The number of girls in a class is one third of the number of boys. Which one of the following numbers cannot represent the total number of children in the class?

Options

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

Answer

To solve the problem, we need to determine which of the given options cannot represent the total number of children in the class, given that the number of girls is one third of the number of boys.

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of boys in the class be represented as \( x \). According to the problem, the number of girls is one third of the number of boys, which can be expressed as:
\[ \text{Number of girls} = \frac{x}{3} \]

2. **Calculate Total Students**:
The total number of students in the class can be calculated by adding the number of boys and girls:
\[ \text{Total students} = x + \frac{x}{3} \]
To combine these, we need a common denominator:
\[ \text{Total students} = \frac{3x}{3} + \frac{x}{3} = \frac{4x}{3} \]

3. **Express Total in Terms of \( t \)**:
Let \( t \) represent the total number of students:
\[ t = \frac{4x}{3} \]
Rearranging this equation to solve for \( x \):
\[ x = \frac{3t}{4} \]

4. **Determine Divisibility Condition**:
For \( x \) to be an integer, \( t \) must be divisible by 4. This means that the total number of students \( t \) must satisfy the condition:
\[ t \mod 4 = 0 \]

5. **Evaluate Options**:
Now, we will check each of the provided options to see if they are divisible by 4.

- **Option 1: 48**
\[ 48 \div 4 = 12 \quad (\text{Divisible by 4}) \]
- **Option 2: 44**
\[ 44 \div 4 = 11 \quad (\text{Divisible by 4}) \]
- **Option 3: 42**
\[ 42 \div 4 = 10.5 \quad (\text{Not divisible by 4}) \]
- **Option 4: 40**
\[ 40 \div 4 = 10 \quad (\text{Divisible by 4}) \]

6. **Conclusion**:
The only option that cannot represent the total number of children in the class is **42**.

### Final Answer:
The number that cannot represent the total number of children in the class is **42**.