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382 questions

Question 1Question →

According to city records, every commercial project approved by the Planning Board this year required an environmental impact study. Furthermore, any project that requires an environmental impact study is subject to a 60-day public review period. Records also indicate that most of the commercial projects approved by the Planning Board this year received a municipal development grant. However, under city charter, no project that receives a municipal development grant is exempt from the city's prevailing wage ordinance.

Based on the information provided, which of the following statements must be true? Select all that apply.

Select all that apply

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Answer: Every commercial project approved by the Planning Board this year is subject to a 60-day public review period.; At least some projects subject to a 60-day public review period are not exempt from the city's prevailing wage ordinance.

Answer

The correct answers are the statement that every commercial project approved this year is subject to the review period, and the statement that at least some projects subject to the review period are not exempt from the wage ordinance.
Both correct statements can be logically deduced with complete certainty. The first follows directly from chaining two absolute rules: if a project is an approved commercial project, it needs an environmental study, and if it needs an environmental study, it requires a public review period. The second follows by combining quantifiers: since all approved commercial projects undergo public review, and most of them receive a grant (which means they cannot be exempt from the wage ordinance), it must be true that at least some projects undergoing public review are not exempt from the wage ordinance.

Step-by-Step Solution

1
Diagram the absolute conditional statements to form a logical chain.
Commercial Project (CP) → Environmental Impact Study (EIS) → Public Review Period (PRP).
To establish the guaranteed baseline properties of all commercial projects approved this year.
2
Diagram the quantifier statements and negative conditional rules.
CP -[most]→ Municipal Grant (MG), and MG → Not Exempt (~Exempt).
To identify what is true for the majority of these commercial projects.
3
Synthesize the chains to find derivative inferences.
Since all CP are PRP, and most CP are MG (which means most CP are ~Exempt), there is an overlap: some things that are PRP must also be ~Exempt.
To systematically pre-phrase the necessary truths before evaluating the choices.

Key Concept

Drawing formal logic deductions by combining transitive conditional chains with proportion quantifiers (some/most).
Estimated Time:1m 45s
Question 2Question →

Legal Scholar: The proposed legislation mandating transparency for pre-trial risk assessment algorithms is intended to eliminate racial bias in bail decisions. Under this mandate, developers must publicly disclose the precise mathematical weights their algorithms assign to various risk factors. However, the datasets used to train these algorithms are heavily skewed by historically biased arrest records. Since merely publishing these weights will not alter how the underlying algorithms mathematically process this historically biased training data, the proposed legislation will ultimately fail to eliminate racial bias in bail decisions.

Which of the following are assumptions on which the legal scholar’s argument depends? (Select all that apply.)

Select all that apply

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Answer: The requirement to disclose algorithmic weights will not compel developers to retrain their systems using unbiased data prior to publication.; Magistrates will not utilize the disclosed mathematical weights to systematically identify and counteract the bias in the algorithms' recommendations when making bail decisions.

Answer

The correct assumptions are that the disclosure requirement will not compel developers to retrain their algorithms with unbiased data, and that magistrates will not use the disclosed weights to manually counteract the bias in their final decisions.
The argument concludes that the legislation will fail to eliminate bias in 'bail decisions' strictly because publishing weights does not alter how algorithms process biased data. For this conclusion to hold, the author MUST assume two things: first, that the threat of publication won't cause developers to fix the data beforehand (which would eliminate the bias), and second, that the end-users of the algorithm (the magistrates) won't use the newly transparent weights to manually correct the bias in their actual decisions. If either of these events occurred, the legislation could succeed, thereby destroying the author's conclusion.

Step-by-Step Solution

1
Analyze the core argument structure.
Conclusion: The legislation will fail to eliminate racial bias in bail decisions. Premises: Transparency only forces the publication of weights; training data is biased; publishing weights doesn't change how algorithms process this data.
Deconstructing the stimulus separates facts from the author's inferential leaps.
2
Identify logical gaps between the premises and the conclusion.
The author assumes that because the legislation doesn't alter the algorithm's *internal math post-publication*, it cannot affect the *developer's behavior pre-publication* or the *human judge's final decision*.
Necessary assumptions almost always live in the unstated space between the exact mechanism described in the premises and the final outcome claimed in the conclusion.
3
Apply the Negation Test to candidate answers.
Negating the statement about developers retraining algorithms destroys the conclusion. Negating the statement about magistrates manually counteracting bias destroys the conclusion.
The Negation Test is the definitive proof of a necessary assumption. If negating an option invalidates the argument, that option is logically required.

Key Concept

Identifying Necessary Assumptions using the Negation Technique, particularly recognizing defender assumptions that rule out alternate pathways to success.
Question 3Question →

Maritime Regulator: The proposed automated docking protocol relies entirely on continuous satellite telemetry rather than traditional visual guidance from harbormasters. Therefore, mandating this new protocol for all commercial vessels entering the bay will definitively decrease the frequency of docking collisions and subsequently reduce the port's overall operational liabilities.

Which of the following statements function as required assumptions to logically bridge the gaps in the regulator's argument? Select all that apply.

Select all that apply

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Answer: Relying on continuous satellite telemetry rather than traditional visual guidance leads to fewer docking collisions.; A decrease in the frequency of docking collisions will result in a reduction of the port's overall operational liabilities.

Answer

The correct selections are the statement connecting satellite telemetry to fewer collisions, and the statement connecting decreased collisions to reduced operational liabilities.
The argument contains a chain of reasoning with two explicit logical leaps. The author moves from a factual premise (the protocol uses satellite telemetry instead of visual guidance) to a claim about safety (fewer collisions) and then to a claim about finances (reduced liabilities). For the argument to be logically valid, it strictly requires assumptions that connect these disparate concepts together. The correct statements act as these necessary bridges.

