Question

How do you solve 'If x/5 and x/9 are both positive integers, which of the following must also be an integer?
A: x/40 B: x/25 C: x/18 D: x/15 E: x/10
i'm not sure how to solve this :c

Answer 1

I would say A

Answer 2

why? o:

Answer 3

If x is divisible by five and by nine, then it's divisible by their product, which is 45. But 45 is 15 * 3, so if it's divisible by 45 it's certainly divisible by 15.

Answer 4

ohh, so it's x/15?

Answer 5

If x/5 is an integer, then we can write that x = 5*y, where y is an integer.

if x/9 = 5*y/9 is an integer, than we can write y = 9z, where z is also an integer. Thus,

x = 5*9*z = 45 z, where z is an integer.

So x / 15 = 3 z, which must surely be an integer.

Yes, to answer your question.

Answer 6

thanks (: i get it