"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!!