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Question 1401Question →

Financial Columnist: In 2015, traditional brick-and-mortar retailers accounted for 80 percent of all retail corporate bankruptcies, while online-only retailers accounted for the remaining 20 percent. Since then, the total number of online-only retailers operating in the market has quadrupled. Last year, traditional brick-and-mortar retailers accounted for only 55 percent of all retail corporate bankruptcies, whereas online-only retailers accounted for 45 percent. It is clear from these figures that the financial stability of traditional brick-and-mortar retailers has improved since 2015, as they are now experiencing fewer bankruptcies annually than they did previously.

Which of the following most accurately describes a flaw in the financial columnist's reasoning?

Show answer & explanation

Answer: It infers a decline in an absolute quantity based solely on a decline in the proportion of a whole, without establishing whether the total pool has remained stable.

Answer

The correct answer is the option stating that the argument infers a decline in an absolute quantity based solely on a decline in the proportion of a whole, without establishing whether the total pool has remained stable.
The correct answer perfectly diagnoses the mathematical vulnerability in the columnist's reasoning. The author observes that brick-and-mortar stores represent a smaller slice of the bankruptcy 'pie' (55% down from 80%). From this, they conclude that the actual amount of brick-and-mortar bankruptcies has decreased. This logic only works if the total size of the pie remained the same or shrank. If the total number of corporate bankruptcies across all sectors skyrocketed over those years, 55% of the new total could easily represent a much larger absolute number of failed businesses than 80% of the old total. The author fails to establish whether the total pool remained stable, making the conclusion invalid.

Step-by-Step Solution

1
Identify the premises.
Premise 1: In 2015, brick-and-mortar = 80% of bankruptcies. Premise 2: Last year, brick-and-mortar = 55% of bankruptcies. Premise 3: The number of online retailers has quadrupled.
Deconstructing the argument structure is required to isolate what evidence the author is relying upon.
2
Identify the main conclusion.
Brick-and-mortar retailers are now experiencing fewer absolute bankruptcies annually than they did in 2015.
Locating the conclusion reveals the exact claim that needs to be scrutinized for logical leaps.
3
Analyze the relationship between the premises and the conclusion.
The author takes a decrease in a percentage (from 80% to 55%) and assumes it equates to a decrease in an absolute number (fewer bankruptcies overall).
This exposes the core mechanism of the author's reasoning.
4
Determine why this reasoning is flawed.
A percentage only has absolute meaning relative to its total. If the total number of retail bankruptcies grew massively between 2015 and last year, 55% of the new, massive total could be a much larger number than 80% of the small 2015 total.
This uncovers the specific vulnerability in the argument: the failure to establish a stable baseline total.
5
Match the identified flaw to the answer choices.
The correct option accurately describes concluding an absolute decline from a proportional decline without considering the total.
Selecting the answer choice that perfectly matches our structural abstraction.

Key Concept

Percentages vs. Numbers Flaws
Estimated Time:2m 0s
Question 1402Question →

Marine biologist: In the coastal waters of the Vespian Sea, significant increases in the ghost jellyfish population consistently occur shortly after periods of unusually heavy rainfall. Heavy rainfall washes large quantities of agricultural runoff into the sea, resulting in massive blooms of phytoplankton. Because phytoplankton is the primary food source for ghost jellyfish, we can conclude that these phytoplankton blooms are the cause of the periodic surges in the jellyfish population.

Which one of the following is an assumption on which the marine biologist's argument depends?

Show answer & explanation

Answer: Heavy rainfall does not alter the coastal water environment in other ways that serve as the actual trigger for the surges in the ghost jellyfish population.

Answer

The argument assumes that heavy rainfall does not alter the coastal water environment in other ways that serve as the actual trigger for the surges in the ghost jellyfish population.
The correct answer identifies a 'defender' assumption necessary for the causal conclusion. The author observes that rainfall precedes the jellyfish surges and concludes that the phytoplankton blooms caused by the rainfall are responsible. For this causal relationship to hold, we must assume that the rainfall itself (such as a change in salinity or temperature) is not the actual, direct cause of the surges. If we negate this option—meaning the rainfall DOES alter the environment in ways that act as the actual trigger—the argument's conclusion that the phytoplankton blooms are responsible is destroyed.

