WAEC 2019 · Paper 1 · Q5

If $7 + y \equiv 4 \pmod 8$ , find the least value of $y$ with $10 \le y \le 30$ .

Worked solution (try it first)

Take 7 from both sides: $y \equiv 4 - 7 = -3 \pmod 8$ .
Add 8 to make it positive: $y \equiv 5 \pmod 8$ , so $y$ is one of 5, 13, 21, 29, ….
The least of these with $10 \le y \le 30$ is 13, option B.