The number of cycles needed to execute the following loop in pipeline processor?
Certainly it would be common for a pipeline stage to stall until the next stage is available, but there is no reason a CPU couldn't arrange to have buffers between stages that were independent of either stage. The logic would be harder, but as it could gain a cycle advantage in the situation shown it may be worth doing so. 

As to whether the given answer is correct, IMO either should be accepted, unless the syllabus specifies one behavior or the other as correct. I do not know anything about the syllabus mentioned, so can't comment on that.