I have this GRE question that I'd like to know how to solve. I want to solve it in as simple a way as possible, since it is GRE material. In particular, I don't want to use "congruences" or modulo arithmetic that I came across in other posts.
Here it is:
When the positive integer $n$ is divided by $3$ the remainder is $2$. When it is divided by $5$, the remainder is $1$. What is the least possible value of $n$?
Here's my effort: $$n=3q_1+2\tag1$$ $$n=5q_2+1\tag1$$
Great! I now have 2 equations and 3 unknowns. Can someone help me out please? Thanks. (I can imagine going through all positive integers and plugging them in to find the appropriate integer, but that seems rather trivial and inelegant. Is there another way?)