If the number `243 x 51` is divisible by 9 then the value of the digit marked as `x` would be:

Options

A. 3
B. 1
C. 2
D. 4

Answer

To determine the value of the digit marked as `x` in the number `243x51` such that the entire number 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 of the Number**: The number we are working with is `243x51`. The digits are 2, 4, 3, x, 5, and 1.

3. **Calculate the Sum of the Known Digits**:
- Add the known digits together:
\[ 2 + 4 + 3 + 5 + 1 = 15 \]
- So, the sum of the digits including `x` becomes:
\[ 15 + x \]

4. **Set Up the Condition for Divisibility by 9**: We need to find the value of `x` such that:
\[ 15 + x \text{ is divisible by } 9 \]

5. **Check Possible Values for `x`**: The possible values for `x` are 0 through 9. We will check each value to see if it makes `15 + x` divisible by 9.

- For `x = 0`:
\[ 15 + 0 = 15 \quad (\text{not divisible by 9}) \]
- For `x = 1`:
\[ 15 + 1 = 16 \quad (\text{not divisible by 9}) \]
- For `x = 2`:
\[ 15 + 2 = 17 \quad (\text{not divisible by 9}) \]
- For `x = 3`:
\[ 15 + 3 = 18 \quad (\text{divisible by 9}) \]
- For `x = 4`:
\[ 15 + 4 = 19 \quad (\text{not divisible by 9}) \]
- For `x = 5`:
\[ 15 + 5 = 20 \quad (\text{not divisible by 9}) \]
- For `x = 6`:
\[ 15 + 6 = 21 \quad (\text{not divisible by 9}) \]
- For `x = 7`:
\[ 15 + 7 = 22 \quad (\text{not divisible by 9}) \]
- For `x = 8`:
\[ 15 + 8 = 23 \quad (\text{not divisible by 9}) \]
- For `x = 9`:
\[ 15 + 9 = 24 \quad (\text{not divisible by 9}) \]

6. **Conclusion**: The only value of `x` that makes `15 + x` divisible by 9 is `x = 3`.

### Final Answer:
The value of the digit marked as `x` is **3**.

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