What literary device involves the use of exaggerated statements that should not be taken literally?

The use of exaggerated statements that should not be taken literally is known as hyperbole. This literary device is employed to create a strong impression, evoke emotions, or emphasize a point through exaggeration. For instance, saying "I'm so hungry I could eat a horse" clearly highlights a sense of extreme hunger without intending for it to be taken as a factual statement. Hyperbole allows writers to convey feelings and situations in a dramatic and imaginative way, which can engage the reader's attention and reinforce the point being made.

Metaphor and simile serve to create comparisons, but they do so without exaggeration. A metaphor implies a direct comparison between two unlike things, while a simile explicitly uses "like" or "as" for comparison. Personification attributes human qualities to non-human entities, but it does not involve exaggeration. Hyperbole stands out as the device specifically characterized by its extreme and non-literal nature, making it the correct answer in this context.