need to prepare for $5$ out of $6$ outcomes Four of six possible essay questions will be on the exam. If two questions are in part $A$ and two questions are in part $B$, and one question must be chosen from both part $A$ and $B$, how many essay questions must be studied for? I think it's $5$ but am not sure.

TBH honest the original directions were ambiguous but I think part A will have the same number as questions in it as part B, and one question must be chosen from part A and one question must be chosen from part B.

For completeness sake here is the original


  Four of  the questions  from  below  will  be  on  the  exam,  divided
  into  Part  A  and  Part  B.  You  will  have  to  answer  one 
  question  from  part  A,  and  one question  from
Yes, that's right.

Assuming that the exam has two parts, A and B, both consisting of two essay questions, chosen from a collection of 6 possible questions, of which you must pick and answer one for each part, you will have to study for 5 of them. If you study for less, there is a chance that you haven't studied for both questions in at least one of the parts.

The number of parts to the exam doesn't matter, what matters is the smallest number of questions to a part, $k$ and the total number of questions, $n$. You will have to study for $n-k+1$ questions, otherwise there is a possibility that the part will feature exactly the $k$ questions you didn't study for.
Yes, that's right.

Assuming that the exam has two parts, A and B, both consisting of two essay questions, chosen from a collection of 6 possible questions, of which you must pick and answer one for each part, you will have to study for 5 of them. If you study for less, there is a chance that you haven't studied for both questions in at least one of the parts.

The number of parts to the exam doesn't matter, what matters is the smallest number of questions to a part, $k$ and the total number of questions, $n$. You will have to study for $n-k+1$ questions, otherwise there is a possibility that the part will feature exactly the $k$ questions you didn't study for.