Concept:This is a third conditional sentence about an unreal past situation, where "had" is used to introduce the condition without using "if."
Explanation:"Would have passed" tells us that Sarah did not actually pass her examination.
The missing condition needs the past perfect form: "she had studied hard."
In formal English, the word "if" can be dropped and "had" moves before the subject.
So "had she studied hard" means the same as "if she had studied hard."
The full correct sentence is: "Sarah would have passed her examination had she studied hard."
The other options, "should," "has," and "could," do not form a grammatically correct past conditional clause.
Answer:B. had