WAEC Mathematics 2014 Paper

Concept:In modular arithmetic, two numbers are equal modulo $m$ if their difference is exactly divisible by $m$.Explanation:First, compute the left-hand side of the given statement: $9 + 8 = 17$.For the statement $9 + 8 = 5$ to be true in some modulus $m$, we need $17 \equiv 5 \pmod{m}$.This congruence means that $m$ must divide the difference $17 - 5$.Calculate the difference: $17 - 5 = 12$.Therefore, the required modulus is the number that divides $12$ exactly.Among the given options, only $m = 12$ makes this true, because $12 \div 12 = 1$ with remainder $0$.Thus, $17 \equiv 5 \pmod{12}$, so $9 + 8 = 5$ holds in modulo $12$.Answer:The correct option is C. mod $12$.