Weight of a person can be expressed as a function of their age. The function usually
varies from person to person. Suppose this function is identical for two brothers,
and it monotonically increases till the age of 50 years and then it monotonically
decreases. Let a1 and a2 (in years) denote the ages of the brothers and a1 < a2.
Which one of the following statements is correct about their age on the day when
they attain the same weight?
Options:
(A) a1 < a2 < 50
(B) a1 < 50 < a2
(C) 50 < a1 < a2
(D) Either a1 = 50 or a2 = 50
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.7)**
**1. Governing Concept & Theory**:
This problem evaluates **Quantitative Aptitude** within the General Aptitude module (2 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 **(B)** (`a1 < 50 < a2`) 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 **(B)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2025 master key with 100% accuracy.
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