1. The Logic Structure :
- The Clue: The second half of the sentence (the support clause) describes Blake as "intellectually formidable" and "exceptionally resilient" (tough). These traits are the direct opposites of "fragility" or "weakness."
- The Inference: If the reality of his character is strength, then the "reputation" for weakness must be false, unfounded, or misleading.
- Selection: Spurious (A). This is a high-frequency GRE word meaning "not being what it purports to be; false or fake." It perfectly labels a reputation that contradicts the facts.

2. Evaluating the Choices :
- A. spurious: (Correct) False or fake. If the reputation is spurious, the claim of "fragility" is debunked by the evidence of his "resilience."
- B. pervasive: (Thematic Trap) Means spreading widely throughout an area or a group. While a reputation can be pervasive, this word ignores the logical contradiction set up by the colon. It describes the reach of the reputation, not its accuracy.
- C. intractable: (Category Trap) Means hard to control or deal with. This is a "highregister" distractor; while a reputation might be hard to change, the sentence is focused on whether the reputation is true.
- D. negligible: (Logic Trap) Means so small or unimportant as to be not worth considering. The reputation is "chronic" (long-lasting), so it is not "negligible" (minor); it is simply "incorrect."
- E. ambivalent: (Category Trap) Means having mixed feelings or contradictory ideas. A "reputation" itself cannot be ambivalent; only the people holding the reputation can be.