3. Given the sets $A=\{x \mid 5 x-a \leqslant 0\}, B=\{x \mid 6 x-b>0\}, a, b \in \mathbf{N}$, and $A \cap B \cap \mathbf{N}=$ $\{2,3,4\}$, the number of integer pairs $(a, b)$ is
A. 20
B. 25
C. 30
D. 42
$$
\text { Since }\left(\frac{b}{6}, \frac{a}{5}\right] \cap \mathbf{N}=\{2,3,4\} \Rightarrow\left\{\begin{array} { l } 
{ 1 \leqslant \frac { b } { 6 } < 2 , } \\
{ 4 \leqslant \frac { a } { 5 } < 5 }
\end{array} \Rightarrow \left\{\begin{array}{l}
6 \leqslant b<12 \text {, } \\
20 \leqslant a<25 .
\end{array}\right.\right.
$$

Thus, the number of integer pairs $(a, b)$ that satisfy the condition is 30. Therefore, the answer is $C$.