The ratio of boys to girls in a class is 7 to 3.
Among the options below, an acceptable value for the total number of
students in the class is:
Options:
(A) 21
(B) | 37
(C) 50
(D) 73
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.1)**
**1. Governing Concept**:
- **Topic**: Quantitative Aptitude & Ratio Multiples
- Given ratio of boys to girls is $7 : 3$.
- Total ratio units $= 7 + 3 = 10$.
- Because the number of students must be an integer, the total number of students in the class must be an integral multiple of $10$:
$\text{Total students} = 10k, \quad k \in \mathbb{N}$
- Among the options $\{21, 37, 50, 73\}$, only $50 = 10 \times 5$ is a multiple of 10 (giving $35$ boys and $15$ girls).
**2. Option Analysis**:
- **Option (A) [21] is INCORRECT**: Not divisible by 10 (yields non-integer students).
- **Option (B) [37] is INCORRECT**: Prime number, not divisible by 10.
- **Option (C) [50] is CORRECT**: Exactly divisible by 10 ($k = 5 \implies 35\text{ boys}, 15\text{ girls}$).
- **Option (D) [73] is INCORRECT**: Not divisible by 10.
**3. Final Answer**:
- **Correct Choice**: **C**
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