If the three digit number 24x is divisible by 9, what is the value of x?

Options

A. `3`
B. `2`
C. `4`
D. `6`

Explanation

To determine the value of \( x \) in the three-digit number \( 24x \) such that it is divisible by 9, we can follow these steps:

### Step 1: Understand the divisibility rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.

### Step 2: Write the sum of the digits
The digits of the number \( 24x \) are 2, 4, and \( x \). Therefore, the sum of the digits is:
\[ 2 + 4 + x = 6 + x \]

### Step 3: Set up the condition for divisibility by 9
For \( 24x \) to be divisible by 9, the sum \( 6 + x \) must be divisible by 9.

### Step 4: Test values of \( x \) from 0 to 9
We will substitute values of \( x \) from 0 to 9 and check if \( 6 + x \) is divisible by 9.

- **If \( x = 0 \)**:
\[ 6 + 0 = 6 \quad (\text{not divisible by 9}) \]

- **If \( x = 1 \)**:
\[ 6 + 1 = 7 \quad (\text{not divisible by 9}) \]

- **If \( x = 2 \)**:
\[ 6 + 2 = 8 \quad (\text{not divisible by 9}) \]

- **If \( x = 3 \)**:
\[ 6 + 3 = 9 \quad (\text{divisible by 9}) \]

- **If \( x = 4 \)**:
\[ 6 + 4 = 10 \quad (\text{not divisible by 9}) \]

- **If \( x = 5 \)**:
\[ 6 + 5 = 11 \quad (\text{not divisible by 9}) \]

- **If \( x = 6 \)**:
\[ 6 + 6 = 12 \quad (\text{not divisible by 9}) \]

- **If \( x = 7 \)**:
\[ 6 + 7 = 13 \quad (\text{not divisible by 9}) \]

- **If \( x = 8 \)**:
\[ 6 + 8 = 14 \quad (\text{not divisible by 9}) \]

- **If \( x = 9 \)**:
\[ 6 + 9 = 15 \quad (\text{not divisible by 9}) \]

### Step 5: Conclusion
The only value of \( x \) that makes \( 6 + x \) divisible by 9 is \( x = 3 \).

Thus, the value of \( x \) is:
\[ \boxed{3} \]