Dealing with remainders

[Rabbitaoy]

I often run into problems that deal with remainders.

say if the problem gives you the below two conditions:
1. X divided by 3 gives you a remainder of 5
2. X divided by 7 gives you a remainder of 2

what's the quickest way to find a few possibilities of X?
The way I'm doing it at the moment is by listing out a few possibilities for either condition, and looking for a number that qualifies both conditions. However, this might take a long time.

Thanks a lot.

[Tani]

Given x divided by a has a remainder of b, you can express x as: an + b.

Your example is incorrect because you can never have a remainder greater than the number you are dividing by.

Try this example:

x divided by 7 has a remainder of 1
x divided by 5 has a remainder of 3

7n + 1 = 5m + 3
7n = 5m + 2
n = (5m + 2)/7

Then look for a value of m such that 5M + 2 is an integer. For this problem 1 would work, giving you x = 8; also 8 would work, giving you x = 43.