Step-by-Step Solution

1
Identify the core argument structure.
Premise 1: Heavy rainfall correlates with jellyfish surges. Premise 2: Heavy rainfall causes phytoplankton blooms. Conclusion: Phytoplankton blooms cause the jellyfish surges.
Understanding the exact causal chain claimed by the author is essential for finding logical gaps.
2
Identify the logical gap in the causal reasoning.
The author observes that Event A (rainfall) is followed by Event C (jellyfish surge). The author claims that Event A causes Event B (phytoplankton), and therefore Event B causes Event C. The gap is the possibility that Event A causes Event C directly or through an unstated Event D.
Causal arguments based on correlated events often fail to account for alternate mechanisms triggered by the same initial event.
3
Evaluate the options using the Negation Technique.
Negating the correct answer yields: 'Heavy rainfall DOES alter the environment in other ways that serve as the actual trigger for the surges.' If this were true, the conclusion that phytoplankton caused the surges would fall apart.
A necessary assumption must be fundamentally true for the argument to survive; negating it will destroy the conclusion.

Key Concept

Assumptions in Causal Arguments (Ruling out alternate causes)
Question 1403Question →

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

Click a left item, then click its matching right item

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.

Matches

Show answer & explanation

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 1404Question →

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

Click a left item, then click its matching right item

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

Show answer & explanation

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 1405Question →

Sociologist: A society can only be considered free if its citizens are not subject to systemic coercion. As modern neuroscience has demonstrated, every human action is the inevitable result of prior neurological states governed by inflexible natural laws. Since our actions are dictated by these inescapable natural laws, they are completely determined by forces outside our control. Thus, we are constantly subject to systemic coercion. Therefore, no human society can truly be considered free.

Which of the following accurately describe a logical flaw in the sociologist's reasoning? Select all that apply.

Select all that apply

Show answer & explanation

Answer: It equivocates with respect to the concept of "coercion," using it to refer to interpersonal or political oppression in one context and physical determinism in another.; It illicitly shifts the meaning of the term "free" from a state of political or social liberty to a state of metaphysical independence.

Answer

The argument is flawed because it illicitly shifts the meanings of two key terms: it uses "coercion" to mean both social oppression and physical determinism, and "free" to mean both political liberty and metaphysical independence.
The sociologist's argument relies entirely on using words in wildly different senses. It uses a political and sociological definition of 'coercion' (meaning oppression by human agents or institutions) in its first premise, but then applies the term 'coercion' to the inflexible laws of physics and neuroscience. Consequently, the concept of being 'free' shifts from meaning 'politically free' to 'metaphysically free' (possessing free will over natural laws). The options describing these illicit semantic shifts correctly identify the logical flaw.

Step-by-Step Solution

1
Analyze the first premise to identify the initial context of the key terms.
The argument defines a "free" society as one where citizens are not subject to "systemic coercion," establishing a clear political and sociological context.
Understanding the original context of the terms is necessary to detect a semantic shift later in the argument.
2
Analyze the subsequent premises and the conclusion.
The argument introduces neuroscience and natural laws, claiming that humans are "completely determined by forces outside our control." It equates this determinism with "systemic coercion," leading to the conclusion that no society is "free."
This reveals how the argument attempts to bridge scientific determinism with sociological conditions.
3
Compare the usage of key terms across the premises.
The terms "free" and "coercion" change meanings entirely. In the sociological premise, they refer to human political agency and human-driven oppression. In the scientific premise, they refer to metaphysical free will and physical causality.
Identifying this dual-meaning shift reveals the central logical flaw of equivocation.
4
Evaluate the answer choices against the identified flaw.
The choices describing the specific semantic shifts in "coercion" and "free" accurately pinpoint the argument's vulnerability.
In a multi-select format, identifying all manifestations of the core flaw is required for the correct answer.

Key Concept

Equivocation occurs when a single term is used in two different senses within the same argument, creating a false logical bridge between unrelated concepts.
Question 1406Question →

City Council Member: Over the past fifteen years, our city's transition to using a new synthetic asphalt binder has directly caused a steady decrease in our annual road maintenance costs. Since we plan to continue using this synthetic binder exclusively, we can confidently project that our annual road maintenance costs will continue to decrease over the next ten years.

Which one of the following most accurately describes a flaw in the city council member's reasoning?

Show answer & explanation

Answer: takes for granted that a trend observed in the past will necessarily persist into the future

Answer

The correct answer identifies that the argument illicitly assumes a historical trend will continue indefinitely into the future.
The argument commits a classic Time Shift Flaw. It takes a historical trend (a steady decrease in maintenance costs over 15 years) and improperly projects it into the future. It fails to consider that the initial savings might have represented a one-time optimization curve, and that costs cannot decrease indefinitely (eventually hitting a floor).

