WAEC Mathematics 2019 Paper

Concept:A congruence $a \equiv b \pmod{8}$ means $a - b$ is divisible by $8$.We need the least value of $y$ in the given range that satisfies the congruence.Explanation:Start with $7 + y \equiv 4 \pmod{8}$.Subtract $7$ from both sides: $y \equiv 4 - 7 \pmod{8}$.This gives $y \equiv -3 \pmod{8}$.Add $8$ to get a positive remainder: $y \equiv -3 + 8 \equiv 5 \pmod{8}$.So $y$ must have the form $y = 5 + 8k$, where $k$ is an integer.Check values in the range $10 \le y \le 30$.For $k = 1$, $y = 5 + 8 = 13$.This is the least value in the range that satisfies the congruence.Answer:$y = 13$Option B.