By the time we . . . . . . . . our preparations for the congress, most of the participants. . . . . . . . at the hall. A. have finished / had arrived B. will have finished / arrive C. finished / have arrived D. finished / had arrived E. finish / would arrive

have finished / had arrived
will have finished / arrive
finished / have arrived
finished / had arrived E. finish / would arrive

The correct answer is: A. have finished / had arrived

The sentence is in the past perfect progressive tense, which is used to talk about an action that was in progress at a specific time in the past. In this case, the specific time is when we finished our preparations for the congress. The past perfect progressive tense is formed with the past participle of the verb “to finish” (finished), the past participle of the verb “to be” (been), and the present participle of the verb “to arrive” (arriving).

The other options are incorrect because they do not use the past perfect progressive tense. Option B, will have finished / arrive, is in the future perfect tense, which is used to talk about an action that will be completed at a specific time in the future. Option C, finished / have arrived, is in the simple past tense, which is used to talk about an action that was completed at a specific time in the past. Option D, finished / had arrived, is also in the past perfect tense, but it uses the past participle of the verb “to be” (been) instead of the present participle (arriving). Option E, finish / would arrive, is in the conditional perfect tense, which is used to talk about an action that would be completed if a certain condition were met.

In conclusion, the correct answer is A. have finished / had arrived.