The Otago Daily Times understands the university suspected a student of cheating on a microbiology exam on the morning of the burglary.
The dentistry student said university officials did not tell them the papers had been taken and said they "just had to do it".
"I was ... annoyed because I was pretty happy that I was done [finished examinations]."
The dentistry class celebrated after the initial exam with a function at Larnach Castle on Saturday evening.
The anonymous student said he had probably done better the second time and he felt his classmates thought the same thing.
"They couldn't change the exam so we just sat the same one."
He said the university had "rushed us through" the exam again because all the papers needed to be marked before graduation.
University officials asked students sitting the exam again not to tell their classmates so other students would not speculate.
"They couldn't give us a grade without re-sitting the exam."
An Otago University Students' Association spokeswoman confirmed a dental exam had already been re-sat. She said 10 different exams had been stolen and "different options [were] being offered to students affected.
She could not confirm that the university had offered a re-sit, an internal grade, a rewrite at home or an ungraded pass to affected students.
University of Otago head of communications Megan McPherson said examination scripts in a range of subjects, mainly completed on Saturday, were affected, including several second year papers, English 240, politics 204, microbiology 223, dentistry 551, a sports medicine paper and a health promotion paper.
Ms McPherson acknowledged some students who had already left the university and travelled elsewhere could find it difficult to re-sit exams.
They could potentially be sat at other centres and the university was also taking individual circumstances into account in discussing matters with students, she said.
Ms McPherson was also asked about puzzling aspects of the burglary, including that some knowledge of the registry building layout and some planning appeared to have been involved, and the possibility that a student may have wished to remove their own examination answer for some reason.
Yesterday, university deputy vice-chancellor academic, Prof Vernon Squire said staff contacted the students affected and his immediate concern was for them.
"We understand how upsetting and disappointing this is for the students. The considerable effort they have put into their study and exams has essentially been ruined by this reprehensible criminal act.
"We are making arrangements with the students to prepare for a likelihood that their scripts will not be returned."
The university was urging anyone to come forward if they had any information about the theft.
A Southern district police spokesman said a detective was investigating the burglary and was following lines of inquiry.
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