Vishvamitra has some guavas of same shape, size and colour . He wants to distribute them equally among some of his chosen disclples. In order to do this he can cut a guava into uniform pieces only . Which of the following statements is /are false ?
(i) He can divide 7 guavas equally among his 12 disciples, such that no any guava is cut into more then 6 pieces.
(ii) He can divide 6 guavas equally among his 12 disciples, such that no any guava is cut into more then 3 pieces.
(iii) He can divide 11 guavas equally among his 15 disciples, such that no any guava is cut into more then 6 pieces.
(iv) He can divide 7 guavas equally among his 15 disciples, such that no any guava is cut into more then 6 pieces.

Options

A. (i)
B. (ii)
C. (iii)
D. (iv)

Answer

To solve the problem, we need to analyze each statement one by one to determine whether it is true or false based on the conditions given.

### Step-by-Step Solution:

1. **Statement (i)**: He can divide 7 guavas equally among his 12 disciples, such that no guava is cut into more than 6 pieces.
- Total pieces possible = 7 guavas × 6 pieces/guava = 42 pieces.
- Each disciple would get = 42 pieces ÷ 12 disciples = 3.5 pieces.
- Since 3.5 is not a whole number, this statement is **false**.

2. **Statement (ii)**: He can divide 6 guavas equally among his 12 disciples, such that no guava is cut into more than 3 pieces.
- Total pieces possible = 6 guavas × 3 pieces/guava = 18 pieces.
- Each disciple would get = 18 pieces ÷ 12 disciples = 1.5 pieces.
- Since 1.5 is not a whole number, this statement is **false**.

3. **Statement (iii)**: He can divide 11 guavas equally among his 15 disciples, such that no guava is cut into more than 6 pieces.
- Total pieces possible = 11 guavas × 6 pieces/guava = 66 pieces.
- Each disciple would get = 66 pieces ÷ 15 disciples = 4.4 pieces.
- Since 4.4 is not a whole number, this statement is **false**.

4. **Statement (iv)**: He can divide 7 guavas equally among his 15 disciples, such that no guava is cut into more than 6 pieces.
- Total pieces possible = 7 guavas × 6 pieces/guava = 42 pieces.
- Each disciple would get = 42 pieces ÷ 15 disciples = 2.8 pieces.
- Since 2.8 is not a whole number, this statement is **false**.

### Conclusion:
All statements (i), (ii), (iii), and (iv) are false.