The values of y for which the 4 digit nuinber 60 y3 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 \( 60y3 \) is divisible by 9, we can follow these steps:

### Step 1: Understand the Rule for Divisibility by 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 \( 60y3 \) are:
- 6
- 0
- \( y \)
- 3

### Step 3: Calculate the Sum of the Digits
Now, we need to calculate the sum of these digits:
\[ 6 + 0 + y + 3 = 9 + y \]

### Step 4: Set Up the Condition for Divisibility
For \( 60y3 \) to be divisible by 9, the sum \( 9 + y \) must be divisible by 9.

### Step 5: Analyze the Expression
The expression \( 9 + y \) can be simplified:
- If \( y = 0 \), then \( 9 + 0 = 9 \) (divisible by 9)
- If \( y = 9 \), then \( 9 + 9 = 18 \) (divisible by 9)
- If \( y = 1, 2, 3, 4, 5, 6, 7, 8 \), then \( 9 + y \) will not be divisible by 9.

### Step 6: List the Valid Values of \( y \)
From the analysis, the values of \( y \) that make \( 9 + y \) divisible by 9 are:
- \( y = 0 \)
- \( y = 9 \)

### Conclusion
The values of \( y \) for which the number \( 60y3 \) is divisible by 9 are \( 0 \) and \( 9 \).

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