80. B. to open / to damage  
81. A. Taking / to occur  
82. C. to translate / to help  
83. B. buy / having  
84. A. to have made  
85. B. cutting / to have  
86. C. to do / to have  
87. B. to get / to find  
88. C. driving  
89. A. to have been rising  
90. D. to be gossiping / looking  
91. A. getting / driving  
 

80. Somehow, he managed to open the locked door without damaging it.

The correct option is A. to open / damaging. This is the correct infinitive construction after "managed".
81. Taking alcohol with medication causes serious health issues.

The correct option is C. Taking / occurring. This is the correct gerund construction after "causes".
82. The text was too long for me to translate on my own so I asked Sinh to help me with it.

The correct option is C. to translate / to help. This is the correct infinitive construction after "too long" and "asked".
83. I'd rather buy a new television because it's not worth having such an old TV set repaired.

The correct option is B. buy / having. This is the correct gerund construction after "worth".
84. You seem to have made a mistake adding these two numbers.

The correct option is A. to have made. This is the correct perfect infinitive construction after "seem".
85. My mother thinks my hair needs cutting, but I don't want it cut yet.

The correct option is B. cutting / to have. This is the correct gerund construction after "needs" and the correct infinitive construction after "want".
86. What do you suggest doing after work today to have some fun?

The correct option is B. doing / to have. This is the correct gerund construction after "suggest" and the correct infinitive construction after "to have".
87. I think I've lost my coat button trying to find one that matches the color on the bus in that crowd, so I need to get/find it.

The correct option is C. get / find. This is the correct infinitive construction after "need".
88. I will never forget being driven in that snowstorm for hours.

The correct option is C. driving. This is the correct gerund construction after "forget".
89. The Himalayas are known to have been rising for the past fifty million years.

The correct option is A. to have been rising. This is the correct perfect infinitive construction after "are known".
90. They seemed to be gossiping about us because they kept looking at us while they were talking.

The correct option is B. to have been gossiping / looking. This is the correct perfect infinitive construction after "seemed" and the correct gerund construction after "kept".
91. I don't think it will be easy for me to get used to driving on the left in Britain.

The correct option is D. to get / to driving. This is the correct infinitive construction after "easy" and "to get used to".