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Critical Reasoning: Discrepancies and Flaws

65 questions

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Question 61Question →

To evaluate overall tap water safety across a metropolitan region containing over 100,000 residential units, a municipal environmental agency tested water samples collected exclusively from 500 newly constructed apartment complexes built within the last two years. Finding no detectable levels of lead or industrial contaminants in any of the tested samples, the agency concluded that the region's entire residential tap water infrastructure is free from lead contamination.

The reasoning in the agency's argument is most vulnerable to criticism on the grounds that it

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Answer: draws a definitive conclusion about the entire residential water system based on a sample of buildings that, owing to their recent construction, may not be representative of older structures.

Answer

The argument is vulnerable because it draws a conclusion about all residential buildings based on a sample of newly constructed complexes, which are likely subject to modern lead-free building codes and thus unrepresentative of older housing stock.
The correct answer highlights a classic sampling bias: testing only recently built properties creates a selection bias because modern plumbing standards typically prohibit lead materials. Concluding that all 100,000+ residential units are lead-free based on a sample that excludes older, higher-risk structures is a flawed generalization.

Step-by-Step Solution

1
Identify the conclusion and evidence
Conclusion: The region's entire residential tap water infrastructure is free from lead contamination. Evidence: Water samples from 500 apartment complexes built in the last two years showed no detectable lead.
Understanding the gap between the evidence and the conclusion reveals logical vulnerabilities.
2
Evaluate the sample representation
The sample consists strictly of buildings built within the last two years, whereas the conclusion generalizes to over 100,000 residential units across the entire metropolitan region.
Sampling only recent construction introduces systematic bias, as modern building regulations typically forbid lead piping materials that may exist in older buildings.
3
Match with the correct flaw description
The option noting that newly constructed buildings may not represent older structures correctly points out the sampling flaw.
An unrepresentative sample invalidates a broad generalization.

Key Concept

Sampling and Generalization Flaws (Unrepresentative Sample Bias)
Estimated Time:2m 0s
Question 62Question →

To qualify for the Municipal Green Architecture Grant, a building renovation project must reduce its annual energy consumption by at least 40 percent. The recent renovation of the historic Sterling Theater successfully reduced its annual energy consumption by 45 percent. Therefore, the Sterling Theater project will definitely receive the Municipal Green Architecture Grant.

Which of the following best describes the flaw in the reasoning above?

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Answer: It treats a requirement necessary for obtaining the grant as if it were a sufficient condition to guarantee receiving the grant.

Answer

The argument's flaw is that it treats a necessary prerequisite (reducing energy consumption by at least 40 percent) as though it were a sufficient condition that guarantees receiving the grant.
The passage establishes that achieving a 40 percent energy reduction is a necessary condition ('must') to qualify for the grant. The author observes that the Sterling Theater achieved a 45 percent reduction and concludes that it will definitely receive the grant. This reasoning is flawed because satisfying a necessary condition makes a project eligible, but does not guarantee that the grant will be awarded; there may be other criteria, budget limitations, or competitive evaluations involved. Thus, the argument incorrectly treats a necessary condition as a sufficient one.

Step-by-Step Solution

1
Analyze the premises and conditional statement
The text states that reducing energy consumption by at least 40 percent is a mandatory requirement ('must') to qualify for the grant. This establishes energy reduction as a necessary condition.
Identifying indicator words like 'must' helps distinguish necessary conditions from sufficient conditions.
2
Analyze the evidence and conclusion
The Sterling Theater achieved a 45 percent reduction (satisfying the necessary condition), and the author concludes that the project will 'definitely receive' the grant.
The author concludes that satisfying the entry requirement guarantees the final outcome.
3
Identify the logical vulnerability
Satisfying a necessary requirement makes an applicant eligible to be considered, but does not guarantee selection (there could be limited funds, additional criteria, or competing applicants).
Mistaking eligibility (necessary) for a guarantee of success (sufficient) is a classic formal logic flaw.

Key Concept

Confusing Necessary and Sufficient Conditions
Estimated Time:1m 30s
Question 63Question →

To receive Series A funding from Vantage Ventures, a biotech startup must demonstrate successful Phase I safety trials for its lead drug candidate. BioSphere Therapeutics recently completed its Phase I trials with zero reported adverse events among all trial participants. The company's founders concluded that because they satisfied the firm's mandate by completing Phase I safety trials, Vantage Ventures will definitely approve their application for Series A funding. Which of the following best describes the vulnerability in the founders' reasoning?

Show answer & explanation

Answer: It treats a condition that is necessary for securing funding as though it were sufficient to guarantee that funding.