Step-by-Step Solution

1
Identify the core premises of the argument.
Premise: The new protocol uses satellite telemetry instead of visual guidance.
Deconstructing the argument structure is the first step in finding logical gaps.
2
Identify the core conclusions of the argument.
Conclusion: The new protocol will decrease docking collisions AND reduce overall operational liabilities.
Understanding exactly what the author is trying to prove reveals which terms are 'rogue' or unsupported.
3
Identify new terms in the conclusion that do not appear in the premises.
The concepts of 'decreased frequency of docking collisions' and 'reduced operational liabilities' are introduced in the conclusion without prior support.
In a Supporter Assumption question, rogue terms in the conclusion must be explicitly linked to the premises.
4
Formulate the required bridging statements.
Bridge 1: Satellite telemetry must lead to fewer collisions. Bridge 2: Fewer collisions must lead to reduced liabilities.
These connections are absolutely necessary for the argument's logic to flow from the premises to the stated conclusions.

Key Concept

Identifying multiple logical gaps in an argument and selecting the exact supporter assumptions required to link rogue conclusion elements back to the premises.
Question 4Question →

Agronomist: In a multi-year agricultural study across several commercial grain farms, fields planted with hairy vetch as a winter cover crop produced subsequent corn yields that were on average 20 percent higher than those from fields left fallow during the winter. Because hairy vetch is known to fix atmospheric nitrogen into the soil, this substantial increase in yield must be directly attributable to the additional nitrogen provided by the cover crop.

Which of the following statements, if true, most seriously weaken the agronomist's argument? Select all that apply.

Select all that apply

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Answer: Fields planted with hairy vetch retained significantly higher soil moisture throughout early summer droughts than fallow fields, and moisture retention is the primary determinant of corn yields in these regions.; Farmers participating in the study applied identical high levels of synthetic nitrogen fertilizer to all fields, raising soil nitrogen well above the maximum threshold usable by corn plants.

Answer

The argument is weakened by the statement establishing soil moisture retention as an alternate cause for the higher yields, as well as the statement demonstrating that preexisting synthetic fertilizer levels already saturated the crops' nitrogen requirements.
The correct statements undermine the argument by challenging the causal attribution: one introduces an alternative causal factor (enhanced moisture retention during critical drought periods) that fully accounts for the yield disparity, while the other shows that nitrogen levels were already saturated beyond the threshold of utility, eliminating the possibility that supplemental nitrogen caused the yield improvement.

Step-by-Step Solution

1
Identify the conclusion and the supporting premises in the stimulus
Premise: Fields with hairy vetch cover crops produced 20 percent higher corn yields than fallow fields. Premise: Hairy vetch fixes atmospheric nitrogen. Conclusion: The yield increase must be directly attributable to the additional nitrogen.
Isolating the structural components reveals the core causal claim made by the author.
2
Identify the underlying assumptions and potential points of vulnerability
The author assumes that nitrogen fixation is the only relevant difference caused by the cover crop and that additional nitrogen was capable of driving yield gains in this setting.
Causal arguments can be weakened by offering an alternative cause for the effect or showing that the proposed cause could not have produced the effect.
3
Evaluate each option to find all statements that undermine the causal connection
Introducing moisture retention as the decisive factor provides an alternative explanation, while showing that nitrogen was already supplied past the crop's uptake capacity negates the proposed causal mechanism.
Both findings directly attack the link between the cover crop's nitrogen fixation and the observed yield increase.

Key Concept

Weakening causal arguments through alternative explanations and demonstrating the ineffectiveness of the proposed cause
Estimated Time:1m 30s
Question 5Question →

An environmental audit of reclaimed sub-boreal wetland zones established the following criteria for ecosystem stabilization:

• Any wetland zone that undergoes successful peat layer restoration exhibits stable anaerobic methanogenesis, unless it experiences persistent sulfur runoff.
• Every wetland zone that exhibits stable anaerobic methanogenesis maintains a neutral pH level throughout its rooting substrate.
• No wetland zone that maintains a neutral pH level in its rooting substrate supports the proliferation of invasive reed canary grass.
• During the previous assessment cycle, Zone 14 underwent successful peat layer restoration and did not experience persistent sulfur runoff.

If the statements above are true, which of the following statements must also be true? (Select all that apply.)

Select all that apply

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Answer: Zone 14 maintains a neutral pH level throughout its rooting substrate.; Any wetland zone in the audit that supports the proliferation of invasive reed canary grass does not exhibit stable anaerobic methanogenesis.

Answer

The statements establishing that Zone 14 maintains a neutral pH level throughout its rooting substrate and that any wetland zone supporting invasive reed canary grass proliferation does not exhibit stable anaerobic methanogenesis must both be true.
The deduction concerning Zone 14 directly follows from a complete forward chain through the conditional rules triggered by its factual premises. The deduction concerning any zone with canary grass proliferation represents a valid contrapositive linking the absence of proliferation back to the absence of stable anaerobic methanogenesis.

Step-by-Step Solution

1
Diagram the formal conditional rules from the stimulus.
Rule 1: (Peat Restoration AND NOT Sulfur Runoff) → Stable Methanogenesis. Rule 2: Stable Methanogenesis → Neutral pH. Rule 3: Neutral pH → NOT Invasive Canary Grass Proliferation.
Establishing explicit conditional chains allows for unambiguous forward deductions and contrapositives.
2
Evaluate the factual findings regarding Zone 14.
Zone 14 satisfies both components of the antecedent in Rule 1, establishing that Zone 14 exhibits Stable Methanogenesis → Neutral pH → NOT Invasive Canary Grass Proliferation.
Modus ponens guarantees each successive necessary condition for Zone 14.
3
Derive universal contrapositive inferences for the entire audited population.
By linking Rule 2 and Rule 3: Stable Methanogenesis → NOT Invasive Canary Grass Proliferation. The contrapositive is: Invasive Canary Grass Proliferation → NOT Stable Methanogenesis.
A conditional claim and its contrapositive are logically equivalent.

