The following text discusses computational complexity theory.
The P versus NP problem remains one of mathematics' greatest unsolved questions. Problems in P can be solved efficiently; problems in NP can be verified efficiently. Whether every problem easily verified can also be easily solved—whether P equals NP—would have profound implications for cryptography, optimization, and artificial intelligence. Most researchers believe P ≠ NP, but proof has remained elusive for over fifty years.
Which choice best describes the function of the last sentence?
It resolves the problem by providing the accepted answer.
It indicates the scientific consensus while noting the unresolved nature.
It provides technical definitions of mathematical terms.
It introduces a new problem unrelated to P versus NP.
Correct Answer: B
Choice B is the best answer. The last sentence notes consensus (most believe P ≠ NP) while acknowledging the unresolved nature (proof remains elusive).
- Evidence: The sentence states: "Most researchers believe P ≠ NP" (consensus). It adds: "but proof has remained elusive" (unresolved).
- Reasoning: It balances the majority opinion with the lack of mathematical certainty.
- Conclusion: The function is to indicate consensus while noting it's unresolved.
💡 Strategy: Look for "Most researchers believe" (Consensus) + "but" (Unresolved).
Choice A is incorrect because the problem remains unsolved. Choice C is incorrect because definitions appear earlier. Choice D is incorrect because it continues the same topic.