Math olympiad question

The question is:

There were 3 people on an island, person A, person B, and person C. These three people are either a gentleman or a liar. A gentleman always tell the truth and a liar always tell a lie. One day, a man came to the island and asked person A, "are you a gentleman or a liar?" Person A answered but the man could not hear what he said. He then asked person B, "what did person A say?" Person B answered, "he said that he was a liar." Person C then said "person B is a liar!"

A. You cannot tell whether person A is a gentleman or a liar

B. Person C is a liar and person B is a gentleman

C. Person B is a liar and person C is a gentleman

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1) A and D are true

2) A and C are true

3) None of them are true

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