Question

A number is divisible by 18 if it is an even number divisible by 9. True or false. Please give a counterexample if it is FALSE

Answer 1

It is true. Let's walk through a few multiples of 9.

9 x 1 = 9
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45
...
9 x 115 = 1035
9 x 116 = 1044

As you can see, when you multiply two odd numbers, your product is also negative. A negative number cannot be divisible by 18 because 18 is even. However, all even multiples of 9 WILL be divisible by 18 because when you multiply 9 by the next even number, you are really just adding 18 each time.

Answer 2

TRUE.
The even multiples of 9 are 18,36,54,72,90,108. These are all divisible by 18. The odd multiples, 9,27,45,63,81,99 etc are not divisible by 18.