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Question 281Question →

Match each causal argument with the specific category of assumption required for its conclusion to logically follow.

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Items

In the decade after Valoria adopted a standardized national curriculum, test scores nationwide increased by 15%. Therefore, the new curriculum directly improved student academic performance.
Surveys indicate that individuals who regularly engage in vigorous physical exercise report significantly fewer symptoms of depression. Clearly, vigorous exercise prevents depressive symptoms.
An analysis of public records shows that municipalities with the highest number of public parks also boast the highest average life expectancies. This demonstrates that access to public parks extends human lifespan.
A consumer group concluded that Brand X's new smartphone battery drains 30% faster than average, based entirely on the complaints submitted to their online forum over the past month. The new battery is therefore fundamentally flawed in its design.

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Answer

The curriculum argument matches with eliminating alternate causes. The exercise argument matches with ruling out reverse causation. The public parks argument matches with assuming no third independent variable. The battery argument matches with assuming sample representativeness.
Each pairing correctly addresses the specific logical gap in the causal argument. The curriculum argument requires eliminating alternate historical causes. The exercise argument must rule out reverse causation. The parks argument must eliminate a common underlying cause. The battery argument must defend its biased sample.

Step-by-Step Solution

1
Analyze the first argument regarding Valoria's curriculum and test scores.
Identifies that a chronological sequence (curriculum introduced, then scores increased) is used to establish direct causation.
To determine the required assumption, which in chronological causal arguments is typically the elimination of alternate concurrent causes.
2
Analyze the second argument regarding exercise and depression.
Identifies a correlation where the cause and effect could easily be swapped (does exercise prevent depression, or does depression prevent exercise?).
To recognize the classic vulnerability of reverse causation in correlational arguments involving human behavior and psychology.
3
Analyze the third argument regarding public parks and life expectancy.
Identifies a correlation between two phenomena that are likely byproducts of a shared demographic characteristic, such as high socioeconomic status.
To spot the flaw of ignoring a third, independent underlying factor causing both elements of the correlation.
4
Analyze the fourth argument regarding battery complaints.
Identifies that the evidence is drawn exclusively from an online complaint forum, which inherently attracts users experiencing problems.
To highlight a biased sample error, where the assumption must defend the representativeness of the data used to claim the causal flaw.

Key Concept

Assumptions in Causal Arguments
Question 282Question →

Match each of the following arguments regarding a city transit authority's transition to electric buses (Left) with the newly discovered piece of evidence (Right) that most effectively strengthens its specific conclusion.

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Items

Since the deployment of electric buses on Route 5, daily passenger volume has increased by 15 percent. Commuters must therefore prefer the quieter, smoother ride provided by electric vehicles.
The electric buses have required mechanical servicing far less frequently than the diesel buses they replaced. Thus, electric powertrains are inherently more durable than traditional diesel engines.
Particulate pollution along Route 5 has dropped significantly since the electric fleet began operations. This proves that the retired diesel buses were the primary source of airborne contaminants in the area.
Traffic collisions involving buses on Route 5 have decreased by 30 percent since the transition. Consequently, electric buses must be structurally safer and easier to maneuver in traffic.

Matches

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Answer

The passenger volume argument pairs with the ticket prices evidence; the mechanical servicing argument pairs with the bus age evidence; the pollution argument pairs with the constant traffic emissions evidence; the collision argument pairs with the driver cohort evidence.
In causal reasoning, an argument is logically strengthened when a plausible alternative cause for the observed effect is eliminated. Because all four arguments share the same contextual scenario, surface-level keyword matching is ineffective. Instead, each correct match pairs a specific conclusion with a premise that directly neutralizes its most critical confounding variable.

Step-by-Step Solution

1
Analyze the passenger volume argument to identify its causal gap.
The argument assumes ride quality caused the ridership increase, ignoring other potential incentives.
Matching it with the evidence that ticket prices and schedules remained unchanged strengthens the claim by ruling out these prominent economic alternatives.
2
Examine the mechanical servicing argument's assumption regarding durability.
The argument assumes engine type, rather than vehicle age, is the reason for reduced maintenance.
Matching it with the evidence that the diesel buses were newer than the electric ones strongly bolsters the claim by showing the electric buses performed better despite an age disadvantage.
3
Evaluate the pollution argument's causal claim.
It assumes the bus switch was the sole reason for improved air quality, ignoring other local factors.
Matching it with the evidence that other emissions remained steady strengthens the argument by isolating the bus fleet as the single variable responsible for the change.
4
Assess the collision reduction argument.
It assumes the vehicles themselves are safer, ignoring the human element of driving.
Matching it with the evidence that the drivers and their training were identical rules out improved human performance as the cause, heavily supporting the vehicle safety conclusion.

Key Concept

Strengthening causal arguments by systematically ruling out alternative explanations and isolating the causal variable.
Question 283Question →

Read the following passage carefully. Then, match each explicit detail from the text (on the left) with the specific logical inference it most strongly supports (on the right).

In the late nineteenth and early twentieth centuries, urban theorists responded to the squalor of industrialization through two distinct, though occasionally intersecting, philosophical paradigms. The City Beautiful movement, championed by Daniel Burnham, sought to impose moral and civic virtue upon the urban populace through monumental, neoclassical grandeur. Burnham’s philosophy posited that aesthetically unified public spaces would organically inspire civic loyalty, thereby mitigating social unrest. Consequently, City Beautiful projects prioritized municipal centers, grand boulevards, and elaborate park systems, often at the expense of addressing the structural poverty endemic to the residential wards they displaced.

Conversely, Ebenezer Howard’s Garden City movement approached urban dysfunction not as an aesthetic deficit, but as a socio-economic crisis necessitating spatial decentralization. Howard advocated for the creation of self-contained, limited-population satellite communities encircled by permanent agricultural greenbelts. Unlike Burnham, who sought to retrofit existing metropolises with monumental civic cores, Howard’s model was fundamentally preventative. By strictly regulating land use to prevent overcrowding and integrating industry with natural landscapes, Howard believed the Garden City would naturally suppress the economic stratification inherent to the unregulated capitalist metropolis.

