WAEC Mathematics 2018 Paper

Concept:We need the smallest positive integer $x$ that satisfies the modular equation $3x \equiv 4 \pmod{5}$.Explanation:For a number to be congruent to $4 \pmod{5}$, it must leave a remainder of $4$ when divided by $5$.Check the possible values of $x$ from the options.For $x = 1$, $3x = 3$, and $3 \equiv 3 \pmod{5}$, not $4$.For $x = 2$, $3x = 6$, and $6 \equiv 1 \pmod{5}$, not $4$.For $x = 3$, $3x = 9$, and $9 \equiv 4 \pmod{5}$.Since $x = 3$ works and is smaller than $x = 4$, it is the least required value.Alternatively, multiply both sides by the modular inverse of $3$ modulo $5$, which is $2$, giving $x \equiv 8 \equiv 3 \pmod{5}$.Answer:$x = 3$, which corresponds to Option C.