real analysis - Baire application to sequence of functions

Let $\{f_k\}$ be a sequence of continuous functions $f_k:\mathbb{R} \mapsto [0,\infty).$
Which of those statements can be true? (Not simultaneously)

1) The sequence $\{f_k\}$ is not bounded iff $x$ is in $\mathbb{Q}$

2) The sequence $\{f_k\}$ is not bounded iff $x$ is not in $\mathbb{Q}$

3) $\lim_{k \to \infty} f_k (x)= \infty$ iff $x$ is not in $\mathbb{Q}$

Hint: use Baire theorem.
I have no clue how to approach this problem.