Write (T) for true and (F) for false against each of the following statements :
(i) If a number is divisible by 4. it must be divisible by 8 .
(ii) If a number is divisible by 8 . it must be divisible by 4 .
(iii) If a number divides the sum of two number exactly. it must exactly divide the num .bers separately.
(iv) If a number is divisible by both 9 and 10 . it must be divisible by 90.
(v) A number is divisible by 18 if it is divisible by both 3 and 6 .
(vi) If a number is divisible by 3 and 7 . it must be divisible by 21.
(vii) The sum of two consecutive odd number is always divisible by 4 .
(viii) If a number divides two number exactly. it must divide their sum exactly.

Answer

To solve the question, we will evaluate each statement one by one and determine if they are true (T) or false (F).

### Step-by-Step Solution:

1. **Statement (i)**: If a number is divisible by 4, it must be divisible by 8.
- **Evaluation**: This statement is **False (F)**. For example, the number 4 is divisible by 4 but not by 8.

2. **Statement (ii)**: If a number is divisible by 8, it must be divisible by 4.
- **Evaluation**: This statement is **True (T)**. Since 8 is a multiple of 4 (8 = 4 x 2), any number divisible by 8 will also be divisible by 4.

3. **Statement (iii)**: If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
- **Evaluation**: This statement is **False (F)**. For example, consider the numbers 4 and 8. The sum is 12, which is divisible by 3, but neither 4 nor 8 is divisible by 3.

4. **Statement (iv)**: If a number is divisible by both 9 and 10, it must be divisible by 90.
- **Evaluation**: This statement is **True (T)**. The least common multiple (LCM) of 9 and 10 is 90, so any number divisible by both must also be divisible by 90.

5. **Statement (v)**: A number is divisible by 18 if it is divisible by both 3 and 6.
- **Evaluation**: This statement is **False (F)**. For example, the number 12 is divisible by both 3 and 6 but not by 18.

6. **Statement (vi)**: If a number is divisible by 3 and 7, it must be divisible by 21.
- **Evaluation**: This statement is **True (T)**. Since 21 is the product of 3 and 7 (3 x 7 = 21), any number divisible by both must be divisible by 21.

7. **Statement (vii)**: The sum of two consecutive odd numbers is always divisible by 4.
- **Evaluation**: This statement is **True (T)**. For example, the consecutive odd numbers 5 and 7 sum to 12, which is divisible by 4.

8. **Statement (viii)**: If a number divides two numbers exactly, it must divide their sum exactly.
- **Evaluation**: This statement is **True (T)**. If a number divides two numbers, it will also divide their sum.

### Final Answers:
- (i) F
- (ii) T
- (iii) F
- (iv) T
- (v) F
- (vi) T
- (vii) T
- (viii) T