Question

State true or false:
(i) If a number is divisible by 3 then it is also divisible by 9.
(ii) If a number is divisible by 8 then it is also divisible by 4.
(iii) If a number is divisible by 12 then it is divisible by both 3 and 4.
(iv) If sum of two consecutive odd numbers in always divisible by 4.
(v) If two numbers are co-prime at least one of them must be a prime number.​

Answer 1

Which of the following statements are true?

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

$\bf{False.}$ We can prove it with the help of an example. 12 is divisible by 3 but it is not divisible by 9.

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

$\bf{True.}$ If a given number is divisible by some number then it is also divisible by its factor.

(c) A number is divisible by 18, if it is divisible by both 3 and 6.

$\bf{False.}$ 12 is divisible by both 3 and 6 but it is not divisible by 18.

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

$\bf{True.}$ This is because if a number is divisible by two given co-prime numbers then it is also divisible by their product. We know that 9 and 10 are co-primes and their product is equal to 90.

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

$\bf{False.}$ Take an example, 8 and 9 are co-prime numbers and none of them is a prime number.