N is a positive integer. When N is divided by 3, the remainder is 2. When N is divided by 4, the remainder is 1. What is the remainder when N is divided by 12?

The easiest way to do this is to just look at numbers that fit, find a common one and then see what it is mod12

N=3K+2

so N = 2,5,8,11,14,17,20 etc

N=4G+1

so N = 1,5, etc

find a number that is in both lists.