Explanation

The clue is that Gatsby grows progressively more flagrant in his spending and his lifestyle, so the word in the blank must mean something like inclined to spend money unwisely. Ignominy means shame and volubility means talkativeness, but nothing in the sentence indicates that
he feels shame or talks incessantly.

Repute and stature mean fame; though Gatsby is a famous character, the blank does not refer to his fame. Dissipation and profligacy can both mean inclined to wastefulness, and produce equivalent, appropriate sentences.

Hence options B and E are correct!