MathNet 2006 — Part 03 Question 135

Suppose $A = \{x \mid 5x - a \le 0\}$, $B = \{x \mid 6x - b \gt 0\}$, $a, b \in \mathbb{N}$, and $A \cap B \cap \mathbb{N} = \{2, 3, 4\}$. The number of such pairs $(a, b)$ is ( ).