He … be fat, but he is still smart.

Analyze the question: The sentence is "He ........ be fat, but he is still smart." The "but" shows a concession: we admit something might be true, then contrast it with something else. We need a modal verb that expresses possibility in the present.

Concept: Modal verbs of possibility/concession:

• may is used for present or future possibility. In a concessive structure, "He may be fat, but..." means "It is possible, and I concede, that he is fat, but..."
• might is a weaker, more tentative form of "may". It is also grammatically acceptable here, and in everyday English "He might be fat, but..." is common.
• could expresses ability or a past or hypothetical possibility. It is less natural for this concessive sense.
• can expresses ability or general permission. "He can be fat" suggests he is sometimes fat, which doesn't fit.

Working:

1. The sentence has a concessive meaning: "Granted that he is fat, he is still smart."
2. The classic WASSCE pattern for this is "may ... but ...", as in "He may be poor, but he is honest."
3. The verb is in the present tense ("he is still smart"), so the present-tense form may matches best and keeps the tense consistent.
4. Might could also work in informal usage, but it is more tentative and is usually preferred in past or hypothetical contexts. Since the sentence is in the present, may is the best fit.

Answer: The best choice is A. may.

Tip: Remember the pattern "may ... but ..." for concession: He may be rich, but he is not happy. When two options are both plausible, choose the one that matches the tense of the rest of the sentence.