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

### Step-by-Step Solution:

1. **Understand the Rule of Divisibility by 9**: A number is divisible by 9 if the sum of its digits is divisible by 9.

2. **Identify the Digits**: The digits of the number \( 24x \) are 2, 4, and \( x \).

3. **Calculate the Sum of the Digits**:
\[ \text{Sum} = 2 + 4 + x = 6 + x \]

4. **Set Up the Divisibility Condition**: We need \( 6 + x \) to be divisible by 9.

5. **Find Possible Values of \( x \)**:
- The possible values for \( x \) (which is a single digit) are from 0 to 9.
- We will check for each value of \( x \) to see when \( 6 + x \) is divisible by 9.

6. **Check Each Value**:
- If \( x = 0 \): \( 6 + 0 = 6 \) (not divisible by 9)
- If \( x = 1 \): \( 6 + 1 = 7 \) (not divisible by 9)
- If \( x = 2 \): \( 6 + 2 = 8 \) (not divisible by 9)
- If \( x = 3 \): \( 6 + 3 = 9 \) (divisible by 9)
- If \( x = 4 \): \( 6 + 4 = 10 \) (not divisible by 9)
- If \( x = 5 \): \( 6 + 5 = 11 \) (not divisible by 9)
- If \( x = 6 \): \( 6 + 6 = 12 \) (not divisible by 9)
- If \( x = 7 \): \( 6 + 7 = 13 \) (not divisible by 9)
- If \( x = 8 \): \( 6 + 8 = 14 \) (not divisible by 9)
- If \( x = 9 \): \( 6 + 9 = 15 \) (not divisible by 9)

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

### Final Answer:
The value of \( x \) is \( 3 \).

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