Study the given statements carefully and select the correct option.
Statement - 1:12100332 is divisible by 11.
Statement - 2 : A number is divisible by 8, if the number formed by last two digits of the number is divisible by 8

Options

A. Both Statement-1 and Statement-2 are true.
B. Both Statement-1 and Statement-2 are false
C. Statement-1 is true but Statement-2 is false.
D. Statement-1 is false but Statement-2 is true.

Answer

To determine the correctness of the given statements, we will analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** 12100332 is divisible by 11.

**Rule for divisibility by 11:** A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or divisible by 11.

1. **Identify the digits and their positions:**
- The number is 12100332.
- Positions: 1(1st), 2(2nd), 1(3rd), 0(4th), 0(5th), 3(6th), 3(7th), 2(8th).

2. **Sum of digits in odd positions:**
- Odd positions: 1 (1st), 1 (3rd), 0 (5th), 3 (7th).
- Sum = 1 + 1 + 0 + 3 = 5.

3. **Sum of digits in even positions:**
- Even positions: 2 (2nd), 0 (4th), 3 (6th), 2 (8th).
- Sum = 2 + 0 + 3 + 2 = 7.

4. **Calculate the difference:**
- Difference = |Sum of odd positions - Sum of even positions| = |5 - 7| = 2.

5. **Check if the difference is divisible by 11:**
- 2 is not divisible by 11.

**Conclusion for Statement 1:** The statement is false.

### Step 2: Analyze Statement 2
**Statement 2:** A number is divisible by 8 if the number formed by the last two digits of the number is divisible by 8.

**Rule for divisibility by 8:** A number is divisible by 8 if the last three digits of the number form a number that is divisible by 8.

1. **Identify the last two digits of the number 12100332:**
- Last two digits = 32.

2. **Check if 32 is divisible by 8:**
- 32 ÷ 8 = 4, which is a whole number.

**Conclusion for Statement 2:** The statement is true.

### Final Conclusion
- Statement 1 is false.
- Statement 2 is true.

### Answer
Both statements cannot be true at the same time. Therefore, the correct option is that Statement 1 is false and Statement 2 is true.

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