While both movements sought to remedy the moral decay attributed to industrial slums, their structural methodologies implied divergent views on human behavior. The City Beautiful movement operated on the assumption that individuals are primarily influenced by their visual and civic environment; thus, grandeur begets order. Howard's model, however, suggested that social harmony is fundamentally a byproduct of economic and spatial equilibrium, implying that aesthetic improvements without corresponding structural economic changes are ultimately superficial.

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Items

Burnham's projects frequently resulted in the displacement of existing residential wards to build elaborate park systems.
Howard advocated for self-contained communities strictly bounded by permanent agricultural greenbelts.
Burnham's philosophy posited that aesthetically unified public spaces would organically inspire civic loyalty.
Howard's model suggested that social harmony is fundamentally a byproduct of economic and spatial equilibrium.

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Answer

The correct pairings logically connect specific textual details to their unstated necessary implications: displacement of wards implies housing stability was sacrificed; permanent greenbelts imply physical preclusion of endless outward expansion; the belief that aesthetics inspire loyalty implies chaotic spaces fail to do so; and the belief in economic equilibrium implies superficial aesthetic projects are insufficient.
Each correct pairing requires identifying a specific factual detail provided in the passage and recognizing the unstated but logically necessary deduction that flows directly from it. The correct inferences do not rely on outside knowledge or cross the boundary between the two contrasting viewpoints presented.

Step-by-Step Solution

1
Analyze the consequences of the City Beautiful movement displacing residential wards.
It logically supports the inference that the immediate housing stability of the impoverished was sacrificed to achieve monumental civic grandeur.
The passage states that displacement occurred 'at the expense of' addressing the structural poverty in those very wards.
2
Evaluate the function of Howard's permanent agricultural greenbelts.
It logically supports the inference that a Garden City was structurally precluded from accommodating unlimited outward population growth.
A 'permanent' physical barrier encircling a community inherently places a hard limit on its physical geographic expansion.
3
Examine Burnham's premise regarding aesthetically unified public spaces.
It logically supports the inference that City Beautiful advocates would assume visually chaotic districts fail to mitigate urban disorder.
If unified grandeur is the mechanism required to inspire order and loyalty, its absence logically fails to yield that result.
4
Assess Howard's view on social harmony and economic equilibrium.
It logically supports the inference that aesthetic improvements alone would be viewed as insufficient to resolve urban crises.
The passage explicitly notes that Howard's framework views aesthetic improvements without structural economic changes as 'superficial.'

Key Concept

Inferring necessary logical consequences from explicit textual details while avoiding viewpoint misattribution.
Question 284Question →

Match each candidate necessary assumption on the left with its logically precise contradictory on the right. This strict formulation is essential for properly testing assumptions in formal arguments.

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Items

All genetically modified crops require less water than traditional varieties.
If the central bank raises interest rates, inflation will stabilize.
Most of the artifacts discovered at the excavation site date back to the Bronze Age.
No local businesses will survive the economic downturn without government subsidies.
Some current medical treatments rely on compounds derived from endangered plants.

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Answer

Each assumption is matched with its precise logical contradictory: 'All' with 'At least one not', 'If A then B' with 'A and not B', 'Most' with 'Half or fewer', 'No' with 'At least one', and 'Some' with 'None'.
Applying the Negation Technique correctly involves identifying the minimal condition necessary to make the original statement false. For quantifiers, 'All' negates to 'Not all' (at least one does not), 'None' negates to 'Some' (at least one does), 'Some' negates to 'None', and 'Most' (more than half) negates to 'Half or fewer'. For conditional statements (If A then B), the negation is that the sufficient condition (A) occurs without the necessary condition (B).

Step-by-Step Solution

1
Analyze the quantifier or logical structure in each candidate assumption statement.
Identified 'All', 'If... then', 'Most', 'No', and 'Some' as the key logical operators.
Identifying the formal logic structure is the prerequisite for generating a precise logical contradictory.
2
Formulate the exact logical contradictory for each identified structure.
'All' negates to 'Not all'. 'If A then B' negates to 'A and not B'. 'Most' negates to 'Half or fewer'. 'No' negates to 'Some'. 'Some' negates to 'None'.
This negation technique requires the minimal claim necessary to destroy the original statement.
3
Match the formulated negations to the provided options.
The pairings are accurately aligned based on their strict logical contradictories.
This ensures the correct application of the technique without overreaching or committing formal logic errors.

Key Concept

The Negation Technique requires finding the exact logical contradictory of a statement. This means identifying the minimal claim required to make the original statement false, avoiding polar opposites (like negating 'All' to 'None') or mistaken conditional negations.
Question 285Question →

Each of the arguments below is vulnerable to criticism on the grounds that it illicitly shifts the meaning of a key term. Pair each flawed argument with the abstract description that most accurately diagnoses its specific equivocation.

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Items

The head coach demands that all athletes attend rigorous practice sessions daily in order to refine their physical conditioning and teamwork. However, our team physician has maintained a highly successful medical practice for over two decades without ever participating in daily physical drills. Therefore, the coach's requirement is unnecessarily burdensome.
The new municipal taxation policy is heavily criticized by opponents for unfairly discriminating against the owners of small, family-run businesses. Yet, the fundamental duty of any municipal regulatory agency is to properly discriminate among different economic sectors based on their distinct market impacts and community needs. Thus, the criticism of the taxation policy is logically unfounded.
The fundamental laws of thermodynamics dictate that the total entropy in any completely isolated system must inevitably always increase over time. Since it is our primary civic duty as responsible citizens to strictly obey the law at all times, laboratory scientists are morally obligated to ensure that the isolated systems in their experiments exhibit increasing entropy.
A prominent literary reviewer recently claimed that the acclaimed novelist's latest manuscript completely lacks a consistent narrative structure, confusing the reader. But this new manuscript is entirely consistent with the author's previous award-winning works, which also featured deliberately disjointed timelines and fragmented storytelling. Therefore, the reviewer's claim regarding the manuscript's narrative is demonstrably false.

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Answer

The correct pairings accurately match the ambiguous term exploited in each argument (practice, discriminate, law, consistent) with the abstract description of how its meaning illicitly changes between the premises and the conclusion.
Each correct pairing successfully diagnoses the dual meanings of the ambiguous terms exploited in the arguments. The coach/physician argument shifts 'practice' from training to a profession; the taxation argument shifts 'discriminating' from prejudice to selection; the thermodynamics argument shifts 'law' from descriptive science to prescriptive rules; and the literary argument shifts 'consistent' from internal coherence to historical alignment.

