Official Solution: At a museum, all visitors in a certain tour group were either students or teachers. Some visitors rented audio guides, and the rest did not. If 12 students did not rent audio guides, whereas 24 teachers did rent audio guides, how many teachers were in the tour group? Let:
students who rented audio guides \(= x\)
teachers who did not rent \(= y\)

The question asks for the total number of teachers: \(24 + y\).
(1) The number of students who rented audio guides was twice the number of teachers who did not rent audio guides.
This implies \(x = 2y\).

But we still do not know \(y\), so we cannot find \(24 + y\). Not sufficient.
(2) The total number of visitors in the group who rented audio guides was twice the total number of visitors who did not rent audio guides.
This implies:
\(x + 24 = 2(12 + y)\)
\(x = 2y\)

This is exactly the same information as in statement (1). So we still cannot find \(y\), and therefore we cannot find the total number of teachers. Not sufficient.
(1) + (2) Together, the two statements still give only \(x = 2y\). So the total number of teachers, \(24 + y\), still cannot be determined. Not sufficient.
Answer: E