Question

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

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

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

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

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

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

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

Answer 1

Statements: (i),(ii),(iii),(iv),(vi),(vii) are true (correct me if I am wrong somewhere)

Answer 2

Answer:

(1) no , if a number is divisible by 3 it not must be divisible by9

(2)yes , if a number divisible 9 it is must be divisible by 3

(3)no,if a number is divisible by 18 it not must be divisible by both 3 and 6

(4)no,if a number is divisible by 10 and 9 it not must be divisible by 90

(5)no

(6)