Step-by-Step Solution

1
Analyze the sports/medicine argument to locate the semantic shift.
Identified that 'practice' changes meaning from 'athletic training' to 'a medical business'.
Finding the specific term that bridges the premises but changes definition reveals the equivocation.
2
Analyze the taxation argument to locate the semantic shift.
Identified that 'discriminating' changes meaning from 'unjust prejudice' to 'judicious distinction'.
This shows how a valid regulatory function is improperly used to dismiss a claim of unfair bias.
3
Analyze the thermodynamics argument to locate the semantic shift.
Identified that 'law' changes meaning from 'a scientific description of nature' to 'a prescriptive civic duty'.
This uncovers the flaw of treating a natural inevitability as a moral or legal obligation.
4
Analyze the literary critique argument to locate the semantic shift.
Identified that 'consistent' changes meaning from 'internally coherent structure' to 'matching a past historical pattern'.
This highlights how the author's historical habits are improperly used to disprove a claim about internal narrative logic.

Key Concept

Equivocation (Uncertain Use of a Term) occurs when an argument relies on a key word or phrase having one meaning in a premise and an entirely different meaning in another premise or the conclusion.
Estimated Time:3m 0s
Question 286Question →

Match each logical argument (left) with the specific piece of evidence (right) that most powerfully strengthens its conclusion by resolving its core structural vulnerability.

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Items

An analysis revealed that companies allowing remote work saw a 15% increase in output per employee. Thus, working from home eliminates office distractions and directly boosts individual efficiency.
Immediately after the government lowered the capital gains tax, foreign investment in domestic tech startups doubled. Therefore, the tax cut successfully incentivized international investors.
Because fragments of a rare meteor were found alongside fossilized dinosaur bones in the crater, the meteor impact must have been the direct cause of the sudden extinction in this region.
To combat urban heat islands, our city should mandate white reflective roofs, just as the city of Solaris did ten years ago to dramatically lower its ambient temperatures.

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Answer

The correct pairings are: Remote work (Left 1) with Time-tracking logs (Right 2); Tax cut (Left 2) with Global downturn (Right 3); Meteor impact (Left 3) with Radiometric dating (Right 4); and Urban heat roofs (Left 4) with Meteorological data (Right 1).
Each correct pairing directly addresses the unstated assumption in the argument. Left 1 is strengthened by Right 2 because it eliminates the alternative that productivity rose due to longer hours. Left 2 is strengthened by Right 3 because it eliminates the alternative of a global market boom. Left 3 is strengthened by Right 4 by proving the timeline supports causality. Left 4 is strengthened by Right 1 because it validates the analogy between the two cities.

Step-by-Step Solution

1
Analyze each argument to identify its conclusion and its underlying vulnerability (e.g., alternative causes, weak analogies).
Identified four distinct gaps: alternate cause for productivity, alternate cause for investment, temporal/causal gap in extinction, and relevance gap in the city analogy.
Understanding the specific flaw in an argument is necessary before one can identify the evidence that repairs it.
2
Evaluate the available evidence statements on the right to see which logically seals a corresponding gap.
Matched each evidence statement to an argument based on how it defends against a vulnerability (e.g., ruling out increased work hours to support efficiency).
Strengthening an argument often involves eliminating alternative explanations or confirming the validity of a comparison.

Key Concept

Identifying and resolving structural vulnerabilities in causal and analogical reasoning.
Question 287Question →

Match each everyday argument to the formal valid deduction pattern that accurately describes its logical structure.

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Items

If the city council approves the budget, the park will be renovated. The city council approved the budget. Therefore, the park will be renovated.
If the plant is a fern, it reproduces via spores. This plant does not reproduce via spores. Therefore, it is not a fern.
The suspect either fled to Canada or is hiding locally. The suspect did not flee to Canada. Therefore, the suspect is hiding locally.
If it rains, the soil gets wet. If the soil gets wet, the seeds will sprout. Therefore, if it rains, the seeds will sprout.

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Answer

Argument 1 matches Modus Ponens, Argument 2 matches Modus Tollens, Argument 3 matches Disjunctive Syllogism, and Argument 4 matches Hypothetical Syllogism.
Each everyday argument perfectly matches the formal structure of a standard deductive argument pattern, relying on established rules of logic to guarantee the truth of its conclusion.

Step-by-Step Solution

1
Analyze the first argument regarding the city council budget.
The structure is 'If A then B. A is true. Therefore B is true.'
This is the classic definition of Modus Ponens (Affirming the Antecedent).
2
Analyze the second argument regarding the fern reproducing.
The structure is 'If A then B. B is false. Therefore A is false.'
This is the classic definition of Modus Tollens (Denying the Consequent).
3
Analyze the third argument regarding the suspect fleeing.
The structure is 'Either A or B. A is false. Therefore B is true.'
This is the classic definition of Disjunctive Syllogism (Elimination).
4
Analyze the fourth argument regarding rain and seeds.
The structure is 'If A then B. If B then C. Therefore, If A then C.'
This is the classic definition of Hypothetical Syllogism (Chain Conditionals).

Key Concept

Identifying the formal structure of valid deductive arguments.
Question 288Question →

Match each logical argument with the specific piece of additional evidence that would most strongly support its conclusion by addressing its underlying logical vulnerability.

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Items

Office workers using the new 'AeroType' ergonomic keyboard reported significantly less wrist fatigue over a one-month period than workers using standard keyboards. Thus, the AeroType keyboard effectively reduces typing strain.
In a recent poll conducted entirely within the downtown financial district, 75% of respondents supported the proposed city-wide transit tax. Therefore, the tax is likely to have broad support among all registered city voters.
The experimental 'Sun-Glow' tomato variety yielded 40% more fruit than traditional varieties during controlled greenhouse tests. Consequently, local farmers adopting this variety will see massive increases in their actual outdoor harvests.
Accounting firm Alpha saw a 20% increase in employee output after switching to a fully remote work model. Therefore, law firm Beta will also experience a significant productivity boost if it adopts a fully remote model.