Key Concept

Deductive Conditional Chaining and Contrapositive Inference
Estimated Time:2m 0s
Question 6Question →

An educational researcher reviewed data from a large district of elementary school students. The researcher noted that students who regularly participate in after-school chess clubs consistently achieve higher grades in computer science classes. Based on this observation, the researcher concluded that playing chess directly enhances a student's computer science abilities.

Which of the following statements, if true, expose the flaw in the argument by providing a valid alternative explanation for the observed correlation? Select all that apply.

Select all that apply

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Answer: Students who already possess strong analytical skills necessary for computer science are naturally drawn to joining chess clubs.; Schools that offer after-school chess clubs are generally located in districts with high funding, which also allows them to provide superior computer science instruction.

Answer

The correct statements are the ones that suggest students' analytical skills draw them to chess (reverse causation) and that well-funded schools provide both chess clubs and better instruction (third variable).
The correct options directly undermine the researcher's conclusion by demonstrating classic alternative explanations for a correlation. One option demonstrates a 'third variable' scenario where district funding acts as the true cause for both the presence of chess clubs and high grades. The other option demonstrates 'reverse causality', suggesting that students who are already good at computer science are simply more inclined to play chess.

Step-by-Step Solution

1
Identify the argument's premises and conclusion.
Premise: There is a correlation between chess club participation and high computer science grades. Conclusion: Playing chess causes better computer science abilities.
Deconstructing the argument is necessary to evaluate its logical structure.
2
Identify the logical flaw.
The argument assumes causation based solely on correlation.
Recognizing the correlation vs. causation flaw tells you what kind of evidence would undermine the conclusion.
3
Evaluate the options for valid alternative explanations.
Find options that present a third variable causing both phenomena or suggest the causal relationship is backward.
Alternative explanations directly weaken a causal conclusion by showing the correlation could exist for other reasons.

Key Concept

Correlation vs. Causation
Question 7Question →

Chronobiologist: A recent two-year study monitored adolescent students who completed their academic assignments during early morning hours rather than late evening hours. These morning-studying students reported substantially higher sleep quality and improved memory retention. Therefore, shifting mentally demanding tasks from late evening to early morning directly optimizes sleep architecture and cognitive performance in adolescents.

Which of the following statements, if true, most seriously weaken the chronobiologist's argument? (Select all that apply)

Select all that apply

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Answer: Students who voluntarily shifted their study schedule to the morning already adhered to stricter household limits on evening screen exposure, an independent factor known to improve adolescent sleep quality.; Adolescents with naturally advanced circadian rhythms, who inherently experience superior sleep consolidation and baseline memory retention, are disproportionately more likely to adopt morning study routines.

Answer

The statements establishing an alternative confounding cause (household screen time limits) and a self-selection bias based on preexisting biological chronotypes both weaken the argument by undermining the author's direct causal conclusion.
The conclusion asserts a direct causal relationship based purely on a correlation observed between study timing and sleep/memory metrics. The statement showing that morning studiers were subject to stricter evening screen time limits provides an alternative causal explanation for the improved sleep. Similarly, the statement showing that students with naturally advanced circadian rhythms already possess superior sleep consolidation demonstrates that baseline biological differences, rather than the schedule change itself, likely account for the observed benefits.

Step-by-Step Solution

1
Identify the conclusion and underlying premises in the argument.
Premise: Morning-studying adolescents had better sleep quality and memory scores than evening studiers. Conclusion: Shifting mentally demanding tasks to the morning directly causes optimized sleep architecture and cognitive retention.
Weaken questions require targeting the unstated logical gap between the correlation observed in the premise and the causal link asserted in the conclusion.
2
Formulate potential vulnerabilities in the causal inference.
The author assumes no confounding third variables (such as other lifestyle habits) and no self-selection bias (inherent physiological differences between morning and evening types) explain the observed correlation.
Causal claims based on observational studies are inherently vulnerable to alternate causes, reverse causality, and selection bias.
3
Evaluate each choice against the causal gap.
The option citing stricter household screen limits introduces a plausible confounding variable, and the option noting inherent circadian advantages explains the correlation via selection bias. Both undermine the conclusion.
Introducing credible alternative explanations directly breaks the necessary assumption that the homework timing itself caused the beneficial outcomes.

Key Concept

Alternative Causal Explanations and Selection Bias
Estimated Time:1m 30s
Question 8Question →

Which of the following arguments contain a reasoning flaw that arises specifically from confusing a necessary condition with a sufficient condition? Select all that apply.

Select all that apply

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Answer: A thriving coral reef ecosystem always contains a diverse population of symbiotic algae. The reef off the coast of San Marcos contains a diverse population of symbiotic algae, which means it must be a thriving coral reef ecosystem.; If a municipality increases its public transportation budget, downtown traffic congestion will decrease. The city council decided against increasing the public transportation budget, so downtown traffic congestion will not decrease.

Answer

The argument about the coral reef ecosystem (which commits an illegal reversal) and the argument about the public transportation budget (which commits an illegal negation).
The correct arguments demonstrate the two primary ways to confuse necessary and sufficient conditions. The coral reef argument illustrates an illegal reversal by assuming that meeting a necessary requirement (having diverse algae) is sufficient to guarantee the outcome. The public transportation argument illustrates an illegal negation by assuming that failing to meet a sufficient condition (increasing the budget) guarantees that the outcome (decreased congestion) will not occur.

