What is the minimum value of 'Y' for which 267Y2 is divisible by 3?
A. 2
B. 1
C. 0
D. 5

Options

A. C
B. A
C. D
D. B

Answer

To find the minimum value of 'Y' for which the number 267Y2 is divisible by 3, we can follow these steps:

### Step 1: Understand the divisibility rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3.

**Hint:** Remember that the sum of the digits must be a multiple of 3.

### Step 2: Identify the digits of the number
The digits of the number 267Y2 are 2, 6, 7, Y, and 2.

**Hint:** Write down all the digits clearly to avoid confusion.

### Step 3: Calculate the sum of the known digits
Add the known digits together:
- 2 + 6 + 7 + 2 = 17

**Hint:** Make sure to add all the digits correctly.

### Step 4: Include 'Y' in the sum
Now, the total sum of the digits becomes:
- Sum = 17 + Y

**Hint:** This sum must be checked for divisibility by 3.

### Step 5: Find the nearest multiple of 3
The nearest multiple of 3 that is greater than or equal to 17 is 18.

**Hint:** List out the multiples of 3 to find the nearest one.

### Step 6: Set up the equation
We need:
- 17 + Y = 18 (the nearest multiple of 3)

**Hint:** This will help you find the minimum value of Y.

### Step 7: Solve for 'Y'
Subtract 17 from both sides:
- Y = 18 - 17
- Y = 1

**Hint:** Ensure that you perform the subtraction correctly.

### Step 8: Conclusion
The minimum value of 'Y' for which 267Y2 is divisible by 3 is **1**.

**Final Answer:** B. 1