Matches

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Answer

Argument 1 matches with the evidence regarding work hours and breaks. Argument 2 matches with the demographic evidence. Argument 3 matches with the greenhouse calibration evidence. Argument 4 matches with the workflow comparison evidence.
Each correct pairing matches an argument with the specific premise that resolves its unique logical vulnerability. Argument 1 requires ruling out alternative causes for reduced fatigue. Argument 2 requires proving the survey sample is representative. Argument 3 requires demonstrating that experimental conditions apply to the real world. Argument 4 requires establishing that the two compared firms are relevantly similar.

Step-by-Step Solution

1
Analyze Argument 1 to identify the logical gap.
The argument assumes a causal relationship between the keyboard and reduced fatigue, ignoring potential differences between the two groups of workers.
Finding an alternate cause that is eliminated by the evidence is the standard way to strengthen a causal claim.
2
Analyze Argument 2 to identify the logical gap.
The argument relies on a survey of a specific neighborhood to make a claim about an entire city.
Strengthening a survey-based argument requires demonstrating that the sample is adequately representative of the whole.
3
Analyze Argument 3 to identify the logical gap.
The argument assumes that success in a controlled greenhouse environment will seamlessly translate to outdoor farming.
Strengthening this requires evidence showing the two environments are functionally identical regarding the crop's needs.
4
Analyze Argument 4 to identify the logical gap.
The argument assumes that because a strategy worked for an accounting firm, it will work for a law firm.
Strengthening an argument by analogy requires proving that the two subjects share critical similarities relevant to the conclusion.

Key Concept

Strengthening Arguments by Identifying and Resolving Logical Gaps
Question 289Question →

Analyze the four conditional arguments below. Match each argument (left) with the specific missing assumption (right) that is logically sufficient to bridge the gap between the argument's premises and its conclusion.

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Items

A municipality is eligible for the state urban renewal grant only if its population density exceeds 5,000 residents per square mile. The municipality of Springfield recently constructed three expansive suburban housing developments. Therefore, Springfield is not eligible for the state urban renewal grant.
Unless a pharmaceutical company completes a comprehensive Phase III clinical trial, its novel therapeutic drug will not be approved by the federal regulatory board. Apex Pharma's novel cardiovascular drug was officially approved by the board today. Thus, Apex Pharma's drug must have been tested on a genetically diverse patient population.
Any biomedical research project that utilizes CRISPR-edited embryonic stem cells requires rigorous federal oversight to proceed legally. Dr. Aris's current neurological research project does not require rigorous federal oversight to proceed legally. Therefore, Dr. Aris's current project is not funded by the National Science Institute.
If an autonomous vehicle's navigation system relies exclusively on optical cameras, it will fail to operate safely in severely inclement weather. The newly released Zenith self-driving car operates perfectly safely in severely inclement weather. Therefore, the Zenith car must incorporate active lidar sensor technology.

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Answer

Argument 1 pairs with Assumption 1, Argument 2 with Assumption 2, Argument 3 with Assumption 3, and Argument 4 with Assumption 4.
Each argument contains a stranded premise and a conclusion that requires a specific conditional link to be logically valid. By applying the contrapositive and properly diagramming the conditional indicators ('unless', 'only if', 'any', 'if'), the exact missing sufficient assumption can be identified and mapped to each argument.

Step-by-Step Solution

1
Translate the conditional rules in each argument's premises into formal logic.
Arg 1: Eligible -> >5000. Arg 2: Approved -> Phase III. Arg 3: CRISPR -> Oversight. Arg 4: Exclusively Optical -> Fail Safely.
Accurately diagramming conditional indicators ('only if', 'unless', 'any', 'if') is required to identify the logical endpoints of the existing premises.
2
Determine the intermediate inference drawn from the application of the second premise.
Arg 1: No direct inference yet. Arg 2: Apex completed Phase III. Arg 3: Dr. Aris does not use CRISPR. Arg 4: Zenith is not Exclusively Optical.
The intermediate inference reveals what the argument has successfully proven before jumping to its unsupported conclusion.
3
Identify the logical gap between the intermediate inference and the stated conclusion.
Arg 1 needs: Constructed Housing -> Density ≤ 5000. Arg 2 needs: Phase III -> Diverse. Arg 3 needs: Not CRISPR -> Not NSI Funded (or NSI -> CRISPR). Arg 4 needs: Not Exclusively Optical -> Lidar.
A sufficient assumption must perfectly connect the proven inference to the unproven conclusion without triggering logical fallacies.
4
Evaluate the right-side items to find the exact conditional matches.
The assumptions provided directly reflect the exact gaps identified in Step 3.
Matching the derived necessary/sufficient bridges confirms the correct pairings.

Key Concept

Assumptions in Conditional Logic
Estimated Time:3m 0s
Question 290Question →

Analyze the following arguments drawn from various corporate and public policy contexts. Pair each argument with the abstract description that most accurately identifies its specific error in reasoning regarding numbers and percentages.

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Items

In 2015, independent coffee shops captured 12% of total national coffee sales. By 2025, their market share rose to 28%. Clearly, independent coffee shops sold a greater volume of coffee in 2025 than they did a decade earlier.
During the summer months, the municipal pool recorded 150 instances of minor injuries, compared to just 30 instances at the local lake. Therefore, swimming at the municipal pool is inherently more dangerous than swimming at the local lake.
According to a public health report, 85% of pedestrian accidents in the downtown district last year involved individuals crossing at designated crosswalks, whereas only 15% involved individuals crossing elsewhere. This demonstrates that using a designated crosswalk makes a pedestrian more likely to be struck by a vehicle.
Five years ago, the manufacturing division accounted for 40% of our company's total expenses. Today, it accounts for only 25%. This proves that the manufacturing division has successfully reduced its operating costs over the past five years.

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Answer

The coffee shop argument matches with the flaw of assuming an increased proportion entails an increased absolute quantity. The municipal pool argument matches with the flaw of relying on absolute incident numbers without comparing baseline frequencies. The crosswalk argument matches with the flaw of using a high proportion of total events to infer likelihood without considering the prevalence of the conditions. The manufacturing division argument matches with the flaw of assuming a decreased share reflects a reduction in absolute amount.
Each argument commits a distinct variation of the Percentages vs. Numbers flaw. By identifying the exact premise type (absolute number vs. percentage) and the specific conclusion type (absolute number vs. rate), each argument maps uniquely to its corresponding abstract flaw description.

