In the context of paintings, any mention of ballet dancers (and/or racecourses) will always suggest Degas to anyone with even a rudimentary knowledge of the subject. Absinthe, however, is a different matter.
The first of the two paintings referred to in this question was painted by Degas in 1875 and/or 1876. The title that the artist originally gave to it was Dans un Café. Other early titles (according to Wikipedia) were A Sketch of a French Café and Figures at Café.
In 1893, when the painting was exhibited in London, the title was changed (also according to Wikipedia) to L'Absinthe; and this is "the title by which it is now commonly known."
Wikipedia also notes, however, that Degas's painting is also known in English as The Absinthe Drinker (despite the fact that there are two drinkers in it) or Glass of Absinthe (similar issue).
Still with me? Good ... because it's about to get even more complicated!
In around 1859 – some 16 years before Degas painted L'Absinthe – another French painter, Edouard Manet, executed a painting that has always been known as The Absinthe Drinker – or Le Buveur d'absinthe in French. (This is considered – again according to Wikipedia – to be Manet's "first major painting and first original work.")
So ... if asked who painted The Absinthe Drinker, the more correct answer is probably "Manet". In this particular question, the mention of The Ballet Class points us (as I mentioned at the top) in the direction of Degas; but while this resolves most of the ambiguity, it would have been better (IMHO) to give one or more of the several other titles for Degas's absinthe painting: Absinthe (in English), L'Absinthe (in French), Dans un Café, A Sketch of a French Café, or Figures at Café.
© Macclesfield Quiz League 2022