If the number 467X4 is divisible by 9, find the value of the digit marked as X.

Options

A. 5
B. 4
C. 7
D. 6

Answer

To determine the value of the digit marked as X in the number 467X4 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 down the digits of the number
The digits of the number 467X4 are 4, 6, 7, X, and 4.

### Step 3: Calculate the sum of the known digits
First, we calculate the sum of the known digits:
- 4 + 6 + 7 + 4 = 21

### Step 4: Include the unknown digit X in the sum
Now, we include the unknown digit X in the sum:
- Total sum = 21 + X

### Step 5: Set up the condition for divisibility by 9
For the number to be divisible by 9, the total sum (21 + X) must be divisible by 9.

### Step 6: Find possible values for X
We can check the values of X (which can be from 0 to 9) to find which makes (21 + X) divisible by 9.

- If X = 0, then 21 + 0 = 21 (not divisible by 9)
- If X = 1, then 21 + 1 = 22 (not divisible by 9)
- If X = 2, then 21 + 2 = 23 (not divisible by 9)
- If X = 3, then 21 + 3 = 24 (not divisible by 9)
- If X = 4, then 21 + 4 = 25 (not divisible by 9)
- If X = 5, then 21 + 5 = 26 (not divisible by 9)
- If X = 6, then 21 + 6 = 27 (divisible by 9)
- If X = 7, then 21 + 7 = 28 (not divisible by 9)
- If X = 8, then 21 + 8 = 29 (not divisible by 9)
- If X = 9, then 21 + 9 = 30 (not divisible by 9)

### Step 7: Conclusion
The only value of X that makes the sum (21 + X) divisible by 9 is X = 6.

Thus, the value of the digit marked as X is **6**.

---