Step-by-Step Solution

1
Analyze the coffee shop argument.
Identified a shift from a percentage increase (12% to 28%) to a conclusion about an absolute volume increase.
To map it to the description that critiques assuming proportion growth guarantees absolute growth.
2
Analyze the municipal pool argument.
Identified a shift from higher raw incident numbers (150 vs 30) to a conclusion about relative danger or rate.
To map it to the description that critiques using absolute numbers without relative frequency baselines.
3
Analyze the crosswalk argument.
Identified a shift from a high percentage of total accidents occurring in a specific condition to concluding that the condition inherently increases likelihood.
To map it to the description that critiques ignoring the baseline prevalence of the condition in the broader population.
4
Analyze the manufacturing division argument.
Identified a shift from a percentage decrease (40% to 25%) to a conclusion about an absolute cost reduction.
To map it to the description that critiques assuming a decreased relative share means a decreased absolute amount.

Key Concept

Identifying statistical reasoning errors where an argument conflates proportional shares (percentages) with actual sizes (absolute numbers), or vice versa, without providing necessary baseline context.
Question 291Question →

Analyze the four brief arguments below. Pair each argument with the abstract description that best characterizes its flaw in reasoning regarding numerical or proportional evidence.

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Items

Ten years ago, 5% of patients discharged from Valley Hospital were readmitted within a month. This year, the readmission rate is 8%. Therefore, Valley Hospital is readmitting more patients this year than it did a decade ago.
Last year, the state recorded 400 fires in electric vehicles and over 10,000 fires in gas-powered cars. Clearly, any given electric vehicle is far less likely to catch fire than a gas-powered car.
In 2015, popcorn accounted for 60% of snack bar revenues at the cinema. Today, popcorn accounts for only 40% of snack revenues. Thus, the cinema's total sales volume of popcorn must have declined since 2015.
Since introducing the new pest-resistant seeds, the total number of crops lost to insects in the region has doubled. This proves the new seeds are less effective at preventing insect damage per acre planted than the previous seeds.

Matches

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Answer

The correct pairings match the specific numerical or proportional shift in each argument to its abstract logical flaw description.
Each correct pairing accurately identifies whether the specific argument is flawed by improperly moving from a percentage to a raw number (as seen in the Hospital and Cinema arguments) or by improperly moving from a raw number to a percentage/rate (as seen in the Electric Vehicles and Farming arguments).

Step-by-Step Solution

1
Analyze the Valley Hospital argument regarding readmission.
Identify that it moves from a percentage increase to an absolute number increase.
This maps to the description about inferring an increase in absolute numbers solely from an increase in a percentage.
2
Evaluate the electric vehicle argument regarding fires.
Identify that it compares raw numbers to make a claim about probability.
This maps to concluding a lower probability from a smaller raw number without considering total group sizes.
3
Assess the cinema popcorn argument regarding revenues.
Identify that it assumes a dropping percentage means a dropping total amount.
This maps to presuming a decline in proportion guarantees a decline in absolute quantity.
4
Analyze the crop seed argument regarding insect damage.
Identify that it uses an increased total number to claim a worse per-acre rate.
This maps to deriving a proportional claim from an absolute increase while ignoring overall volume changes.

Key Concept

Percentages vs. Numbers Flaws
Estimated Time:2m 0s
Question 292Question →

An art historian is evaluating several necessary assumptions underlying a controversial proposal to restore a Renaissance sculpture. To test the validity of these assumptions using the Negation Technique, match each candidate assumption on the left with the logically precise negated statement on the right that would be used to evaluate whether the argument's conclusion is destroyed.

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Items

Every chemical solvent currently used in the restoration process alters the original microscopic texture of the marble.
The proposed laser ablation technique requires an environment with precisely zero airborne particulates.
Some of the previously applied synthetic resins have caused irreversible discoloration to the deeper pigment layers.
If the restoration committee approves the intervention, the historical authenticity of the sculpture will be permanently compromised.

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Answer

Match the Universal affirmative to the Particular negative (Every -> At least one does not), the Required condition to Possibility without (Requires -> Can be executed without), the Existential to the Universal negative (Some -> None), and the Conditional to Sufficient without Necessary (If A then B -> A could happen without B).
Applying the Negation Technique requires producing the precise logical contradictory of a statement. Creating a negation that is too strong (e.g., negating 'some' as 'all do not' is correct, but negating 'all' as 'none' is a flaw) will distort the evaluation of the argument.

Step-by-Step Solution

1
Analyze the logical structure of the first assumption (Every...).
Identify it as a universal affirmative statement.
To correctly negate a universal claim, we must not use another universal (like 'None'); we must show that the universal rule is broken by at least one exception.
2
Analyze the logical structure of the second assumption (requires).
Identify it as presenting a necessary condition.
The negation technique tests if the argument survives without the assumption. If the technique can be executed without the requirement, the assumption is successfully negated.
3
Analyze the third assumption (Some...).
Identify it as an existential statement (meaning 'at least one').
The logical opposite of 'at least one is' is 'exactly zero are' (None).
4
Analyze the fourth assumption (If... then...).
Identify it as a conditional relationship.
To falsify a conditional claim, we must demonstrate that the trigger (sufficient condition) can occur without guaranteeing the outcome (necessary condition).

Key Concept

Applying the Negation Technique
Question 293Question →

Identify the specific logical gap present in each scenario by pairing the causal argument with the unstated premise required for its conclusion to hold true.

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Items

Seniors who frequently play complex strategic board games demonstrate higher cognitive retention. Therefore, playing these games prevents cognitive decline.
After the national park banned off-road vehicles, the endangered spotted owl population recovered. Thus, vehicle noise was previously suppressing the owl population.
A survey reveals a strong correlation between a startup's investment in ergonomic office furniture and its employees' reported job satisfaction. Consequently, comfortable furniture directly increases employee happiness.

