Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.

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Solution

(i) False, it is not necessary that it must be divisible by 9. (0.5 marks)
(ii) True. (0.5 marks)
(iii) False, it is not necessary that it must be divisible by 8. (0.5 marks)
(iv) True. (0.5 marks)
(v) False, it must be divisible by 9 and 2 both. (0.5 marks)
(vi) True. (0.5 marks)

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Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

If a number is divisible by $9$ and $10$ both, then it must be divisible by $90 .$

If a number is divisible by $3$ , it must be divisible by $9$ .

Q. Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.

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(i) False, it is not necessary that it must be divisible by 9. (0.5 marks) (ii) True. (0.5 marks) (iii) False, it is not necessary that it must be divisible by 8. (0.5 marks) (iv) True. (0.5 marks) (v) False, it must be divisible by 9 and 2 both. (0.5 marks) (vi) True. (0.5 marks)

(i) False, it is not necessary that it must be divisible by 9. (0.5 marks)
(ii) True. (0.5 marks)
(iii) False, it is not necessary that it must be divisible by 8. (0.5 marks)
(iv) True. (0.5 marks)
(v) False, it must be divisible by 9 and 2 both. (0.5 marks)
(vi) True. (0.5 marks)