Perspicacious: having a keen mental understanding or perception; shrewd; astute; discerning.
Perspicacity: keen mental understanding or perception; shrewdness; astuteness.
Note: Do not confuse perspicacious with perspicuous or perspicacity with perspicuity. Consider the following discussion:
If you display perspicacious qualities, you appear to have good judgment; you are perceptive, and therefore you have perspicacity. If you display perspicuous qualities, you are clear of statement, lucid; you make things clear, and hence you have perspicuity. These relatively low frequency pairs may be hard to keep distinct, but there are those who will fault you for confusing them: look them up rather than risk using them inaccurately, or choose instead some words you understand.
—Kenneth G. Wilson The Columbia Guide to Standard American English (1993)