Question

In 2022, June Huh was awarded the Fields medal. He was also a poet, did not win any medals in the International Mathematics Olympiads, and dropped out of college. Based only on this information, which statement can be inferred with certainty?

• A. Every Fields medalist has won a medal in an International Mathematics Olympiad.
• B. Everyone who has dropped out of college has won the Fields medal.
• C. All Fields medalists are part-time poets.
• D. Some Fields medalists have dropped out of college.

Hint:

In logical inference questions, "some" means "at least one." A single confirmed example is enough to establish such statements, while universals ("every", "all") require proof for all cases and are easily refuted by one counterexample.

Answer 1

The Correct Option is D

Step 1: Translate the facts.
We know at least one person (June Huh) is both a Fields medalist and a college dropout.

Step 2: Test each option.
(A) False. June Huh is a Fields medalist who did not win any IMO medal \(\Rightarrow\) counterexample.
(B) Not inferable. From one dropout who won, we cannot conclude that all dropouts won the Fields medal.
(C) Not inferable. Knowing one medalist is (or was) a poet does not imply all medalists are poets.
(D) True. "Some" means "at least one." Since June Huh is a Fields medalist who dropped out, the statement holds with certainty.

Final Answer:
\[ \boxed{\text{(D) Some Fields medalists have dropped out of college.}} \]