Step-by-Step Solution

1
Analyze the argument's structure.
Premise: Using the new binder caused costs to decrease steadily over the past 15 years. Conclusion: Costs will continue to decrease over the next 10 years because the binder will still be used.
Deconstructing the argument is the first step to evaluating its logical validity.
2
Identify the gap between the premise and the conclusion.
The argument uses historical data (past 15 years) to make a definitive projection about the future (next 10 years) without guaranteeing conditions will remain the same.
Finding the unwarranted assumption reveals the logical flaw.
3
Determine the specific logical fallacy committed.
The author assumes that a past trend of cost reduction will continue indefinitely. It is entirely possible that the maximum cost-saving benefit of the new binder has already been reached, and costs will now stabilize.
Naming the specific flaw (Time Shift Flaw) makes it easier to match with the correct abstract answer choice.
4
Evaluate the options against the identified flaw.
The correct option perfectly describes the assumption that a past trend will persist into the future.
This confirms the answer without falling for trap choices that describe different fallacies.

Key Concept

Time Shift Flaws occur when an argument improperly projects past or present conditions, trends, or behaviors into the future without establishing that the underlying circumstances will remain unchanged.
Question 1407Question →

Ethicist: A society's moral progress regarding a specific issue is accurately measured by the extent to which its citizens apply informal social sanctions, such as boycotts, to harmful behavior. In Oakhaven, legislative penalties for corporate pollution have grown significantly stricter over the past decade. However, Oakhaven's citizens currently rarely apply informal social sanctions to companies that pollute. Therefore, Oakhaven has not made any moral progress regarding environmental protection over the past decade.

Which one of the following is an assumption required by the ethicist's argument?

Show answer & explanation

Answer: The extent to which Oakhaven citizens apply informal social sanctions to polluting companies is not greater now than it was a decade ago.

Answer

The assumption that the extent of informal social sanctions is not greater now than it was a decade ago.
The ethicist concludes that no moral progress has been made over the past decade based solely on the fact that informal sanctions are currently rare. Because the ethicist defines moral progress as an increase in the extent of these sanctions, concluding that no progress occurred requires assuming that sanctions haven't increased. If we logically negate this answer choice to state that the extent of sanctions *is* greater now than a decade ago, it would mean progress *has* occurred, completely destroying the conclusion. Thus, this assumption is strictly required.

Step-by-Step Solution

1
Identify the core structure of the argument.
Conclusion: Oakhaven has not made moral progress over the past decade. Premises: Moral progress is measured by the extent of informal social sanctions; Oakhaven citizens currently 'rarely' apply these sanctions.
Deconstructing the argument is the necessary first step to locating logical gaps.
2
Identify the logical gap between the premises and the conclusion.
The premises describe a static, current state ('rarely' apply sanctions), but the conclusion makes a claim about a change over time ('has not made moral progress over the past decade').
Progress implies a relative comparison between two points in time, which the explicitly stated premises fail to provide.
3
Apply the Negation Technique to test potential assumptions.
Negating the correct choice results in: 'The extent of sanctions IS greater now than it was a decade ago.' If the extent of sanctions has increased, then by the ethicist's own definition, moral progress HAS been made. The conclusion collapses.
A necessary assumption, when logically negated, will completely undermine the argument's conclusion.

Key Concept

Applying the Negation Technique to identify necessary assumptions involving temporal comparisons and relative changes.
Estimated Time:2m 0s
Question 1408Question →

Music historian: A newly discovered manuscript of symphonies attributed to the 18th-century composer Antonietta contains complex harmonic progressions previously thought to have been invented decades later. Chemical analysis definitively dates both the paper and the ink to the 1720s, during Antonietta's active years. Therefore, Antonietta pioneered these advanced harmonic progressions.

The argument above depends on the assumption that Antonietta did not simply transcribe the innovative compositions of an uncredited contemporary.

Show answer & explanation

Answer: True

Answer

True. The statement identifies a necessary assumption required to logically link the physical existence of the manuscript to the claim that Antonietta originated the musical ideas.
The statement accurately identifies a necessary assumption. The argument jumps from the existence of a 1720s manuscript bearing Antonietta's name to the conclusion that she conceptually originated the music. For this conclusion to survive, one must assume she was the true creator. Using the Negation Test, if she were merely transcribing another composer's original work, she could not be considered the pioneer, and the argument collapses entirely. Thus, the assumption is necessary.

