Passé, archaic. Apologists are defenders—in this case, people who are trying to make the politician and strategist seem like a good guy. However, the clues “in his day” and the lack of interest among a “modern public” indicate that the politician’s views are outdated. Only passé and archaic match. (The accent mark on passé exists because the word came into English from French.) Note that trap answer erroneous just means wrong and doesn’t really fit the clues, nor is it appropriate for discussing matters of culture and opinion.

Probity, equity. There are allegations of preferential treatment or unfairness at the local level, and these are threatening to spill over into criticisms that the system is unfair or partial at the national level. But we are told that the system’s fairness is not currently in dispute at that level, so we are looking for synonyms for fairness or impartiality. The correct answers are equity and probity.

Apprising, counseling. Cassirer “correctly” exposed forgeries to a credulous (that is, gullible) art world. Thus, he was helping or advising the art world. Only apprising and counseling match.

Gauche, uncouth. The two words must match ostentatious. Both gauche and uncouth get aross the idea of showing off in a low-class way (as is often associated with the “newly rich”). Remember not to insert your own opinions eccentric and idiosyncratic are near-synonyms, but are a trap.

Triage, prioritize. We need two words that match the clue “to metaphorically separate the wheat from the chaff.” (Chaff is the inedible part of wheat that is discarded before the wheat can be made into flour.) We can also use the clues regarding “the only way that a person can function” given an “influx of information.” Delete and eliminate are attractive traps, but doesn’t match the idea of separating “the wheat from the chaff.” Only triage (think of what emergency room physicians do) and prioritize match.

Diversity, mutation. The geneticists mentioned are studying a population descended from a rather small number of people a rather long time ago. Geneticists—who study genes, of course—would be interested in how this population changed over time (or, mutated) and became different from one another (diversity). Note that none of the other answers are logical at all.

Expeditious, swift. The pivot indicates that the answers will oppose the clue quagmire—that is, Afghanistan’s problems are messy and entrenched. So, what kind of victory is not likely? A fast or easy one.

Feasible, viable. We need two words that are like pragmatic, which means practical. Feasible and viable relate to the practical considerations of whether the plan is workable or likely to succeed. The only other pair of similar words, partisan and prejudiced, have the exact incorrect meaning—they are more similar to ideological than pragmatic.

Bald, overt. The earlier “evasions and equivocations” are ways to avoid a question or “flip-flop” on an issue. This “latest statement” is “unlike” the evasions and equivocations because it is an explicit, clear, or obvious lie. Bald and overt are the only matches. Note the trap answers tacit and implicit, which are synonyms that mean the exact opposite (hinted at, unspoken) of what we need.

Paean, eulogy. A retrospective would be an exhibit that shows the history and progression of the artist’s work, but this exhibit only shows the good parts (it “glosses over” the weaker work and omits the artist’s “dissolution”). Thus, we need a word that has something to do with praising. Paean and eulogy are the only matches. Note that a paean is generally a song or speech of praise and is being used a bit metaphorically here. Many people only know eulogy as a speech given at a funeral, but can actually refer to any speech (or in this case, art exhibit) of praise.