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Answer

The board games argument assumes no reverse causation; the national park argument assumes no alternate concurrent event caused the outcome; and the office furniture argument assumes no third factor caused both correlated elements.
Each causal argument leaves a specific logical gap that must be bridged by an assumption. The board games argument is vulnerable to reverse causation. The park argument is vulnerable to an alternate independent cause occurring simultaneously. The furniture argument is vulnerable to a third variable causing both observed elements.

Step-by-Step Solution

1
Analyze the board games argument to identify the nature of its logical leap.
The premise is a correlation between game playing and cognitive retention. The conclusion asserts game playing causes retention.
Identifying the relationship helps determine that the argument must assume individuals with high retention aren't simply more drawn to complex games (ruling out reverse causation).
2
Examine the national park argument's premise-to-conclusion structure.
The premise relies on a chronological sequence (a ban occurred, then owls recovered).
When a conclusion jumps from sequential events to causality, the necessary assumption must rule out other simultaneous events (like new conservation efforts) acting as alternate causes.
3
Evaluate the office furniture argument's causal claim.
The argument observes a static correlation between furniture and satisfaction and concludes direct causation.
To solidify this link, the argument must assume a third underlying factor (e.g., overall company prosperity) isn't independently causing both the ability to buy furniture and the high morale.

Key Concept

Assumptions in Causal Arguments
Question 294Question →

Match each paradoxical scenario on the left with the additional piece of information on the right that most helps to resolve the apparent discrepancy.

Click a left item, then click its matching right item

Items

A boutique bakery raised the prices of its signature pastries significantly, yet the total volume of these pastries sold per week increased.
A municipality initiated a massive tree-planting campaign specifically to lower summer temperatures, but the average summer heat in the targeted neighborhoods actually rose.
A regional airline significantly reduced its scheduled flights to rural airports, expecting a loss, yet its total revenue from rural routes increased.
A university made its premium lecture recordings freely accessible to attract more paying students, but subsequent enrollment in its paid online certificate programs dropped.

Matches

Show answer & explanation

Answer

The bakery matches the social media luxury trend; the tree-planting matches the asphalt paving; the airline matches the monopoly pricing; the university lectures matches the educational substitution effect.
Each correct pairing provides the missing contextual factor that allows both seemingly incompatible premises in the scenario to coexist logically. They supply alternative causes, overriding variables, or mathematical relationships (like price versus volume) that resolve the apparent discrepancies.

Step-by-Step Solution

1
Analyze the bakery scenario
Identify the paradox: higher prices usually mean lower sales volume, but here volume increased.
Understanding the core conflict is necessary to find the bridge.
2
Match the bakery scenario
Pair it with the social media luxury trend resolution.
This introduces a shift in demand that overrides the normal effect of a price increase.
3
Analyze and match the tree-planting scenario
Pair the tree-planting (which should cool the area) with the asphalt paving (which heats the area).
The asphalt introduces an external variable that causes the unexpected temperature rise.
4
Analyze and match the airline scenario
Pair the reduced flights with monopoly pricing.
Revenue equals volume times price; if volume drops but revenue rises, price must have increased significantly to compensate.
5
Analyze and match the university scenario
Pair the free lectures with the elimination of the incentive to pay.
This explains why the promotional effort perfectly substituted the paid product and reduced paid enrollments.

Key Concept

Bridging Conflicting Premises by identifying external variables, offsetting factors, or unintended behavioral consequences.
Question 295Question →

Evaluate the flawed causal claims, predictions, and historical hypotheses presented below. Which specific piece of new evidence provides the most robust logical support for each argument's main conclusion? Match each argument (left) to its strongest supporting evidence (right).

Click a left item, then click its matching right item

Items

An anthropologist argues that the sudden adoption of bronze tools by the highland Q'ero tribes resulted from peaceful trade with lowland empires, not military conquest. The discovered bronze artifacts lack the decorative engravings typical of lowland soldiers' weapons.
A marine biologist asserts that the unprecedented bleaching of the Aethel Coral Reef is primarily caused by chemical runoff from a newly opened coastal desalination plant, rather than the recently documented slight increase in local ocean temperatures.
A retail analyst predicts that the bookstore chain PageTurner will see a significant increase in profit margins next quarter. The chain recently replaced its human cashiers with automated kiosks, which cost considerably less to operate than paying employee wages.
A neurologist hypothesizes that frequent engagement with short-form video content fundamentally reduces an adult's baseline attention span. A clinical survey found that adults who watch short-form videos for over three hours daily performed significantly worse on sustained-focus tests than non-watchers.

Matches

Show answer & explanation

Answer

The correct matches validate causal links by establishing controls, ruling out reverse causality, eliminating negative side-effects, and corroborating structural assumptions.
Each correct match directly addresses the specific logical vulnerability of its corresponding argument. The archaeological evidence removes the military utility of the bronze, the ecological evidence isolates the chemical variable from the temperature variable, the financial evidence protects the cost-savings from revenue losses, and the medical evidence proves the chronological direction of the psychological effect.

Step-by-Step Solution

1
Analyze the Anthropology argument (L1)
Identify the logical gap: A lack of decorative engravings does not definitively prove the tools were not used in war.
Matching it with the evidence of functionally non-martial tools (R1) closes this gap, supporting the peaceful trade conclusion.
2
Analyze the Marine Biology argument (L2)
Identify the logical gap: Both chemicals and heat are present, and heat is a known alternative cause for bleaching.
Matching it with evidence of a control ecosystem (R2) isolates the chemical runoff as the primary culprit, proving heat alone did not cause the bleaching.
3
Analyze the Economics argument (L3)
Identify the logical gap: Lower wage costs only improve profit margins if revenues and other operational costs remain stable.
Matching it with evidence of stable transaction rates and inventory shrinkage (R3) rules out the potential negative side effects of kiosks.
4
Analyze the Neuroscience argument (L4)
Identify the logical gap: The survey is a cross-sectional snapshot, leaving the argument vulnerable to reverse causality (people with short attention spans preferring short videos).
Matching it with longitudinal data proving the groups were equal beforehand (R4) confirms the direction of causation.

Key Concept

Strengthening arguments by closing causal gaps, ruling out alternative explanations, and validating implicit assumptions.
Question 296Question →

The reasoning in each of the short arguments below is flawed due to the uncertain use of a key term or phrase. Select the precise abstract description from the right column that accurately characterizes the semantic shift occurring in each argument.

