The correct choice is (E) obsequious.

The Logic Breakdown
- The Keyword: The most important phrase is "calculated flattery."
- The Contrast: The executive informs his staff that he prefers "constructive criticism" over "calculated flattery." This tells us that the employees he is repulsed by are the ones who use flattery to get ahead.
- The Match: Obsequious means obedient or attentive to an excessive or servile degreeessentially, a "teacher's pet" or someone who uses "calculated flattery" to win favor.

Why the others fail:
- (A) Natty: This means "trimly neat and tidy" (usually referring to clothes). While an executive might have opinions on dress code, it has nothing to do with "flattery" or "criticism."
- (B) Profligate: This means "recklessly extravagant or wasteful." There is no mention of money or resources in the prompt.
- (C) Rapacious: This means "aggressively greedy or grasping." While a greedy employee might be repulsive, it doesn't specifically link to the "flattery" clue.
- (D) Sententious: This means "tending to moralize in a pompous or affected manner." This describes someone who gives unwanted advice, which is almost the opposite of someone who uses flattery to please a boss.