Step-by-Step Solution

1
Identify the logical flaw requested in the question stem.
The target flaw is confusing a necessary condition with a sufficient condition, which manifests as either an illegal reversal (A -> B; therefore B -> A) or an illegal negation (A -> B; therefore ~A -> ~B).
Understanding the exact structural nature of the target flaw is required to evaluate each option.
2
Evaluate the conditional structure of the coral reef ecosystem argument.
Premise: Thriving -> Diverse Algae. Conclusion: Diverse Algae -> Thriving. This is an illegal reversal, which perfectly matches the target flaw.
This determines that the coral reef argument is one of the correct answers.
3
Evaluate the conditional structure of the software application argument.
Premise: Immune -> Patched. Conclusion: ~Patched -> ~Immune. This is a valid application of the contrapositive. There is no logical flaw.
This rules out the software application argument as it is structurally valid.
4
Evaluate the conditional structure of the public transportation argument.
Premise: Increased Budget -> Decreased Congestion. Conclusion: ~Increased Budget -> ~Decreased Congestion. This is an illegal negation, matching the target flaw.
This determines that the public transportation argument is the second correct answer.
5
Analyze the remaining two arguments to confirm they do not contain the target flaw.
The fermented foods argument contains a correlation-to-causation fallacy. The budget division argument confuses percentages with absolute numbers. Neither commits a conditional flaw.
This confirms that no other options should be selected.

Key Concept

Identifying conditional reasoning flaws, specifically illegal reversals and illegal negations, where sufficient and necessary conditions are improperly interchanged.
Question 9Question →

Agricultural researchers recently noted a strong statistical correlation in the region of Valesia over the last decade: during the years when farmers planted the highest percentage of the newly developed 'Sun-Yield' wheat variety, the region also experienced the most severe outbreaks of the locust plague. The researchers concluded that the unique biological makeup of the Sun-Yield wheat must be attracting the locusts to the region.

Which of the following, if true, most effectively demonstrates that the researchers' conclusion is flawed? (Select all that apply.)

Select all that apply

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Answer: Farmers in Valesia are advised by meteorologists to plant Sun-Yield wheat only during years when prolonged droughts are forecasted, and prolonged droughts are known to be the primary environmental trigger for mass locust hatchings.; Valesian farmers typically choose to plant Sun-Yield wheat only after observing unusually high numbers of locust larvae in their soil during the early spring, since Sun-Yield is uniquely capable of surviving a locust infestation.

Answer

The correct answers are the option regarding prolonged droughts acting as a trigger for both events, and the option regarding farmers planting the wheat defensively after observing locust larvae.
The correct answers directly expose the flaw of assuming causation from correlation by providing alternative causal explanations for the observed data. One correct option demonstrates a third, common cause (prolonged droughts) that independently leads to both the increased planting of the wheat and the locust outbreaks. The other correct option demonstrates reverse causality, showing that the anticipated presence of locusts actually causes the farmers to plant the specific wheat variety as a defensive measure, completely undermining the claim that the wheat attracts the locusts.

Step-by-Step Solution

1
Analyze the argument's structure to identify the premises and the main conclusion.
Premise: A high percentage of Sun-Yield wheat correlates with severe locust plagues. Conclusion: The biological makeup of Sun-Yield wheat causes the locusts to be attracted to the region.
Understanding the components of the argument is necessary to evaluate its logical soundness and identify vulnerabilities.
2
Identify the logical flaw committed in moving from the premises to the conclusion.
The argument assumes that a statistical correlation implies a direct causal relationship, ignoring alternative explanations for the correlation.
Recognizing the flaw (Correlation vs. Causation) dictates what kind of evidence will weaken the conclusion.
3
Evaluate the answer choices to find those that exploit this specific flaw by providing valid alternative explanations.
Two options successfully weaken the argument: one provides a third common cause (droughts), and the other establishes reverse causality (locusts cause the planting of the wheat).
Valid correct answers in this context must directly address the erroneous causal leap rather than introducing irrelevant information or strengthening the argument.

Key Concept

Correlation vs. Causation
Question 10Question →

An anthropologist studied several isolated farming communities in the Andean highlands. The study revealed that communities primarily cultivating a specific heirloom variety of quinoa have significantly lower rates of cardiovascular disease than neighboring communities that cultivate standard commercial crops. Based on this observation, the anthropologist concluded that consuming this heirloom variety of quinoa provides unique protective benefits for cardiovascular health.

Which of the following are necessary assumptions required by the anthropologist's argument? (Select all that apply.)

Select all that apply

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Answer: The communities cultivating the heirloom quinoa do not have other unique lifestyle habits that are the primary reason for their comparatively lower rates of cardiovascular disease.; The residents of the communities that cultivate the heirloom quinoa actually consume a significant portion of the heirloom quinoa they produce.

Answer

The correct answers are the options stating that the communities do not have other unique lifestyle habits accounting for their health, and that the residents actually consume the quinoa they produce.
The argument requires two key unstated premises to bridge its logical gaps. First, because it moves from a premise about 'cultivating' to a conclusion about 'consuming', it must assume that the communities are actually eating the crops they grow. Second, because it assumes a causal relationship based on a correlation, it must assume that other potential causes (like different lifestyle habits) are not the true reason for the lower disease rates.