Step-by-Step Solution

1
Identify the argument's premises and main conclusion.
Premise: A 1720s manuscript attributed to Antonietta contains advanced harmonies. Conclusion: Antonietta pioneered these harmonies.
Separating the factual evidence from the author's claim is the required first step to spot logical leaps.
2
Analyze the conceptual gap between the evidence and the conclusion.
The premises prove the manuscript is physically from the 1720s and has her name on it, but the conclusion claims she is the intellectual creator (pioneer) of the music.
Physical authorship of a document does not inherently guarantee originality of the concepts within it.
3
Apply the Negation Test to the proposed statement.
Negated statement: Antonietta DID simply transcribe the innovative compositions of an uncredited contemporary.
The Negation Test is the definitive logical method for verifying if an assumption is strictly necessary.
4
Evaluate the effect of the negated statement on the main conclusion.
If she merely copied another composer's work, the other composer was the pioneer. The conclusion is destroyed, proving the original statement is a necessary assumption.
An assumption is logically necessary if and only if its negation invalidates the argument.

Key Concept

Necessary Assumption (Defender) and the Negation Test
Estimated Time:1m 30s
Question 1409Question →

In the province of Veridia, a new agricultural policy heavily taxed the use of synthetic nitrogen fertilizers to reduce the environmental impact of agricultural runoff. Three years later, official environmental audits show that the total volume of nitrogen runoff originating from Veridian farms has increased significantly. This increase occurred even though the total acreage of farmed land in the province remained constant and the average amount of synthetic nitrogen fertilizer applied per acre decreased by 30 percent.

Which one of the following, if true, most helps to resolve the apparent discrepancy?

Show answer & explanation

Answer: In order to maintain crop yields while reducing synthetic fertilizer use, Veridian farmers heavily substituted organic livestock manure, which leaches nitrogen into soil and runoff water at a substantially higher rate than synthetic fertilizers.

Answer

The correct answer identifies that farmers substituted synthetic fertilizers with organic livestock manure, which has a higher rate of nitrogen leaching.
The correct answer resolves the paradox by introducing an unintended consequence of the tax policy. Because farmers replaced the heavily taxed synthetic fertilizers with organic livestock manure, and because this manure leaches nitrogen at a much higher rate, the total amount of nitrogen running off the farms increased even though the use of the specifically targeted synthetic fertilizer decreased.

Step-by-Step Solution

1
Identify the two seemingly conflicting premises in the stimulus.
Premise 1: Synthetic nitrogen use per acre dropped by 30 percent while farmed acreage remained constant. Premise 2: Total nitrogen runoff specifically originating from Veridian farms increased significantly.
Understanding the exact parameters of the conflict is required to find a viable bridging mechanism.
2
Evaluate the precise scope and wording of the discrepancy.
The runoff originates 'from Veridian farms' and involves 'nitrogen runoff' generally, not just synthetic nitrogen runoff.
This precise wording leaves room for non-synthetic sources of nitrogen on the farms to be the cause of the increase.
3
Analyze the options to find a mechanism that allows both premises to coexist.
The correct option reveals that farmers compensated for the drop in synthetic fertilizer by using organic manure, which leaches nitrogen at a much higher rate.
This provides the necessary context: total synthetic use dropped, but total nitrogen runoff from farms increased due to the substitution of a more runoff-prone fertilizer.

Key Concept

To resolve a paradox, one must find an unstated mechanism, often an unintended consequence or alternative cause, that allows two apparently contradictory facts to both be strictly true without violating the scope of either premise.
Question 1410Question →

Conservationist: The drastic drop in local almond yields over the last two years was caused by the introduction of a new pesticide that devastated the native honeybee population, which had been the primary pollinator of the almonds. To solve this problem, we should release the Blue Orchard mason bee into our almond orchards. The Blue Orchard mason bee is highly resistant to this new pesticide. Therefore, releasing the Blue Orchard mason bee will successfully restore almond yields to their previous levels.

Which of the following statements, if logically negated, would fatally undermine the conservationist's central conclusion? Select all that apply.

Select all that apply

Show answer & explanation

Answer: The Blue Orchard mason bee is capable of effectively pollinating almond trees.; The new pesticide has not directly damaged the almond trees in a way that significantly reduces their capacity to produce almonds.