Click a left item, then click its matching right item

Items

The city's proposed noise ordinance is highly practical, as the police force can easily enforce its specific decibel limits. However, since the ordinance will drive away the vibrant nightlife that funds our tax base, it is clearly not practical.
Company policy guarantees that employees will be fully compensated for any substantial loss incurred during corporate relocation. Therefore, because my transfer to the overseas branch resulted in a profound loss of my sense of community, I am owed financial compensation.
According to the historical society, the preservation of the old courthouse is a matter of profound public interest. Yet this cannot be true, because a recent poll showed that the vast majority of the public has no interest whatsoever in architecture.
The critic claims the director's latest film is utterly senseless, arguing it lacks any coherent narrative or thematic depth. But this is demonstrably false, since the film relies heavily on bright flashing lights and blaring alarms, which strongly impact the senses.

Matches

Show answer & explanation

Answer

The correct matches pair each argument with the precise abstract description of its semantic shift: Practicality (feasibility vs. desirability), Loss (economic vs. emotional), Interest (welfare vs. curiosity), and Senseless (incoherent vs. lacking perceptual stimulation).
Each correct pair accurately identifies the specific word that changes meaning during the course of the argument, and correctly maps the two distinct definitions used to the abstract categories provided in the right-hand items (e.g., feasibility vs. desirability, or economic vs. emotional).

Step-by-Step Solution

1
Analyze the first argument to identify the word whose meaning changes.
The word 'practical' changes from meaning 'capable of being enforced' in the premise to 'having beneficial tax consequences' in the conclusion.
Identifying the dual definitions of the pivoting term is necessary to match it with the abstract description of feasibility versus desirability.
2
Analyze the second argument for a semantic shift.
The term 'loss' shifts from an intended economic meaning in the company policy to an emotional meaning in the employee's claim.
Recognizing the context of the policy (financial) versus the application (emotional) maps directly to the economic/psychological description.
3
Analyze the third argument for its equivocal term.
The phrase 'public interest' (meaning collective welfare) is conflated with the public having an 'interest' (meaning curiosity or engagement) in architecture.
Distinguishing between normative benefit and psychological engagement identifies the correct match.
4
Analyze the fourth argument's semantic pivot.
The word 'senseless' shifts from meaning 'without logical coherence' to meaning 'without sensory impact'.
Contrasting narrative depth with flashing lights reveals the shift between logical and perceptual definitions.

Key Concept

Equivocation (Uncertain Use of a Term)
Estimated Time:2m 30s
Question 297Question →

Match each of the following flawed arguments to the abstract description that most accurately identifies its reasoning error concerning percentages and absolute numbers.

Click a left item, then click its matching right item

Items

Bicycle thefts accounted for 15% of all reported property crimes in the city this year, up from 5% a decade ago. Therefore, there are more bicycle thefts now than there were ten years ago.
Hospital Alpha treated 400 patients for respiratory illness this month, while Hospital Beta treated only 80. Thus, a patient at Hospital Alpha is more likely to be treated for a respiratory illness than a patient at Hospital Beta.
Zeta Tech's share of the global smartphone market fell from 30% to 20% over the last three years. This shows that Zeta Tech is manufacturing fewer smartphones than it did three years ago.
The city's public library received a record 10,000 new book donations this year. Consequently, donated books must represent a larger percentage of the library's total acquisitions this year than in previous years.

Matches

Show answer & explanation

Answer

The bicycle theft argument pairs with the proportion-to-quantity increase flaw; the hospital argument pairs with the quantity-to-rate flaw; the smartphone argument pairs with the share-to-quantity decrease flaw; the library argument pairs with the quantity-to-proportion increase flaw.
Each argument represents one of four directional variations of the percentage vs. number flaw. By precisely identifying whether the premise offers absolute data or proportional data, and whether the conclusion claims an absolute result or a proportional result, you can map each argument to its abstract description.

Step-by-Step Solution

1
Analyze the premise and conclusion of the first argument.
Premise: Proportion increased (5% to 15%). Conclusion: Absolute number increased.
Identifying the shift from a relative metric to an absolute metric isolates the specific percentage-to-number flaw.
2
Analyze the premise and conclusion of the second argument.
Premise: Absolute number is higher (400 vs 80). Conclusion: Likelihood (rate) is higher.
This reveals the inverse flaw: moving improperly from an absolute count to a comparative proportion.
3
Analyze the premise and conclusion of the third argument.
Premise: Market share (proportion) decreased. Conclusion: Absolute number decreased.
This mirrors the first flaw but tests the downward trajectory, confusing a shrinking slice of the pie with a shrinking absolute size of the slice.
4
Analyze the premise and conclusion of the fourth argument.
Premise: Absolute number is at a record high. Conclusion: Percentage must be larger.
This confirms the final mapping, showing an improper leap from a high quantity to a high relative percentage.

Key Concept

Percentages vs. Numbers Flaws
Estimated Time:1m 30s
Question 298Question →

Match each candidate assumption statement on the left with its precise logical negation on the right. Accurately formulating these negations is a crucial step when applying the Negation Technique to evaluate Necessary Assumption questions on the LSAT.

Click a left item, then click its matching right item

Items

Every successful candidate in the election received campaign donations.
Some of the newly discovered artifacts date back to the third century.
Implementing the new protocol is the only way to secure the network.
Most of the board members will vote in favor of the merger.

Matches

Show answer & explanation

Answer

The correct pairings match each statement's quantifier with its mutually exclusive and exhaustive opposite: 'Every' matches with 'At least one... did not'; 'Some' matches with 'None'; 'the only way' matches with 'can be secured without'; and 'Most' matches with 'Half or fewer'.
To apply the Negation Technique accurately, one must find the exact logical opposite of a statement. The logical opposite of 'all/every' is 'not all' (at least one is not). The logical opposite of 'some' (at least one) is 'none' (zero). The logical opposite of a necessary condition ('the only way') is showing the outcome can happen without it. The logical opposite of 'most' (51% to 100%) is 'half or fewer' (0% to 50%).

