Problem

Source:  Kosovo Math Olympiad 2025, Grade 7, Problem 4

Tags: remainder, number theory, Kosovo, national olympiad



When a number is divided by $2$ it has quotient $x$ and remainder $1$. Whereas, when the same number is divided by $3$ it has quotient $y$ and remainder $2$. What is the remainder when $x+y$ is divided by $5$?