Final answer:
The parasympathetic (option 3) nervous system is the division with a long preganglionic neuron and a short postganglionic neuron, responsible for 'rest and digest' functions.
Step-by-step explanation:
The division that has a long preganglionic neuron synapsed with a short postganglionic neuron is the parasympathetic nervous system. The parasympathetic division is part of the autonomic nervous system and it is responsible for the 'rest and digest' functions of the body. The preganglionic parasympathetic neurons are long because they extend from the brainstem or the sacral region of the spinal cord to the ganglia located near or within the target organs. In contrast, preganglionic sympathetic neurons are shorter and often synapse in a ganglion relatively close to the spinal cord, followed by a longer postganglionic axon that reaches the target organ.
The sympathetic division, known as the 'fight or flight' system, prepares the body for quick responses to threats. This system has relatively short preganglionic axons and much longer postganglionic axons. In comparison, the preganglionic parasympathetic neurons have a long path, while the postganglionic parasympathetic neurons cover a shorter distance to reach the effector organs.