Answer

The statements confirming that the mason bee can effectively pollinate almond trees and that the pesticide did not independently damage the trees' production capacity.
The correct statements represent unstated necessary assumptions in the conservationist's argument. When we apply the negation technique to them, the logical chain breaks. If the Blue Orchard mason bee cannot effectively pollinate almond trees, their introduction will fail to restore yields. Likewise, if the pesticide has already directly damaged the trees' capacity to produce almonds, merely replacing the pollinator will not achieve the desired outcome.

Step-by-Step Solution

1
Identify the argument's conclusion and premises.
Conclusion: Releasing the Blue Orchard mason bee will restore almond yields. Premises: Yields dropped because a pesticide killed the primary pollinator (native honeybee), and the mason bee is resistant to this pesticide.
Understanding the core argument structure is required to find unstated logical gaps in the reasoning.
2
Apply the negation technique to each answer choice.
Mentally negate each option to test if its falsity would make the conclusion impossible.
A necessary assumption is a statement that must be true for the conclusion to hold; therefore, its logical opposite must destroy the conclusion.
3
Evaluate the impact of the negated choices on the conclusion.
If the mason bee cannot pollinate the trees, or if the trees themselves are severely damaged by the pesticide, yields cannot be restored. Negating the other options does not prevent yields from returning to their previous levels.
This isolates the assumptions strictly required by the argument's internal logic, distinguishing them from statements that might merely strengthen the argument.

Key Concept

Applying the Negation Technique to Necessary Assumptions
Question 1411Question →

Ornithologist: In the past few decades, populations of the crested scrub-jay living in urban areas have developed significantly shorter beaks than those living in surrounding rural woodlands. This morphological change is an evolutionary adaptation. Shorter beaks are better suited for scavenging human food scraps from flat surfaces, which are abundant in urban areas, whereas the longer beaks of rural jays are necessary for extracting insects from deep crevices in tree bark.

Which of the following statements, if true, strengthen the ornithologist's argument? (Select all that apply.)

Select all that apply

Show answer & explanation

Answer: Urban scrub-jays raised in captivity from hatching on a strict diet of tree-dwelling insects still develop shorter beaks than rural scrub-jays.; When presented with identical human food scraps on a flat surface, scrub-jays with shorter beaks consume the food significantly faster than those with longer beaks.

Answer

The correct statements are the one demonstrating that captive urban jays retain short beaks regardless of diet, and the one confirming that shorter beaks provide a consumption speed advantage on flat surfaces.
The ornithologist argues that the shorter beaks in urban scrub-jays are an evolutionary adaptation specifically suited for scavenging human food scraps. To strengthen this causal claim, we must support the mechanism or rule out alternative explanations. The option involving jays raised in captivity strengthens the argument by ruling out environmental plasticity (e.g., that eating from flat surfaces simply wears down the beak), thereby supporting the claim that the change is genetic. The option comparing food consumption speeds directly validates the premise that shorter beaks provide a tangible mechanical advantage for scavenging on flat surfaces.

Step-by-Step Solution

1
Identify the main conclusion and the supporting premises of the argument.
Conclusion: The shorter beaks of urban scrub-jays are an evolutionary adaptation for scavenging human food scraps. Premises: Urban jays have shorter beaks than rural jays; short beaks are better for flat surfaces; long beaks are needed for tree bark.
Understanding the core argument structure is required before evaluating how to strengthen its logic.
2
Analyze the logical gaps or vulnerabilities in the argument.
The argument assumes the change is genetic/evolutionary rather than a physical result of wear and tear (developmental plasticity). It also assumes the theoretical advantage of short beaks actually translates to a practical advantage in acquiring food.
Identifying weaknesses highlights exactly what kind of new information would shore up the argument's plausibility.
3
Evaluate the answer choices against the identified gaps.
The statement about captive-raised jays proves the trait is genetic, eliminating the alternative cause of physical wear. The statement about consumption speed proves the practical advantage, validating the proposed mechanism.
Correct answers in a strengthen question must directly address and bridge the logical gaps in the author's reasoning.

Key Concept

Strengthen - Ruling out Alternate Causes and Validating Causal Mechanisms
Estimated Time:2m 0s
Question 1412Question →

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.

Click a left item, then click its matching right item

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.

