Two numbers A and B are both divisible by x. The sum A+ B is divisible/not divisible by x

Options

A. a divisible
B. not divisible
C. not determine
D. none of these

Answer

To solve the question regarding whether the sum of two numbers A and B, both divisible by x, is also divisible by x, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to determine if the sum \( A + B \) is divisible by \( x \) given that both \( A \) and \( B \) are divisible by \( x \).

2. **Assume Values for A and B**: Let's take two numbers, \( A = 10 \) and \( B = 15 \). We will also choose \( x = 5 \).

3. **Check Divisibility of A and B by x**:
- For \( A \):
\[ A = 10 \quad \text{and} \quad x = 5 \]
We check if \( 10 \div 5 \) is an integer:
\[ 10 \div 5 = 2 \quad (\text{which is an integer, so } A \text{ is divisible by } x) \]
- For \( B \):
\[ B = 15 \quad \text{and} \quad x = 5 \]
We check if \( 15 \div 5 \) is an integer:
\[ 15 \div 5 = 3 \quad (\text{which is an integer, so } B \text{ is divisible by } x) \]

4. **Calculate the Sum \( A + B \)**:
\[ A + B = 10 + 15 = 25 \]

5. **Check Divisibility of \( A + B \) by x**:
- Now we need to check if \( 25 \div 5 \) is an integer:
\[ 25 \div 5 = 5 \quad (\text{which is an integer, so } A + B \text{ is divisible by } x) \]

6. **Conclusion**: Since both \( A \) and \( B \) are divisible by \( x \) and their sum \( A + B \) is also divisible by \( x \), we can conclude that the sum \( A + B \) is divisible by \( x \).

### Final Answer:
Yes, the sum \( A + B \) is divisible by \( x \).