The values of y for which the 4-digit number 51y3 is divisible by 9 is

Options

A. 2 or 3
B. 0 or 9
C. 0 or 3
D. 3 or 9

Answer

To determine the values of \( y \) for which the 4-digit number \( 51y3 \) 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: Identify the digits of the number
The digits of the number \( 51y3 \) are:
- 5
- 1
- \( y \)
- 3

### Step 3: Calculate the sum of the digits
Now, we will sum the digits:
\[ 5 + 1 + y + 3 \]
Calculating the constant part:
\[ 5 + 1 + 3 = 9 \]
So, the sum becomes:
\[ 9 + y \]

### Step 4: Set up the condition for divisibility by 9
For \( 51y3 \) to be divisible by 9, the sum \( 9 + y \) must also be divisible by 9.

### Step 5: Determine the values of \( y \)
Since \( 9 \) is already divisible by 9, \( y \) must be such that \( y \) itself is divisible by 9. The possible values for \( y \) (which is a single digit) are:
- \( y = 0 \)
- \( y = 9 \)

### Conclusion
Thus, the values of \( y \) for which the 4-digit number \( 51y3 \) is divisible by 9 are:
\[ y = 0 \quad \text{and} \quad y = 9 \]

---