Matches

Show answer & explanation

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 1413Question →

Epidemiologist: To defend against novel pathogens, our health agency is exclusively funding the rapid sequencing of viral genomes to facilitate the swift creation of targeted vaccines. However, targeted vaccines are efficacious only if a critical mass of the population undergoes inoculation. Recent extensive polling reveals a historically unprecedented decline in the public's willingness to accept novel vaccines. Consequently, because of this decline, the agency's funding strategy will inevitably fail to provide an efficacious defense against novel pathogens.

Which one of the following is an assumption required by the epidemiologist's argument?

Show answer & explanation

Answer: The decline in public willingness to accept novel vaccines is significant enough to prevent a critical mass of the population from undergoing inoculation.

Answer

The correct option is the one stating that the decline in public willingness is significant enough to prevent a critical mass of the population from undergoing inoculation.
To evaluate a necessary assumption, apply the Negation Technique: negate the statement and see if it destroys the argument. The author concludes the strategy will inevitably fail because of the recent decline in willingness. The premise states efficacy requires a 'critical mass' of inoculation. If we negate the correct statement, we get: 'The decline is NOT significant enough to prevent a critical mass.' If a critical mass can still be achieved despite the decline, then the vaccines could still be efficacious. This completely destroys the author's conclusion that failure is inevitable, proving this assumption is absolutely required.

Step-by-Step Solution

1
Analyze the argument structure to identify premises and the main conclusion.
Premise 1: Efficacy requires a critical mass. Premise 2: There is a massive decline in public willingness. Conclusion: The strategy will inevitably fail.
Understanding the exact logical flow is necessary to spot the gap between the evidence provided and the absolute certainty of the conclusion.
2
Identify the logical gap or term shift between the premises and the conclusion.
The author jumps from 'a decline in willingness' to the certainty of failure. Since failure happens if there is no 'critical mass', the gap is the assumption that the decline strictly means a critical mass will not be reached.
Necessary assumptions always bridge a gap or eliminate an alternative possibility that would prevent the conclusion from following logically from the premises.
3
Apply the Negation Technique to the most likely answer choices.
Negating the correct statement creates a scenario where the decline exists, but a critical mass is still reached. This direct contradiction destroys the conclusion.
The Negation Technique is the definitive test for necessary assumptions; if the logical opposite of a choice destroys the argument, that choice is strictly required.

Key Concept

Applying the Negation Technique to Necessary Assumptions
Estimated Time:2m 0s
Question 1414Question →

City Planner: To alleviate the severe traffic congestion in the downtown area, the city council has proposed implementing a substantial toll for vehicles entering the district during peak hours. This toll will certainly cause a dramatic reduction in the number of private passenger vehicles entering the downtown area during these hours. Therefore, implementing this toll will successfully result in significantly shorter commute times for those individuals who continue to drive into the downtown area.

Which of the following statements are assumptions required by the city planner's argument? Select all that apply.

Select all that apply

Show answer & explanation

Answer: The reduction in private passenger vehicles will not be entirely offset by an influx of commercial or public transit vehicles entering the downtown area.; The duration of commutes in the downtown area is not determined exclusively by factors that are completely unaffected by the volume of vehicle traffic.

Answer

The correct statements are the one ensuring the reduction in vehicles is not offset by other types of traffic, and the one stating commute durations are not exclusively determined by factors independent of traffic volume.
Both correct statements are logically required for the city planner's conclusion to hold. If the reduction in private vehicles were entirely offset by an influx of other vehicles, the overall traffic volume would not decrease, preventing shorter commutes. Similarly, if commute times were determined exclusively by factors unaffected by traffic volume, then reducing vehicle volume would have no effect on commute duration. Applying the negation technique to either of these statements logically destroys the author's conclusion.

Step-by-Step Solution

1
Analyze the argument structure to identify the core premise and the main conclusion.
Premise: A toll will dramatically reduce private vehicles entering downtown. Conclusion: This will result in significantly shorter commute times for those who continue to drive downtown.
Isolating the core argument is the essential first step in identifying the logical gap.
2
Identify the logical gap between the premise and the conclusion.
The argument assumes that a reduction in private vehicles directly and successfully translates to shorter commute times, ignoring potential offsetting variables.
Necessary assumptions must bridge this gap or defend the argument against alternative scenarios that would block the conclusion.
3
Apply the negation technique to each candidate option.
Negating the correct options completely destroys the conclusion. Negating the incorrect options leaves the argument logically intact.
The negation technique is the definitive test for validating a necessary assumption.

Key Concept

Applying the Negation Technique to Necessary Assumptions
Question 1415Question →

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.

