Final answer:
The rapid fluctuations of quasars indeed imply that they must be very small, as the region generating these rapid changes in brightness must be sufficiently compact to allow for such quick variations observable from Earth.
Step-by-step explanation:
The statement that rapid fluctuations of quasars show that the objects must be very small is True. The time variability of quasars is indeed a result of the compactness of the region where the energetic emissions occur. For instance, if a quasar's light output changes significantly in a very short period, like a second, and remains so for some time, this implies that the region producing that light must be small because the light, which travels at a fixed speed, could not cover a large distance in such a short time. Light travel time constraints mean that for the variations we observe to happen so quickly, the emitting region must be correspondingly small, often not much larger than our own solar system. This is supported by the observation that in the X-ray band, quasars variable even more rapidly, indicating the radiation comes from an even tighter region, likely around a black hole.