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?
Options:
(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.
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2023 Q.4)**
**1. Governing Concept & Theory**:
This problem evaluates **Analytical & Spatial Aptitude** within the General Aptitude module (1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(D)** (`Some Fields medalists have dropped out of college.`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(D)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **D**
- **Evaluation Status**: Matches official GATE 2023 master key with 100% accuracy.
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