Step-by-Step Solution

1
Analyze the argument's structure to identify the premises and the main conclusion.
Premise: Communities cultivating heirloom quinoa have lower cardiovascular disease rates than those cultivating standard crops. Conclusion: Consuming the heirloom quinoa protects cardiovascular health.
Deconstructing the argument is necessary to spot the logical gaps between the evidence provided and the claim being made.
2
Identify the shifts in language and logic between the premises and the conclusion.
There are two major gaps: 1) The shift from 'cultivating' in the premise to 'consuming' in the conclusion. 2) The shift from a mere correlation (quinoa cultivation and low disease rates) to a definitive causal claim (quinoa consumption causes the health benefit).
Identifying these gaps reveals the unstated premises (assumptions) the author relies upon to make the argument work.
3
Evaluate the options using the Negation Technique to test if they are strictly necessary for the conclusion to hold.
Negating the option about lifestyle habits (they DO have other habits causing the health benefits) destroys the conclusion. Negating the option about consumption (they DO NOT consume what they cultivate) severs the link to the conclusion. Both are necessary assumptions.
The Negation Technique is the most reliable way to confirm whether an assumption is truly necessary for a causal argument.

Key Concept

Identifying necessary assumptions in causal reasoning (ruling out alternate causes and bridging language gaps).
Question 11Question →

Agricultural Commissioner: Over the past five years, the proportion of our region's total farmed acreage dedicated to growing the new drought-resistant sorghum has increased from 10 percent to 30 percent. Since farmers typically only expand the cultivation of a crop when it proves highly profitable, the absolute number of acres dedicated to growing drought-resistant sorghum in our region must be exactly three times what it was five years ago.

Which of the following statements must be true in order for the Agricultural Commissioner's conclusion to be logically drawn? Select all that apply.

Select all that apply

Show answer & explanation

Answer: The total farmed acreage in the region is exactly the same today as it was five years ago.; The total number of acres dedicated to crops other than drought-resistant sorghum has decreased over the past five years.

Answer

The statements that must be true are that the total farmed acreage is exactly the same today as it was five years ago, and that the total acreage dedicated to other crops has decreased.
The argument's conclusion requires the total acreage to remain unchanged. If total acreage changed, 30% of the new total would not equal exactly three times 10% of the old total. Consequently, if the total acreage is unchanged and sorghum's share grew by 20 percentage points, the share of all other crops must have shrunk by 20 percentage points, meaning their absolute acreage decreased.

Step-by-Step Solution

1
Analyze the premises and the conclusion.
Premise: Sorghum acreage increased from 10% to 30% of total acreage. Conclusion: Absolute sorghum acreage is exactly three times what it was.
Identifying the structural components highlights the leap between proportional evidence and an absolute numerical claim.
2
Evaluate the mathematical relationship required to make the conclusion valid.
For an absolute number to triple when its corresponding percentage also triples, the baseline total must remain constant.
If the total acreage had grown, the absolute acreage of sorghum would have more than tripled. If it shrank, it would have less than tripled.
3
Determine the necessary mathematical consequences of a constant total.
If the total stays the same and sorghum takes up a larger slice (from 10% to 30%), the slice for all other crops must shrink (from 90% to 70%).
This confirms that both the constant total acreage and the resulting decrease in other acreage are logically necessary assumptions.

Key Concept

To validly infer an absolute numerical change from a percentage change, the underlying total (the baseline) must be known and accounted for.
Estimated Time:1m 30s
Question 12Question →

Public Health Official: A newly constructed water treatment facility in the county uses a chemical agent called Florazine to eliminate bacterial contaminants. Florazine has been proven in laboratory settings to neutralize beneficial aquatic microbes alongside harmful bacteria. Because these beneficial microbes are critical for breaking down heavy metals in the water supply, implementing this new treatment process will ultimately lead to a rise in neurological disorders among county residents.

Which of the following statements must be assumed for the public health official's conclusion to be logically drawn? Select all that apply.

Select all that apply

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Answer: The presence of unbroken-down heavy metals in the county's water supply increases the risk of neurological disorders among its residents.; The concentration of Florazine used at the new facility is sufficient to neutralize enough beneficial microbes to impede the breakdown of heavy metals.

Answer

The correct assumptions are that the presence of heavy metals increases the risk of neurological disorders, and that the concentration of Florazine used at the facility is sufficient to impede the breakdown of these metals.
The argument contains two distinct conceptual gaps. First, it introduces 'neurological disorders' in the conclusion without logically linking it to the 'heavy metals' mentioned in the premises. Second, it assumes that a chemical's behavior in a laboratory setting will translate exactly to the operational reality of the new facility. The correct choices explicitly bridge these two specific gaps; without them, the causal chain from utilizing Florazine to experiencing a rise in neurological disorders is broken.

Step-by-Step Solution

1
Deconstruct the argument to separate premises from the conclusion.
Premises: Florazine neutralizes beneficial microbes that break down heavy metals. Conclusion: Using Florazine will lead to a rise in neurological disorders.
Identifying the structural components is required to spot conceptual gaps.
2
Identify rogue elements and conceptual leaps.
The concept of 'neurological disorders' appears only in the conclusion. There is also a leap from Florazine's effects 'in laboratory settings' to its effects at the actual 'water treatment facility'.
Supporter assumptions are strictly necessary to connect new conclusion concepts back to the premises.
3
Evaluate the options using the Negation Test.
Negating the statement about heavy metals causing disorders destroys the conclusion. Negating the statement about Florazine concentrations at the facility being sufficient also destroys the conclusion.
The Negation Test confirms whether an assumption is strictly logically required.

Key Concept

Bridging Gap (Supporter) Assumptions
Question 13Question →

Zoologist: In colonies of the red-crested macaque, individuals that regularly share food with non-kin spend significantly less time engaging in social grooming. Social grooming is the primary behavior through which macaques establish and maintain their position in the colony's hierarchy. Therefore, by regularly sharing food with non-kin, these macaques are actively diminishing their social standing.

