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Factor: x2−4x−5=(x−5)(x+1)x^2-4x-5=(x-5)(x+1). Roots: 5 and -1. Choice B correct. Other pairs miscalculate factors. On PSAT, root-finding often comes from quick factoring.

“Nevertheless” shows concession followed by contrast: although findings are preliminary (caution), they still hold value (usefulness). Choice A captures this nuance. Choice B (“addition”) misreads the function. Choice C suggests repetition, but the sentence presents opposing concepts. Choice D implies causation, not concession. On the PSAT, mastery of transition words requires distinguishing subtle shades: “therefore” = result, “furthermore” = addition, “however/nevertheless” = contrast. Here, the pivot word strengthens the researcher’s claim by balancing caution with significance.

A 30∘–60∘–90∘30^\circ\text{–}60^\circ\text{–}90^\circ triangle has fixed side ratios relative to the hypotenuse: opposite 30∘30^\circ is 12\tfrac{1}{2} the hypotenuse, and adjacent 30∘30^\circ is 32\tfrac{\sqrt{3}}{2} of the hypotenuse. With hypotenuse 1010, the side opposite 30∘30^\circ is 10×12=510 \times \tfrac{1}{2} = 5, choice A. Choice C, 535\sqrt{3}, corresponds to the side adjacent the 30∘30^\circ angle (the longer leg), not the opposite. Choice B is the hypotenuse itself, and D is too large; it never appears as a leg in a 30∘–60∘–90∘30^\circ\text{–}60^\circ\text{–}90^\circ triangle with hypotenuse 10. Alternatively, use sine: sin⁡30∘=12\sin 30^\circ = \tfrac{1}{2}. The opposite side equals sin⁡30∘×hypotenuse=12⋅10=5\sin 30^\circ \times \text{hypotenuse} = \tfrac{1}{2}\cdot 10 = 5. On the PSAT, memorizing special right-triangle ratios (30-60-90 and 45-45-90) yields quick solutions without calculators and reduces algebraic error. Recognizing when a triangle matches these special cases can convert a multi-step trig computation into a one-step ratio application, freeing time for more involved questions elsewhere on the test.

Percent changes compound multiplicatively, not additively. Choose a convenient baseline, e.g., 100 units in 2023. A 20%20\% increase to 2024 multiplies by 1.201.20, yielding 120120. A 25%25\% decrease to 2025 multiplies by 0.750.75, yielding 120×0.75=90120 \times 0.75 = 90. Compared with the original 100100, the final amount is 9090, which is a −10%-10\% change overall. Choice A is correct. Choices B and D come from adding +20%+20\% and −25%-25\% to get −5%-5\% or mistakenly averaging signs, but the correct method is multiplication of growth factors. Choice C (−5%-5\%) is a classic trap from linear (non-compound) thinking. On the PSAT, treat consecutive percent changes as products of factors: 1+r1 + r for increases, 1−r1 - r for decreases (where rr is decimal). This approach also highlights asymmetry: a 25%25\% drop from 120 is 30, which more than offsets the earlier gain of 20 from 100. As a general rule, to “undo” a p%p\% decrease, you need an increase of p100−p×100%\frac{p}{100-p}\times 100\% (e.g., a 25% decrease requires a 33⅓% increase to get back), reinforcing why sequential changes can’t be summed directly.

Add 7: 2x=162x=16. Divide: x=8x=8. Correct: B. Substitution check: 2(8)-7=16-7=9. Works. The answer is 8, not 7. Correct choice B. On PSAT, linear isolation is critical—keep arithmetic precise.