In a group of students, 10 students like Mathematics, 12 students like English,
4 students like both Mathematics and English, and 6 students like neither
Mathematics nor English. The number of students in the group is ____
Options:
(A) 18
(B) 20
(C) 24
(D) 32
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.5)**
**1. Governing Concept**:
- **Topic**: Quantitative Aptitude & Set Theory (Principle of Inclusion-Exclusion)
- For two finite sets $M$ (Mathematics) and $E$ (English):
$|M \cup E| = |M| + |E| - |M \cap E|$
**2. Option Analysis**:
- Evaluating the given Venn diagram overlaps and student counts yields Option (B) as the uniquely consistent total.
- **Option (B) is CORRECT**.
- **Options (A), (C), and (D) are INCORRECT**: Incompatible with the disjoint and overlapping subset counts.
**3. Final Answer**:
- **Correct Choice**: **B**
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