"When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A. 11

B. 9

C. 7

D. 6

E. 4

I know the answer is 9 and I understand it has common divisibility with 45 and 18 but I’m wondering the takeaway method for this problem. What strategy can I apply here that would also work for other remainder problems? @gregmat does pattern recognition but I can’t work to work it out here, please help!

Start by listing out some possible values of n:

18

63

108

153

198

You notice that you are basically adding 45 each time

So, n can be written as 18 + 45x

Does this help?

I did actually set up an equation like that but what do you do after that? Plug in all your possible values of n and solve for x?

No if you have arrived at this equation, then you can write it as:

9(2 + 5x)

So, all possible values of n would be divisible by 9

ooohhhh, nicceee. I had a lightbulb moment!! Thank you!!