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“Integrates … into a unified narrative” signals breadth and overview. “Synoptic” means providing a comprehensive or general view—exact fit. “Myopic” and “parochial” indicate narrowness; “dogmatic” implies rigid assertion of principles. GRE vocabulary often contrasts scope: broad synthesis vs. narrow focus. Substituting “synoptic” preserves the sentence’s praise for integrative breadth.

For any triangle, the inradius rr satisfies A=rsA = rs, where AA is area and ss is semiperimeter. For a right triangle with legs aa and bb and hypotenuse cc, a quick formula is r=a+b−c2r = \dfrac{a + b - c}{2}. First compute cc: c=92+122=81+144=225=15c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15. Then

r=9+12−152=62=3.r = \frac{9 + 12 - 15}{2} = \frac{6}{2} = 3.

Thus choice B. Alternatively, compute area A=12⋅9⋅12=54A = \frac{1}{2}\cdot 9 \cdot 12 = 54 and semiperimeter s=9+12+152=18s = \frac{9 + 12 + 15}{2} = 18. Then r=A/s=54/18=3r = A/s = 54/18 = 3. Pitfalls include forgetting that for right triangles the incenter lies at distance rr from each side, and mixing up the formula with the circumradius expression. Using the a+b−ca+b-c shortcut is the fastest path on test day.

For five numbers, the median is the 3rd number when ordered. The current list contains 2, 5, 7, 9, and xx. To keep the median at 7, 7 must stay in the middle position; thus xx must be ≥9\ge 9 or ≤5\le 5. Now impose the mean condition: mean 7 implies total sum =5×7=35= 5 \times 7 = 35. The sum of known four numbers is 2+5+7+9=232 + 5 + 7 + 9 = 23. Therefore x=35−23=12x = 35 - 23 = 12. Check ordering: with x=12x=12, the sorted set is 2,5,7,9,122, 5, 7, 9, 12; the median remains 7 and the mean is (2+5+7+9+12)/5=35/5=7(2+5+7+9+12)/5 = 35/5 = 7. Option C is correct. A common error is to choose a value that maintains the median but breaks the mean requirement, or vice versa. Another pitfall is to forget that with an odd count the median is the middle element, not the average of the two middle ones (that only applies to even counts). Always verify both constraints before finalizing the answer.

The editorial claims that tuition cuts caused the 10% rise and generalizes this causal relation universally. This confuses correlation with causation and improperly extrapolates from a single instance to “always.” Option A precisely names both flaws: causal assumption and unwarranted generalization. Option B notes a limitation but doesn’t capture the reasoning error. Option C is irrelevant. Option D introduces a claim not in the argument. On GRE Argument evaluation, look for logical leaps: (1) inferring causation from temporal association, and (2) generalizing without sufficient evidence. Both flaws are present, making A the best choice.

This single-blank Text Completion item hinges on tone and clarity cues. The sentence concedes “themes are complex” but praises the exposition for guiding readers “without confusion.” The blank must convey exceptional clarity. “Pellucid” means transparently clear—exactly the positive counterpart to complexity handled well. “Sententious” suggests moralizing brevity; it says nothing about clarity. “Turgid” means swollen or pompous prose—nearly the opposite of “without confusion.” “Prolix” means tediously wordy, again inconsistent with guidance and lucidity. On GRE Verbal, look for the internal logic: concession (“although complex”) followed by positive evaluation (“admirably … guiding … without confusion”). The correct choice must reconcile that contrast by indicating clarity that overcomes difficulty. A quick paraphrase test—“admirably pellucid”—maps directly onto the stated outcome and eliminates semantic drift. When several choices are negative (turgid, prolix), be wary of picking a merely “academic-sounding” word; the best answer preserves the sentence’s favorable assessment of style and reader experience.