Which of the following statements function as a valid supporter assumption required to bridge the logical gap in the zoologist's argument? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: Any red-crested macaque that spends significantly less time on the primary behavior for maintaining its hierarchical position will experience a decrease in its social standing.; If a red-crested macaque does not experience a diminishment in its social standing, then it has not significantly reduced the amount of time it spends on social grooming.

Answer

The correct statements are the one that directly connects spending less time on hierarchy maintenance to decreased social standing, and its contrapositive which states that a macaque not experiencing diminished standing has not reduced its grooming time.
The zoologist's argument contains a clear gap. The premises establish that food-sharing macaques groom less, and that grooming is the primary way to maintain hierarchy. However, the conclusion abruptly jumps to claiming they are 'actively diminishing their social standing.' To make this conclusion logical, we must assume that failing to engage in the primary hierarchy-maintaining behavior actually results in diminished standing. One correct statement provides this exact conditional link. The other correct statement provides the exact same logical link, just phrased as a contrapositive (if standing is not diminished, grooming was not reduced). Both properly bridge the gap.

Step-by-Step Solution

1
Identify the premises of the argument.
Premise 1: Sharing food = Less time grooming. Premise 2: Grooming = Primary behavior to maintain hierarchy.
Understanding the established facts is the first step in structural argument analysis.
2
Identify the main conclusion.
Conclusion: Sharing food = Diminishing social standing.
Isolating the conclusion highlights the final claim the author is trying to prove.
3
Locate the logical gap (new concept in the conclusion).
The concept of 'diminishing social standing' appears in the conclusion but is never directly linked to 'less time grooming' in the premises.
A supporter assumption must explicitly connect the 'rogue' element in the conclusion to the established premise framework.
4
Formulate the required bridge and evaluate the options.
The required bridge is 'Less time grooming -> Diminishing social standing'. Two options provide this relationship: one directly, and one as a logically equivalent contrapositive.
Supporter assumptions can appear in standard conditional form or as their contrapositive; both successfully validate the inference.

Key Concept

Bridging a logical gap requires identifying a new element in the conclusion and strictly linking it to the premise terminology, either directly or via its contrapositive.
Question 14Question →

Last year, a university required all graduating seniors to attend a career counseling program. This year, the university made the counseling program entirely optional. The university's administration was surprised to find that the total number of graduating seniors who secured employment within three months of graduation decreased significantly this year. However, the employment rate among seniors who participated in the counseling program jumped from 60% last year to 90% this year.

Which of the following statements, if true, contribute to resolving the apparent discrepancy? (Select exactly TWO statements that, when taken together, best explain the statistical anomaly.)

Select all that apply

Show answer & explanation

Answer: A severe regional economic downturn this year drastically reduced the total number of entry-level jobs available to all recent graduates.; Only the most academically accomplished and highly proactive seniors chose to participate in the optional counseling program this year.

Answer

The two statements that resolve the discrepancy are the one citing a regional economic downturn and the one indicating that only highly proactive students participated.
To fully resolve this two-part paradox, we need two distinct facts. First, we must explain why the overall absolute number of employed graduates dropped: a severe economic downturn provides an external reason for a shrinking job market affecting the entire senior class. Second, we must explain why the percentage of successful counseling participants spiked despite the bad economy: when the program became optional, only the most motivated and employable students chose to attend (self-selection bias), artificially inflating the program's success rate compared to the previous year when everyone (including less motivated students) was forced to attend.

Step-by-Step Solution

1
Analyze the paradox
Identify two conflicting facts: Total employment count decreased, but the employment rate for counseling participants increased from 60% to 90%.
Understanding the exact nature of the rate-vs-count anomaly is necessary to find a comprehensive resolution.
2
Evaluate the requirement for a joint resolution
Since the question asks for two statements that jointly resolve the discrepancy, I need one statement to explain the drop in the overall absolute number and another statement to explain the spike in the specific subgroup's percentage.
Neither statement alone can resolve both halves of a complex statistical paradox involving both shifting denominators and self-selection bias.
3
Select the statement explaining the drop in absolute count
The statement regarding the economic downturn explains why overall numbers fell across the entire population regardless of counseling.
An external variable affecting the whole population explains a general downward trend.
4
Select the statement explaining the spike in the subgroup rate
The statement regarding self-selection by highly proactive students explains why the optional program's success rate was so high.
When a program shifts from mandatory to optional, the baseline population changes. Comparing a mandatory cohort (everyone) to an optional cohort (self-selected high achievers) creates an illusion of program improvement.

Key Concept

Resolving complex statistical paradoxes by identifying external causal factors (economic downturn) and population shifts/self-selection bias (mandatory vs. optional attendance).
Question 15Question →

Last year, wheat farmers in the Sunnyside Valley switched from using traditional organic compost to a new synthetic fertilizer called Nitromax. Following this switch, the total yield of wheat per hectare in the valley increased significantly compared to previous years. However, despite this increase in yield per hectare, the total revenue generated by the valley's wheat harvest was substantially lower this year than in any of the previous five years.

Which of the following statements, if true, help to resolve the apparent discrepancy described above? Select all that apply.

Select all that apply

Show answer & explanation

Answer: The use of Nitromax alters the kernel texture of the wheat, causing wholesale buyers to classify the entire harvest as "livestock feed," which commands a drastically lower market price than the "premium baking grade" wheat the valley previously produced.; Due to an unusually harsh frost early in the planting season, farmers in the Sunnyside Valley planted wheat on only one-third of the hectares they had utilized in previous years.

