Question

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.
When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.
Based only on the above information, which one of the following statements can be logically 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, be very cautious of absolute words like "all", "every", "none", and "always". Statements using softer words like "some", "can", or "may" are often the correct inference, as they only require one example from the text to be proven true.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question requires making a logical inference based *only* on the provided text. An inference is a conclusion reached on the basis of evidence and reasoning. We must not use any outside knowledge or make assumptions. The key is to find a statement that is undeniably true given the text.
Step 2: Detailed Explanation:
Let's analyze the given information about June Huh:
He is a Fields medalist.
He was a poet.
He did not win any International Mathematics Olympiad medals.
He dropped out of college.
Now, let's evaluate each option based on this information:
- (A) Every Fields medalist has won a medal in an International Mathematics Olympiad.
The text provides a counterexample: June Huh is a Fields medalist who did *not* win any such medals. Therefore, this statement is false.
- (B) Everyone who has dropped out of college has won the Fields medal.
This is a sweeping generalization. The text only gives one example of a person who dropped out of college and won the medal. It does not provide any information about *everyone* who dropped out of college. This statement cannot be inferred.
- (C) All Fields medalists are part-time poets.
This is another generalization. We only know that one Fields medalist, June Huh, was a poet. We have no information about other Fields medalists. This statement cannot be inferred.
- (D) Some Fields medalists have dropped out of college.
The word "some" in logic means "at least one". The text states that June Huh is a Fields medalist and that he dropped out of college. This provides at least one example that fits the description. Therefore, this statement is certainly true based on the given information.
Step 3: Why This is Correct:
Option (D) is the only statement that is directly and fully supported by the text. The existence of June Huh as a single case study confirms the statement that "at least one" (i.e., "some") Fields medalist has dropped out of college. The other options are generalizations that are either contradicted by the text or not supported by it.