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Do all the test takers listen to the IELTS test at the same time?
Do we get some break in between the different test sections? for example, time gap between Reading and Listening?

Please answer my questions at the earliest possible.

Yes, all test takers listen at the same time.

There is no break between the writing, reading and listening portions of the exam. Most speaking exams should be at a different time but that depends on the institution organizing the exam.