Final answer:
The prefrontal cortex is correlated with test scores and grey matter density and it is involved in cognitive tasks like memory, language, and judgment.
Step-by-step explanation:
The area of the brain correlated with test scores and grey matter density is the prefrontal cortex. This region is heavily involved in cognitive functions such as memory, language, and judgment. Based on studies using brain imaging techniques such as positron emission tomography (PET) scans and functional magnetic resonance imaging (fMRI), the prefrontal cortex has been shown to be more active during tasks that require semantic processing (identifying if a noun is living or non-living) compared to simple perceptual tasks (looking for the letter 'a' in words). Subsequent recall was also better for the semantic task. Similarly, other regions of the cerebral cortex are involved in integrating sensory information, activating motor functions, and supporting complex cognitive activities.