The Logic: Look for the Pivot
The key to this sentence is the word "abstracted."
- Definition: In this context, "abstracted" means preoccupied, distracted, or not paying attention.
- The Contrast: The sentence notes that the solution was "really interesting," but because the teacher was distracted, her evaluation didn't reflect that quality.
- The Goal: We need two words that describe an evaluation done without care, depth, or attention.

The Correct Answers:
B. cursory
E. perfunctory
- Why they work: Both words describe something done quickly, with minimum effort, and without interest or care. A "cursory" glance is a quick, superficial one; a "perfunctory" action is one carried out as a matter of routine without real thought. Both perfectly match the behavior of someone who is "abstracted."

Why the others fail:
- A. philosophical: This implies a deep, academic, or theoretical approach-the opposite of being distracted.
- C. detailed and D. considered: These are "trap" opposites. They describe a thorough evaluation, which is what the student's "interesting solution" deserved, but not what the "abstracted" teacher actually gave.
- F. tangential: While this means "diverging" or "irrelevant," it doesn't quite capture the lack of depth implied by being distracted in the same way that "cursory" and "perfunctory" do.