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 4, it must be divisible by 8.
(d)If a number is divisible by 8, it must be divisible by 4.
(e)A number is divisible by 18, if it is divisible by both 3 and 6.
(f)If a number is divisible by both 9 and 10, it must be divisible by 90.

Explanation

(a) False as `6` is divisible by `3`, but not by `9`.
(b) True, as `9 = 3 xx 3` Therefore, if a number is divisible by `9`, then it will also be divisible by `3`.
(c) False as `12` is divisible by `4`, but not by `8`.
(d) True, as `8 = 2 xx 4` Therefore if a number is divisible by `8`, then it will also be divisible by `2` and `4`.
(e) False as `30` is divisible by `3` and `6` both, but it is not divisible by `18`.
(f) True as `9 xx10 = 90 `Therefore, If a number is divisible by `9` and `10` both, then it will also be divisible by `90`.