

IMO: B