Question

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.

Answer 1

(i) False. 12 is divisible by 3 but not by 9.
(ii) True.
(iii) False. 20 is divisible by 4 but not by 8.
(iv) True.
(v) False. 12 is divisible by both 3 and 6 but it is not divisible by 18.
(vi) True.
(vii) False. 10 divides the sum of 18 and 2 (i.e., 20) but 10 divides neither 18 nor 2.
(viii) True.
(ix) False. 4 and 9 are co-primes and both are composite numbers.
(x) True.