Beginners ----- articles
You are wrong!--- The correct answer is 2. "(a) 'a', (b) 'the'".
'Warren Harding was a president of the United States, but he was not the greatest.'
We need 'a' in the first gap, because there were many presidents of the USA, and Warren Harding was one of these. However, there can only be one 'greatest' so the second gap needs 'the', because it tells us which president Warren Harding was not. (i.e. He was not 'the greatest'.)