Answer

The argument incorrectly treats a necessary prerequisite (completing Phase I safety trials) as a sufficient condition that guarantees funding approval.
The passage establishes that completing Phase I safety trials is a requirement (a necessary condition) for receiving Series A funding from Vantage Ventures. However, the founders conclude that meeting this single requirement guarantees funding approval (treating it as a sufficient condition). The argument fails to consider that other necessary conditions, such as commercial viability or valuation agreements, might also need to be satisfied.

Step-by-Step Solution

1
Identify the premises and modal qualifiers in the argument.
Premise: Securing funding requires Phase I safety trials ('must demonstrate'). Fact: BioSphere completed Phase I safety trials.
This establishes that Phase I safety trials are a necessary condition for obtaining funding.
2
Analyze the conclusion reached by the founders.
Conclusion: Vantage Ventures will definitely approve the funding application because Phase I safety trials were completed.
The founders treat fulfilling the prerequisite as a guarantee of the outcome ('definitely approve').
3
Evaluate the logical gap between the premises and conclusion.
Confusing a necessary condition with a sufficient condition.
Meeting a requirement is necessary to be considered, but other factors (financials, market size, team) may also be required before funding is granted.

Key Concept

Confusing Necessary and Sufficient Conditions
Question 64Question →

An analysis of a technology firm's policy statement reveals a logical flaw based on equivocation:

"Our committee mandates that all software deployments must ensure user security. Comprehensive data encryption guarantees technical security against external cyberattacks. Therefore, deploying robust data encryption fully satisfies a technology firm's ethical security responsibilities toward its customer base."

Match each key term from the argument on the left to the specific shift in meaning it undergoes between the premise context and the conclusion context on the right.

Click a left item, then click its matching right item

Items

Security
Satisfies responsibilities
External cyberattacks

Matches

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Answer

The correct matches are: 'Security' matches with the shift from technical protection to broad ethical safeguarding; 'Satisfies responsibilities' matches with the shift from technical compliance to fulfilling overall moral duties; and 'External cyberattacks' matches with the shift from technical network intrusions to general breaches of user trust.
The argument commits an equivocation flaw by introducing terms under narrow, technical definitions in the premises and quietly broadening their definitions in the conclusion. 'Security' shifts from technical data protection to comprehensive ethical duty; 'Satisfies responsibilities' shifts from meeting specific software parameters to fulfilling complete moral duties; and 'External cyberattacks' shifts from specific cyber intrusions to any violation of consumer trust.

Step-by-Step Solution

1
Analyze how the term 'Security' is introduced in the premise versus the conclusion.
The premise restricts 'security' to technical data encryption against cyber threats, whereas the conclusion equates it to broad corporate ethical duties.
Identifying shifts in definition is essential for exposing equivocation flaws.
2
Examine the scope shift in 'Satisfies responsibilities'.
Meeting technical encryption criteria (a narrow obligation) is conflated with fulfilling all ethical duties owed to users.
The argument uses technical compliance to improperly claim total moral compliance.
3
Evaluate the phrase 'External cyberattacks' across contexts.
Preventing unauthorized digital access is assumed to cover all dimensions of user trust and safety.
Conflating a specific threat type with overall user safety illustrates a shift in semantic scope.

Key Concept

Equivocation and Shift in Term Meaning
Question 65Question →

Council Member: The proposed city ordinance requiring developers to allocate 15 percent of new residential land to municipal green space will inevitably improve overall community public health. We can be certain that dedicated urban parkland enhances resident health because any residential development that incorporates designated green spaces inherently produces superior public health outcomes.

Which of the following best describes the flaw in the council member's reasoning?

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Answer: It supports its conclusion about public health benefits by offering a premise that merely restates that conclusion in different terms.

Answer

The argument commits the flaw of circular reasoning because its premise offers no independent evidence, simply rephrasing the main conclusion.
The correct answer accurately describes the flaw of begging the question (circular reasoning). The council member attempts to justify the claim that green space allocation will improve public health by stating as a premise that green space development inherently produces superior public health outcomes. Because the premise is merely a rephrasing of the conclusion, the argument offers no independent evidence.

Step-by-Step Solution

1
Identify the main conclusion of the argument.
Main Conclusion: The proposed ordinance requiring 15% green space will improve community public health.
Understanding the ultimate claim being made is necessary before evaluating its support.
2
Identify the evidence (premise) offered in support of the main conclusion.
Premise: Dedicated urban parkland enhances resident health because residential green spaces inherently produce superior public health outcomes.
Evaluating the support mechanism reveals how the speaker attempts to prove the claim.
3
Analyze the relationship between the premise and the conclusion.
The premise does not provide external evidence, data, or logical explanation; it assumes that green spaces inherently improve health, which is the exact claim requiring proof.
This logical structure is the classic definition of begging the question or circular reasoning.

Key Concept

Circular Reasoning and Begging the Question
Estimated Time:1m 45s
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