Study the given statements carfully and select the correct option .
Statement -I : 7456824 is divisible by 9 .
Statement -II : A natural number is divisible by 9 , if the sum of the digits of the number is divisible by 3 .

Options

A. Both Statement -I and Statement -II are true .
B. Both Statement -I and Statement -II are false
C. Statement -I is true but Statement -II is false
D. Statement -I is false but Statement -II is true .

Explanation

To solve the problem, we need to analyze the two statements provided.

**Step 1: Check Statement I**
- We need to determine if the number 7456824 is divisible by 9.
- According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is divisible by 9.

**Step 2: Calculate the sum of the digits of 7456824**
- Break down the digits: 7, 4, 5, 6, 8, 2, 4.
- Now, add them together:
- 7 + 4 = 11
- 11 + 5 = 16
- 16 + 6 = 22
- 22 + 8 = 30
- 30 + 2 = 32
- 32 + 4 = 36

**Step 3: Check if the sum (36) is divisible by 9**
- Now, we check if 36 is divisible by 9:
- 36 ÷ 9 = 4, which is a whole number.
- Therefore, 36 is divisible by 9.

**Conclusion for Statement I**
- Since the sum of the digits (36) is divisible by 9, Statement I is **True**.

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**Step 4: Check Statement II**
- The statement claims that a natural number is divisible by 9 if the sum of its digits is divisible by 3.
- While it is true that a number divisible by 9 is also divisible by 3, the reverse is not necessarily true.

**Step 5: Find a counterexample**
- Consider the number 12:
- The sum of the digits is 1 + 2 = 3.
- 3 is divisible by 3, but 12 is not divisible by 9 (12 ÷ 9 = 1.33).
- This shows that Statement II is **False**.

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**Final Conclusion**
- Statement I is True, and Statement II is False.

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