This is probably not an official GMAT question because for inference/draw a conclusion question, the answer choice is typically something that we can prove or nearly prove without making any further assmptions. In this case, the best answer (C) relies on significant assumptions. Also, the question stem talks about a "police record" and the answer choices talk about an "arrest record".

With that said, Answer C is the best answer. If the politician had used drugs for 20 years at the time the statement was written, either the 1964 arrest happened after the statement, or the arrest happened before the statement but within 20 years.

If we place the statement more than 20 years after the arrest, the statement becomes false (the statement claims use of drugs for 20 years). Since the arrest was in 1964, the statement was written at the latest in 1984. Pick C

Again, I don't think this meets the standards of an official GMAT question, so I would be wary about using the source to study.

-Patrick