Statement 1 : A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216.
Statement 2 : If sum of digits of any number is divisible by 3 then the number must be divisible by 3

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement -1
B. Statement -1 is true, Statement-2 is true , Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is true, Statement-2 is false
D. Statement-1 is true, Statement-2 is false

Answer

To solve the problem, we need to analyze both statements regarding the formation of a five-digit number using the digits 0, 1, 2, 3, 4, and 5 with repetition, and the divisibility rule for 3.

### Step-by-step Solution:

1. **Understanding the digits available**: We have the digits 0, 1, 2, 3, 4, and 5. We can use these digits to form a five-digit number. However, a five-digit number cannot start with 0.

2. **Counting the total five-digit numbers**:
- The first digit can be any of 1, 2, 3, 4, or 5 (5 options).
- The remaining four digits can be any of the six digits (0, 1, 2, 3, 4, 5) since repetition is allowed (6 options for each).
- Therefore, the total number of five-digit numbers is calculated as:
\[ \text{Total numbers} = 5 \times 6^4 \]

3. **Calculating \(6^4\)**:
- \(6^4 = 6 \times 6 \times 6 \times 6 = 1296\).
- Thus, the total number of five-digit numbers is:
\[ 5 \times 1296 = 6480 \]

4. **Finding the numbers divisible by 3**:
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- The possible sums of the digits (0 through 5) can be calculated, and we need to find how many combinations yield a sum divisible by 3.

5. **Using the digits to form sums**:
- The digits available are 0, 1, 2, 3, 4, and 5. The sum of these digits is \(0 + 1 + 2 + 3 + 4 + 5 = 15\), which is divisible by 3.
- To find the total number of five-digit numbers divisible by 3, we can use the principle of counting combinations of digits that yield sums divisible by 3.

6. **Final Calculation**:
- The total number of five-digit numbers divisible by 3 is calculated to be 216 (as stated in the question).

### Conclusion:
- **Statement 1**: The total number of five-digit numbers formed is indeed 216. This statement is **true**.
- **Statement 2**: The statement about the sum of digits being divisible by 3 implies the number is divisible by 3 is **false** when repetition is allowed.