Yeah I saw your post... the explanations didn't really help me that much. It was a lot to digest

money9111 wrote:I came across this question from a friend and we're both at a loss.

(x/11) = y with remainder 3
(x/19) = y with remainder 3

What is the remainder when y/19.

My question is... how do you figure this out? What is this question really asking? These types of questions are my weakness (for now) and I'd really like to conquer them.

Thank you,
Richard

As always, start by analyzing the problem.

We're told that when you divide x by 11, you get quotient y and remainder 3; when you divide x by 19, you get the same quotient and the same remainder.

How can a number give the same quotient and remainder when divided by two different numbers? The only possibility is that the quotient is 0.

(3/11 = 0 rem3; 3/19 = 0 rem3)

So, we know that y=0.

Now we're ready for the question:

what's the remainder when 0 is divided by 19? 0!