Answer

The correct statements are the one indicating a drop in the wheat's classification to livestock feed and the one indicating a drastic reduction in planted hectares.
The paradox involves an increase in yield per hectare but a decrease in total revenue. Total revenue depends on yield per hectare, total hectares planted, and price per unit. The correct statements provide independent ways to bridge these facts: one explains that the price per unit drastically dropped because the wheat was downgraded to feed, and the other explains that the total number of hectares planted was drastically reduced. Either of these scenarios allows a higher yield per hectare to coexist with lower total revenue.

Step-by-Step Solution

1
Identify the two apparently conflicting facts in the stimulus.
Fact 1: The yield of wheat per hectare increased significantly. Fact 2: The total revenue generated by the wheat harvest was substantially lower.
Resolving a paradox requires a precise understanding of the two elements that seem contradictory.
2
Determine the mathematical relationship that connects the two facts.
Total Revenue = (Yield per Hectare) × (Total Hectares Planted) × (Price per Unit).
By breaking down total revenue into its components, we can see how revenue could drop despite an increase in yield per hectare.
3
Evaluate the options to find those that explain how total revenue could drop while yield per hectare increased.
The option regarding 'livestock feed' addresses a drop in Price per Unit. The option regarding 'only one-third of the hectares' addresses a drop in Total Hectares Planted.
A correct answer must act as a bridge that allows both original facts to coexist without contradiction.

Key Concept

Resolving Paradoxes: Bridging Conflicting Facts
Question 16Question →

As urban environments expand, many wildlife species face the challenge of surviving in habitats dominated by human activity. While some animals simply relocate, others undergo rapid behavioral adaptations to cope with these new pressures. For instance, researchers have observed that the great tit, a common songbird, has begun singing at significantly higher pitches in cities compared to its forest-dwelling counterparts. This acoustic shift allows the urban birds' calls to be heard over the continuous, low-frequency rumble of city traffic, ensuring they can still attract mates and defend territories.

Which of the following accurately describe the logical function of the author's reference to the great tit's singing behavior in the passage? Select all that apply.

Select all that apply

Show answer & explanation

Answer: To provide a concrete example of a species rapidly adapting its behavior to an urban environment; To illustrate how a specific animal overcomes a challenge created by human activity

Answer

The great tit example functions to provide a concrete example of a species adapting its behavior to an urban environment and to illustrate how a specific animal overcomes a human-created challenge.
The correct choices accurately reflect the structural role of the great tit example. Introduced by the phrase 'For instance,' the detail serves directly to support the previous sentence's claim that animals undergo behavioral adaptations. It fulfills this purpose by providing a concrete illustration of a species adapting (changing its song pitch) and demonstrating how this adaptation successfully overcomes a specific challenge (city traffic noise).

Step-by-Step Solution

1
Analyze the general claim immediately preceding the specific detail.
The preceding sentence states that some animals 'undergo rapid behavioral adaptations to cope with these new pressures.'
Understanding the context of a detail is necessary to determine its rhetorical function.
2
Examine the specific detail and how it connects logically to the preceding claim.
The passage uses the transition phrase 'For instance' and describes how the great tit changes its song pitch to be heard over city noise.
This establishes the logical relationship between the broad claim and the specific evidence.
3
Synthesize the function of the detail based on its relationship to the surrounding context.
The detail serves as a concrete illustration of the adaptation mentioned earlier, showing exactly how one species overcomes a human-made environmental challenge.
This confirms the correct logical role the detail plays in the passage's organization.

Key Concept

Identifying the rhetorical and logical function of a specific detail within the broader context of a reading passage.
Estimated Time:1m 0s
Question 17Question →

In late antiquity, the Mediterranean glass industry was structured around a sharp geographical division between primary production centers and secondary workshops. In primary centers along the Levantine coast, vast raw batches of silica sand and mineral natron (a naturally occurring sodium carbonate harvested almost exclusively from Egypt's Wadi El Natrun) were fused in colossal tank furnaces. The resulting unworked raw glass slabs were subsequently broken into cullet and shipped across the Mediterranean to localized secondary workshops, where artisans remelted the glass at lower temperatures to fashion vessels and window panes. Chemical and isotopic analyses of natron-based glass from fourth- to sixth-century archaeological sites demonstrate remarkable compositional homogeneity across distant regions, confirming that secondary artisans rarely altered the base glass beyond adding minor colorants or decoloring agents.

However, during the late seventh and eighth centuries, this centralized production regime collapsed. Excavations in the Levant and Western Europe reveal a swift transition toward plant-ash fluxes derived from halophytic (salt-tolerant) desert shrubs, which contained elevated concentrations of magnesium and potassium compared to natron. Concurrently, regional compositional variations sharply increased. Some scholars attribute this fragmentation entirely to geopolitical ruptures following the mid-seventh-century Islamic conquests, which disrupted maritime trade routes supplying Egyptian natron to Byzantine secondary workshops. Yet recent stratigraphic evidence indicates that several primary natron furnace complexes in the Levant were abandoned decades before regional trade networks contracted, and that the adoption of plant ash allowed secondary workshops to become fully autonomous by sourcing local biomass rather than depending on a single monopolized mineral supply.

Based on the passage, which of the following statements are logically supported inferences? (Select all that apply.)

Select all that apply

Show answer & explanation

Answer: Secondary glass workshops operating prior to the late seventh century were generally incapable of synthesizing raw glass from unrefined silica sand and mineral fluxes on their own.; The presence of elevated concentrations of potassium and magnesium in a seventh-century Mediterranean glass artifact suggests that the glass was not manufactured using flux derived exclusively from Wadi El Natrun.

