Which ofthe following statements are true?
(a) If anumber is divisible by 3, it must be divisible by 9.
(b) If anumber is divisible by 9, it must be divisible by 3.
(c) Anumber is divisible by 18, if it is divisible by both 3 and 6.
(d) If anumber is divisible by 9 and 10 both, then it must be divisible by90.
(e) If twonumbers are co-primes, at least one of them must be prime.
(f) Allnumbers which are divisible by 4 must also be divisible by 8.
(g) Allnumbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it mustexactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it mustexactly divide the two numbers separately.

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Solution

(a) False
6 is divisible by 3, but not by 9.
(b) True,as 9 = 3 Ã— 3
Therefore, if a number is divisible by 9, then it will also bedivisible by
3.
(c) False
30 is divisible by 3 and 6 both, but it is not divisible by 18.
(d) True,as 9 Ã— 10 = 90
Therefore, if a number is divisible by 9 and 10 both, then it willalso be divisible by 90.
(e) False
15 and 32 are co-primes and also composite.
(f) False
12 is divisible by 4, but not by 8.
(g) True,as 8 = 2 Ã— 4
Therefore, if a number is divisible by 8, then it will also bedivisible by 2 and 4.
(h) True
2 divides 4 and 8 as well as 12. (4 + 8 = 12)
(i) False
2 divides 12, but does not divide 7 and 5.

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Similar questions

Which of the following statements are true?

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

(b) If a number is divisible by 9, it must be divisible by 3.

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

(e) If two numbers are co-primes, at least one of them must be prime.

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their sum.

(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Question 1

Which of the following statements are true:
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) If a number is divisible by 18, it must be divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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.

Q. 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 numbers exactly, it must exactly divide the numbers 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 numbers is always divisible by 4.
(viii) If a number divides two numbers exactly, it must divide their sum exactly.

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