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For a linear function f(x)=mx+bf(x)=mx+b, slope m=17−56−2=124=3m = \dfrac{17-5}{6-2} = \dfrac{12}{4} = 3. Use a point to solve for bb: 5=3⋅2+b⇒b=−15 = 3\cdot2 + b \Rightarrow b = -1. Hence f(x)=3x−1f(x) = 3x - 1. Evaluate at 10: f(10)=3⋅10−1=29f(10) = 3\cdot10 - 1 = 29. Option C is correct. This problem assesses modeling with linear functions and interpreting rate of change, central GRE Quant objectives. An alternative is to notice equal increments: from x=2x=2 to x=6x=6 increases xx by 4 and f(x)f(x) by 12; thus every +1 in xx adds 3 to f(x)f(x). From x=6x=6 to x=10x=10 is another +4, so add 12 to 17 → 29. This “slope as unit rate” view is often faster than writing equations. Beware of arithmetic slips when computing slope or intercept; verify by substituting both given points into your final linear expression. Linear modeling shows up in tables, graphs, and word problems; practice shifting among representations (points, equation, rate description) to improve speed and accuracy.

For any triangle, inradius r=Asr = \dfrac{A}{s}, where AA is area and ss is semiperimeter. For a right triangle, a convenient formula is r=a+b−c2r = \dfrac{a + b - c}{2}, where aa and bb are legs and cc is the hypotenuse. Compute cc via Pythagoras: c=62+82=36+64=10c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = 10. Then r=(6+8−10)/2=4/2=2r = (6 + 8 - 10)/2 = 4/2 = 2. Option B is correct. Alternatively, compute area A=12⋅6⋅8=24A = \frac{1}{2}\cdot 6 \cdot 8 = 24 and perimeter P=6+8+10=24P = 6 + 8 + 10 = 24, so semiperimeter s=12s = 12. Then r=A/s=24/12=2r = A/s = 24/12 = 2. This problem targets GRE geometry fundamentals: right triangles, Pythagorean triples (6-8-10), and circle–triangle relationships. Common errors include mixing up inradius with circumradius (for a right triangle, circumradius =c/2=5= c/2 = 5, not asked) or incorrectly using whole perimeter instead of semiperimeter when applying r=A/sr = A/s. Knowing multiple equivalent formulas and confirming results by two methods helps avoid computational mistakes under time pressure.

The conclusion asserts that mandatory overtime → improved delivery times. The cited reason is “more total hours.” For this to ensure faster delivery, added hours must translate into at least proportionally more effective work. If fatigue or burnout reduces productivity per hour, the net output could stagnate or decline despite longer hours. Thus Option A states a necessary assumption: that productivity per hour does not fall enough to offset the increased hours. If A were false, the conclusion becomes doubtful. Option B concerns wages, not delivery speed. Option C contradicts the goal by introducing scope creep that could independently delay delivery, but it is not an assumption the argument relies on. Option D is about stakeholder satisfaction, which could matter contextually but is not logically necessary for the causal claim relating overtime to delivery speed. On assumption questions, ask, “If this were false, would the conclusion collapse?” Fatigue reducing productivity would indeed undermine the argument, so A is necessary.

The conclusion attributes improved attendance to the software. The reasoning fails if users who chose to adopt the software were already more conscientious. The necessary assumption is that the causal factor is the software itself, not preexisting motivation or discipline. Option A states this explicitly. Option B addresses aesthetics, irrelevant to absenteeism. Option C is context without bearing on causality. Option D speaks to cost savings, not attendance. On GRE assumption questions, ask: what must be true for the evidence to guarantee the conclusion? Here, isolating the software as the driver rather than selection bias is indispensable.

The op-ed moves from correlation (neighborhoods with parks ↔ lower stress) to a causal policy prescription (build parks → reduce stress). For this inference to hold, the presence of parks must be the driver of lower stress, not a byproduct of confounding variables (e.g., higher income, better healthcare, lower crime). Option B states that needed causal bridge explicitly. If B is false—if parks merely correlate with other amenities—the policy may fail to produce the intended outcome. Option A speculates about resident preferences but is not required; preferences could vary while causality still holds. Option C compares cost-effectiveness, which is a budgeting concern, not a logical necessity for the claim that parks reduce stress. Option D concerns measurement consistency; while useful for evaluation, it isn’t the key assumption linking cause to effect. On GRE Argument tasks, identify the leap from observation to prescription and articulate the assumption that rules out alternative explanations and ensures the intervention will work as argued.