Click a left item, then click its matching right item

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.

Matches

Show answer & explanation

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 1416Question →

A city introduced a substantial congestion charge aimed at reducing the number of passenger vehicles entering the downtown area during peak hours. However, six months after the charge's implementation, the number of passenger vehicles entering the downtown area during peak hours had actually increased by 15 percent.

The apparent discrepancy is successfully resolved by the additional fact that surveys show most downtown commuters consider the new congestion charge to be a severe financial burden.

Show answer & explanation

Answer: False

Answer

False
The proposed statement is false because the additional fact does not bridge the gap between the premises; instead, it makes the discrepancy even more baffling. If the congestion charge is viewed as a severe financial burden, one would naturally expect commuters to seek alternatives, leading to a decrease in traffic. Because the fact does not explain the unexpected increase in vehicles, it fails to serve as a valid resolution.

Step-by-Step Solution

1
Identify the two conflicting premises in the stimulus.
Premise 1: A substantial congestion charge was introduced to reduce peak-hour traffic. Premise 2: Peak-hour traffic actually increased by 15 percent.
Resolving a paradox requires first isolating the exact nature of the apparent contradiction.
2
Determine the necessary role of a resolving fact.
A valid resolution must provide a contextual mechanism showing why traffic increased despite the intentional financial penalty.
The correct additional premise must allow both original facts to be simultaneously true without invalidating either one.
3
Evaluate the proposed resolution's impact on the paradox.
The fact that commuters find the charge to be a severe financial burden gives them an even stronger incentive to stop driving. Thus, the traffic increase becomes even more surprising.
A fact that makes an outcome more contradictory is a paradox-deepening trap, not a valid resolution.

Key Concept

Bridging Conflicting Premises
Question 1417Question →

Medical researcher: When evaluated against a placebo in our most recent large-scale trial, the experimental allergy medication reduced the frequency of symptomatic episodes by a statistically significant margin. Therefore, health professionals should recommend this medication as a replacement for current over-the-counter treatments, because patients will obviously benefit from experiencing such a significant improvement in their daily routines.

Which one of the following most accurately describes a flaw in the medical researcher's reasoning?

Show answer & explanation

Answer: shifts illicitly from using a term to indicate that a study's results were unlikely to have occurred by chance to using that same term to indicate that an effect is practically meaningful

Answer

The argument trades on an ambiguity in the word 'significant', using it in a statistical sense in the premise and in a practical, everyday sense in the conclusion.
The correct answer accurately identifies that the argument commits the fallacy of equivocation. In the premise, 'statistically significant' simply means the data shows a measurable difference that is not due to statistical noise or chance—even if the actual reduction in symptoms is microscopic. In the conclusion, the researcher uses 'significant improvement' to mean a major, noticeable change in patients' daily lives. The argument falsely equates these two entirely different meanings of 'significant' to justify replacing current treatments.

Step-by-Step Solution

1
Analyze the argument's structure to identify the premises and the main conclusion.
Premise: The medication reduced symptoms by a 'statistically significant' margin. Conclusion: It should replace current treatments because it provides a 'significant improvement'.
Separating the evidence from the claim helps isolate the logical gap.
2
Evaluate the relationship between the premise and the conclusion for vulnerabilities.
The conclusion assumes that the mathematical certainty of the result (statistical significance) equates to a large, life-changing magnitude of relief (practical significance).
An argument must logically bridge its evidence to its conclusion without changing the meaning of key concepts.
3
Identify the specific logical fallacy being committed based on the vulnerability.
The argument commits an equivocation fallacy by shifting the meaning of the word 'significant' halfway through the reasoning.
A term cannot have two distinct meanings within the same logical proof without invalidating the conclusion.
4
Select the option that accurately describes this semantic shift.
The correct option highlights the shift from 'unlikely to have occurred by chance' to 'practically meaningful'.
This precisely matches the equivocation identified in the text without introducing outside assumptions.

Key Concept

Equivocation (Uncertain Use of a Term)
Question 1418Question →

Botanist: The rare Moonflower typically blooms only when exposed to a specific ultrasonic frequency produced by the wings of the Silver Moth. However, a thriving population of blooming Moonflowers was recently discovered on a remote island where Silver Moths are completely absent. Clearly, another species of insect on this island must produce this same ultrasonic frequency, thereby triggering the flowers to bloom.

Which of the following, if true, most strengthens the botanist's argument?