Step-by-Step Solution

1
Identify the primary logical quantifier or conditional indicator in each statement.
The key indicators are 'Every' (Left 1), 'Some' (Left 2), 'the only way' (Left 3), and 'Most' (Left 4).
The Negation Technique relies on finding the precise mathematical or logical boundary of these indicators.
2
Determine the formal logical opposite for each indicator.
All -> Not All (At least one is not). Some (at least one) -> None. Only way (Necessary) -> Not Necessary. Most (>50%) -> Half or fewer (<=50%).
Logical negation must divide all possibilities into exactly two mutually exclusive outcomes without any overlap.
3
Match the original statements to the right items that reflect these logical opposites.
Left 1 pairs with Right 2. Left 2 pairs with Right 4. Left 3 pairs with Right 3. Left 4 pairs with Right 1.
These pairings provide the exact negations required to test necessary assumptions without committing a flawed negation.

Key Concept

Applying the Negation Technique to Formal Logic Quantifiers
Question 299Question →

Match each paradoxical situation on the left with the statement on the right that most logically resolves the apparent discrepancy.

Click a left item, then click its matching right item

Items

A hospital facing a severe shortage of qualified nurses recently decreased the starting salaries for its newly hired nurses.
Traffic congestion in a city's downtown area worsened after the introduction of a popular free public bicycle-sharing program.
The release of an expensive premium version of a productivity app caused a sudden, massive surge in sales of the previously stagnant basic version.
Despite a massive increase in residential solar panel installations following a new subsidy, the total residential electricity drawn from the city's main grid did not decrease.

Matches

Show answer & explanation

Answer

The hospital paradox is resolved by the tuition program; the traffic paradox by the lane removal and user demographics; the app sales paradox by the shifted perception of value; and the solar panel paradox by the increase in overall energy consumption.
Each correct match provides a new piece of information that bridges the gap between the two seemingly contradictory facts presented in the paradox. By addressing alternative compensation, capacity reduction, psychological price anchoring, and behavioral rebound effects, the correct statements fully resolve their respective discrepancies.

Step-by-Step Solution

1
Analyze the hospital labor shortage paradox.
The discrepancy is lowering wages during a shortage. The resolution must provide an alternative incentive that outweighs the lower pay, which matches the tuition coverage program.
To resolve a labor paradox, we need a factor that increases the job's attractiveness independent of the base salary.
2
Analyze the traffic and bicycle program paradox.
The discrepancy is more alternative transport leading to worse traffic. The resolution must show cars were not reduced while road capacity was, which matches the lane removal and pedestrian usage statement.
A paradox involving worsened conditions despite an apparent solution usually means the solution actively harmed the existing infrastructure or didn't target the actual source of the problem.
3
Analyze the app sales paradox.
The discrepancy is a new expensive product boosting sales of an old stagnant one. The resolution must explain a change in consumer behavior toward the old product, matching the shift in value perception.
When a new product impacts the sales of an existing product, it typically alters the comparative landscape or consumer psychology.
4
Analyze the solar panel paradox.
The discrepancy is increased solar capacity not reducing grid reliance. The resolution must explain an offset in the savings, matching the behavioral shift of using high-consumption appliances.
A paradox where increased efficiency or capacity fails to yield expected reductions often points to a simultaneous increase in usage (a rebound effect).

Key Concept

Identifying the Apparent Discrepancy and bridging the gap with new, logically sufficient information that allows both original facts to coexist.
Question 300Question →

Match each argument (stimulus) with the supporter assumption that is logically necessary to bridge the gap between its premises and its conclusion.

Click a left item, then click its matching right item

Items

If a legal code prioritizes restorative justice over punitive measures, it requires a robust network of community mediators. The nation of Oakhaven lacks the funding necessary to train or employ community mediators. Therefore, Oakhaven's legal code will inevitably fail to lower the national recidivism rate.
A dietary supplement can only be marketed as "performance-enhancing" if clinical trials demonstrate a significant increase in muscular endurance without elevating resting heart rate. The novel compound XT-4 increases endurance by 15%, but trials show it elevates the resting heart rate of users. Thus, XT-4 cannot be patented.
In the genre of abstract expressionism, a painting's artistic merit is determined exclusively by the emotional resonance of its chaotic forms. Sorel's latest canvas exhibits immaculate brushwork but fails to evoke any visceral reaction from its audience. Clearly, Sorel's canvas will not be inducted into the modern art museum's permanent collection.
Societal stability requires a populace that explicitly trusts its governing institutions. Frequent political scandals predictably erode this trust by portraying leaders as self-serving. Since the current administration has been plagued by continuous scandals, the national economy is destined to enter a severe recession.

Matches

Show answer & explanation

Answer

Connect each argument to the assumption that explicitly links the orphaned concept in the conclusion back to the logical chain established in the premises.
Each correct pairing successfully identifies the unstated premise required to make the argument's conclusion logically follow. In supporter assumption questions, the conclusion always introduces a new concept that did not appear in the premises. The correct assumption must explicitly link this new conclusion concept to the concepts established in the premises, effectively 'closing the gap' in the author's reasoning.

Step-by-Step Solution

1
Isolate the conclusion and the premises for each argument.
Identified the final claim and the supporting evidence for all four stimuli.
Structural breakdown is required to spot the exact point where the argument skips a logical step.
2
Identify the 'rogue' or 'orphaned' term in each conclusion.
Found 'fail to lower recidivism' (Argument 1), 'cannot be patented' (Argument 2), 'inducted into permanent collection' (Argument 3), and 'severe recession' (Argument 4).
A valid supporter assumption must mention the new concept introduced in the conclusion.
3
Identify the final proven point in each premise chain.
Found 'cannot prioritize restorative justice' (1), 'cannot be marketed as performance-enhancing' (2), 'lacks artistic merit' (3), and 'loss of societal stability' (4).
The assumption must connect the rogue conclusion term specifically to the end of the premise chain.
4
Match the argument to the assumption that correctly links the two elements using proper conditional or causal direction.
Successfully paired all four arguments with their corresponding linking assumptions.
Verifying the conditional direction (e.g., ensuring a necessary condition is mapped correctly) confirms the assumption validates the argument.

Key Concept

Bridging Gap (Supporter) Assumptions
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