Legal cases can be termed “hard” cases if they raise issues that are

1. (C)
(A) begs the question of the topic and scope—the determinacy of “hard” cases—and comes down squarely on the side of the need for resolving all cases through law alone, something the author rejects. (B) is the choice for those who grab ¶1 and not much else. The definition of “hard” cases is a jumping-off point for the real issue of how such cases are to be decided, and (B) mentions none of that. (D)'s negative judgment of Dworkin's concept of legal principles is not supported by the author—indeed, the author embraces the concept in ¶4. (E) is a pretty radical distortion of this passage's content and tone. Hart's definition of legal terminology as “open textured” implies (quite sensibly) that language has some inherent flexibility of meaning—even legal language—and that judges need to exercise some judgment as a result; but all of that is a far cry from accusations of “inherent inconsistency” and “defects and gaps in the law.”

2. (C)
(A) sounds like a plausible definition of the term “legal principles” on its face, but it has nothing to do with Dworkin or, indeed, with anything else in the passage.
(B) Legal principles, as defined by Dworkin, don’t explain legal rules: They coexist with them, within the body of established law (see lines 35-37). (D) Dworkin believes that law exists outside of legal rules. (E) Dworkin seems to be opposed to the notion that some cases need judicial discretion, so he would not coin the term “legal principles” to mean cases that required same.

3. (D)
(A) The author never posits which—rules or principles—is appealed to more often in hard cases. (B) “Official recognition,” whatever that means, has nothing to do with this “think piece” on legal determinacy, the author's effort to work out a theory of one part of the law. (C) Far from arguing that rules have been superseded by principles, the author believes that both exist in the law. (E) No, the author hints strongly that those cases “in the penumbra of both rules and principles” (lines 56-57) will, in fact, require judges' discretion for their decidability.

4. (B)
(A) “Clear” and “persuasive” don't imply that a work or theory covers a topic “exhaustively.” No evidence for this one. (C) and (D) are each half-right, half-wrong. Interesting, sure; plausible, o.k.; but “impractical” or “unwieldy”? It's unlikely that a theoretical think piece like this one would traffic much in practicality anyway; but if anything, the author does seem to see practical and workable (as opposed to “unwieldy”) value in Hart's concept (see ¶4). (E) Hopelessly wrong. No matter how far back in history Hart's work dates—and of course we get no info to that effect—the author seems to find it relevant and well worth studying.

5. (E)
(A) Nonsense. The in-practice role of the legislative branch is about as far removed from this passage's concerns as can be. (B) is an issue that was raised and disposed of in ¶1. The topic may be “hard” cases, but the scope moves away from their definition to their determinacy, something that (B) ignores but (E) exploits. In terms of the author's main purpose, Dworkin certainly doesn't deserve the pride of place that (C) assigns him. (D) If anyone is in the “critiquing Hart” business, it's Dworkin and not our author, who is trying to synthesize the views of the two thinkers.