Show answer & explanation

Answer: When grown from seed in a silent, controlled laboratory setting, Moonflowers from the remote island will not bloom unless exposed to the specific ultrasonic frequency.

Answer

The option stating that Moonflowers from the island will not bloom in a silent laboratory unless exposed to the specific frequency.
The botanist concludes that another insect species on the island is producing the required ultrasonic frequency. This argument fundamentally relies on the assumption that the island Moonflowers still actually require this frequency to bloom. The correct answer eliminates the alternative explanation that the island population has simply evolved to bloom without any acoustic stimulation. By confirming that the frequency is still biologically necessary for these specific flowers, it strengthens the premise that the frequency must be physically present on the island, thereby bolstering the conclusion.

Step-by-Step Solution

1
Identify the core components of the argument.
Premise: Moonflowers need a specific ultrasonic frequency to bloom, usually from Silver Moths. Premise: Blooming Moonflowers are on an island without Silver Moths. Conclusion: Another insect on the island produces the frequency.
Understanding the structural relationship between premises and conclusion is necessary to evaluate gaps.
2
Identify the logical gap or assumption made by the author.
The author assumes that the Moonflowers on the island still require the ultrasonic frequency to bloom, rather than having adapted to bloom without it.
Arguments often rely on unstated assumptions that, if false, would cause the argument to collapse.
3
Evaluate the answer choices to find one that supports this assumption or rules out an alternative explanation.
The correct answer demonstrates that the island Moonflowers still biologically require the frequency, ruling out the alternative that they evolved to no longer need it.
Eliminating a viable alternative explanation (that the plants changed) forces us to accept that the frequency is present, strengthening the claim that a new insect is providing it.

Key Concept

Ruling Out Alternative Explanations (Defender Assumption)
Estimated Time:1m 30s
Question 1419Question →

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.

Click a left item, then click its matching right item

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

Show answer & explanation

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 1420Question →

Consider the following argument:

Architect: A building cannot be considered a modernist masterpiece unless it prioritizes functional utility over ornamentation and utilizes industrial materials like steel or glass. The new municipal library clearly utilizes industrial materials, featuring a striking glass facade supported by a steel frame. Furthermore, its interior layout was strictly dictated by the practical requirements of storing and accessing books.
Therefore, the new municipal library is a modernist masterpiece.

Statement: The assumption 'Any building whose interior layout is strictly dictated by practical requirements prioritizes functional utility over ornamentation' is sufficient to logically guarantee the architect's conclusion.

Show answer & explanation

Answer: False

Answer

False
The correct answer is False because the original argument commits a flaw of conditional logic by treating necessary conditions as sufficient. While the proposed assumption successfully bridges a semantic gap to prove the library meets all necessary conditions, fulfilling necessary conditions is never logically sufficient to guarantee the conclusion.

Step-by-Step Solution

1
Diagram the conditional logic in the first sentence.
Modernist Masterpiece (MM) -> Prioritizes Functional Utility (PFU) AND Utilizes Industrial Materials (UIM).
The phrase 'cannot be considered... unless' introduces necessary conditions that must be placed on the right side of the conditional arrow.
2
Identify the premises regarding the specific subject (the municipal library).
The library has UIM (glass and steel) and its layout was dictated by practical requirements.
To map the evidence provided against the established conditional rules.
3
Analyze the proposed assumption to see what it adds.
The assumption 'Dictated by practical requirements -> PFU' establishes that the library definitely possesses PFU.
We must evaluate how this new premise changes the argument's validity.
4
Evaluate if the combined premises logically guarantee the conclusion.
With the assumption, we know the library has both PFU and UIM. The conclusion asserts the library is an MM. However, MM -> (PFU AND UIM). Fulfilling the necessary conditions does not guarantee the sufficient condition (MM).
A sufficient assumption must make the conclusion 100% deductively valid. Affirming the consequent commits a formal flaw, so the assumption is insufficient.

Key Concept

Distinguishing between necessary and sufficient conditions in formal logic, and recognizing that bridging a semantic premise gap cannot repair an underlying structural flaw.

Alternative Method

You can quickly eliminate the proposed assumption by looking purely at the logical structure rather than the meaning of the words. The first premise establishes the structure: A -> (B and C). The conclusion asserts A. Since the premises only establish the right side of the conditional, no assumption that merely reinforces the right side can ever prove the left side (A). A sufficient assumption must explicitly state that (B and C) -> A.
Estimated Time:2m 0s
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