2007/08 AHSMC Part 1 Problem 14

The number of incorrect answers for each of questions $1$ and $6$ is $0$ or $5$. The number of incorrect answers for each of questions $2$ and $5$ is $1$ or $4$. The number of incorrect answers for each of questions $3$ and $4$ is $2$ or $3$. A total of $8$ incorrect answers can only be made up from $0+1+3+3+1+0$. However, we would have an equal number of incorrect answers of T and incorrect answers of F. Hence the total must be $9$, and it can be made up from either $0+1+2+2+4+0$ or $0+4+2+2+1+0$. However, the latter yields more incorrect answers of F than incorrect answers of T. It follows that the correct answers for the six questions are F, F, F, T, F and T respectively. Only student $\#4$ has both an incorrect answer of T (for question $5$) and an incorrect answer of F (for question $4$). The answer is (D).