If the number 517 * 324 is completely divisible by 3, then the smallest whole number in place of * will be:

Options

A. 0
B. 1
C. 2
D. None of these

Answer

To find the smallest whole number in place of * in the number 517 * 324 such that the entire number is divisible by 3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Divisibility Rule for 3**: A number is divisible by 3 if the sum of its digits is divisible by 3.

2. **Set Up the Expression**: Let the digit represented by * be \( x \). The number can be expressed as 517x324.

3. **Calculate the Sum of the Digits**: The sum of the digits in the number 517x324 is:
\[ 5 + 1 + 7 + x + 3 + 2 + 4 = 22 + x \]

4. **Check for Divisibility by 3**: We need \( 22 + x \) to be divisible by 3.

5. **Find the Smallest Whole Number for \( x \)**:
- Start testing whole numbers for \( x \) starting from 0:
- If \( x = 0 \): \( 22 + 0 = 22 \) (not divisible by 3)
- If \( x = 1 \): \( 22 + 1 = 23 \) (not divisible by 3)
- If \( x = 2 \): \( 22 + 2 = 24 \) (divisible by 3)

6. **Conclusion**: The smallest whole number that can replace * and make the number divisible by 3 is \( x = 2 \).

### Final Answer:
The smallest whole number in place of * is **2**.