Example 11 (1981 National High School League Question) Given the rectangular parallelepiped $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$, among the following 12 lines: $A B^{\prime} 、 B A^{\prime}$ 、 $C D^{\prime} 、 D C^{\prime} 、 A D^{\prime} 、 D A^{\prime} 、 B C^{\prime} 、 C B^{\prime} 、 A C 、 A^{\prime} C^{\prime} 、 B D 、 B^{\prime} D^{\prime}$, how many pairs of skew lines are there? ( ).
A. 30 pairs
B. 60 pairs
C. 24 pairs
D. 48 pairs
Solution: Choose A. Reason: By decomposition and reduction, the given 12 lines are the diagonals on each face of the rectangular prism $A B C D-A^{\prime} B^{\prime} C^{\prime} D^{\prime}$. First, consider the line $A B^{\prime}$, the diagonals intersecting with it are $A C$, $A D^{\prime}$, $B^{\prime} D^{\prime}$, $B^{\prime} C$, and $A^{\prime} B$, and the diagonals parallel to it are $D C^{\prime}$. Therefore, there are 5 diagonals that are skew to $A B^{\prime}$: $C D^{\prime}$, $A^{\prime} C^{\prime}$, $B D$, $B C^{\prime}$, and $A^{\prime} D$. Similarly, for each diagonal on the faces of the rectangular prism, there are 5 diagonals on the other five faces that are skew to it. Thus, the 12 face diagonals form 60 pairs of skew lines (with repeated calculations). However, in the above counting, each pair of skew lines is counted twice (once for each line), so there are only 30 pairs of skew lines.