The number of boys in a class are three times the number of girls. Which one of the following numbers can't represent the total number of children in the class ?

Options

A. `40`
B. `42`
C. `44`
D. `48`

Explanation

To solve the problem, we need to determine which of the given numbers cannot represent the total number of children in a class where the number of boys is three times the number of girls.

### Step-by-Step Solution:

1. **Define Variables**:
- Let the number of girls in the class be represented by \( x \).
- Since the number of boys is three times the number of girls, we can express the number of boys as \( y = 3x \).

2. **Calculate Total Number of Children**:
- The total number of children in the class can be calculated by adding the number of boys and girls together:
\[ \text{Total} = x + y = x + 3x = 4x \]
- This means the total number of children is a multiple of 4.

3. **Analyze Given Options**:
- We need to check which of the provided options is not a multiple of 4.

4. **Check Each Option**:
- **Option A**: 40
- \( 40 \div 4 = 10 \) (This is a multiple of 4)
- **Option B**: 42
- \( 42 \div 4 = 10.5 \) (This is not a whole number, hence not a multiple of 4)
- **Option C**: 44
- \( 44 \div 4 = 11 \) (This is a multiple of 4)
- **Option D**: 48
- \( 48 \div 4 = 12 \) (This is a multiple of 4)

5. **Conclusion**:
- The only option that cannot represent the total number of children in the class is **Option B (42)**, as it is not a multiple of 4.

### Final Answer:
**Option B (42) cannot represent the total number of children in the class.**