Answer

The logically supported inferences are the statement that pre-seventh-century secondary workshops depended on primary centers for initial raw glass synthesis, and the statement that elevated potassium and magnesium indicate flux other than pure Wadi El Natrun natron.
The supported statements follow directly from the structural and chemical facts in the passage: early secondary workshops were limited to remelting prefabricated raw slabs and lacked full autonomy, and elevated magnesium and potassium serve as diagnostic chemical markers distinguishing plant ash from mineral natron.

Step-by-Step Solution

1
Analyze the division of labor between primary and secondary glassmaking described in the first paragraph.
Primary centers fused raw sand and mineral natron in massive tank furnaces, while secondary workshops only remelted imported cullet at lower temperatures and did not achieve autonomy until later adopting plant-ash fluxes.
This establishes that early secondary workshops lacked the capacity for independent primary synthesis from raw ingredients.
2
Examine the elemental signatures distinguishing mineral natron from plant ash in the second paragraph.
Plant-ash fluxes contain elevated concentrations of magnesium and potassium, whereas natron does not.
This confirms that a glass specimen exhibiting high magnesium and potassium cannot have been fluxed with mineral natron alone.
3
Evaluate the remaining options against the explicit boundaries of the text.
Claims regarding guild regulatory oversight, conquest as the sole catalyst for abandonment, and total cessation of cullet recycling represent unsupported leaps and external historical assumptions.
LSAT inference standards require eliminating any choice containing ungrounded absolute assertions or external explanatory mechanisms not found in the passage.

Key Concept

Synthesizing explicit structural divisions and chemical indicators within an academic passage to draw deductively sound inferences without importing external historical assumptions or unwarranted absolute claims.
Estimated Time:1m 50s
Question 18Question →

Passage A
The prevailing orthodoxy in archaeological theory has long maintained that the construction of early monumental architecture—ranging from the towering ziggurats of ancient Mesopotamia to the expansive earthen mounds of the pre-Columbian Americas—served primarily as a top-down instrument of coercive political power. According to this well-established framework, nascent elites, having recently consolidated control over regional agricultural surpluses, necessitated highly visible and enduring manifestations of their authority to legitimize unprecedented degrees of social stratification. Monumental structures fulfilled this ideological requirement perfectly. The sheer physical scale of these projects demanded the meticulous mobilization of massive labor forces and the coordinated transport of heavy building materials across vast distances. This undertaking was a logistical feat that inherently required and subsequently reinforced the administrative apparatus of the ruling class. Furthermore, by architecturally restricting access to the inner sanctums or elevated platforms of these imposing edifices, elites were able to spatially instantiate their exclusive relationship with the divine or cosmic order, thereby naturalizing their political dominance. The architectural permanence of these structures ensured that the ideological message of elite supremacy was broadcasted continuously across multiple generations. Consequently, within this paradigm, early monumentalism cannot be properly understood apart from the deliberate institutionalization of inequality. It was fundamentally a premeditated strategy designed for reifying elite authority and habituating the broader populace to newly instituted, asymmetrical power dynamics through the very physical landscape they inhabited and navigated daily.

Passage B
Recent ethnographic and archaeological reevaluations robustly challenge the monolithic assumption that all early monumental construction was inherently coercive or inextricably linked to established elite exploitation. Instead, compelling empirical evidence from varied global contexts suggests that in numerous early societies, monumental architecture initially originated as a communal, bottom-up endeavor driven by shared religious conviction and the necessity of collective identity formation. In these specific contexts, the arduous construction process itself, perhaps even more than just the finished edifice, served a critical integrative function for historically decentralized populations. The recurring seasonal gathering of disparate kin groups to contribute voluntary labor and collaboratively transport heavy building materials to a shared sacred site actively fostered social cohesion. This collective effort reinforced vital reciprocal obligations without necessitating the imposition of a coercive administrative hierarchy. While it is historically undeniable that emerging elites eventually co-opted these sacred sites—shrewdly appropriating their accumulated symbolic and religious capital to subsequently justify extreme social stratification—the initial generative impetus was frequently cooperative and remarkably egalitarian. By failing to distinguish between the origins of monumentalism and its later appropriation, traditional theories obscure the profound capacity of early communities for self-directed, cooperative achievement. Recognizing this two-stage developmental sequence reveals that large-scale communal labor and profound monumental expression can historically precede, and indeed exist completely independently of, coercive state apparatuses, serving primarily to bind a disparate community together through a shared framework of cosmological devotion.

Based on the texts provided, which of the following statements regarding monumental architecture do the authors of BOTH passages endorse as a central component of their respective arguments? Select all that apply.

Select all that apply

Show answer & explanation

Answer: Emerging elites leveraged the symbolic or religious capital of monumental architecture to justify and naturalize social stratification.; The significance and spatial organization of monumental structures were intimately connected to a society's cosmological or religious convictions.

Answer

The correct options are those stating that emerging elites leveraged the symbolic capital of monumental architecture to justify social stratification, and that the significance of these structures was intimately connected to religious convictions.
Both authors centrally argue that elites utilized the profound religious and symbolic weight of monumental architecture to legitimize unequal power structures. While Passage A views this as the original purpose and Passage B views it as a later co-optation, the subsequent elite exploitation of these sites is a crucial pillar of both arguments. Furthermore, both passages hinge their structural analyses on the premise that these edifices were intimately tied to cosmological or religious beliefs (Passage A notes the 'exclusive relationship with the divine', while Passage B highlights a 'shared framework of cosmological devotion').

Step-by-Step Solution

1
Analyze Passage A to determine its central argument regarding monumental architecture.
Passage A argues that monumental architecture was originally built by elites as a coercive tool to legitimize social inequality by connecting themselves to the divine.
Understanding the primary thesis of the first text is necessary before comparing it to the second.
2
Analyze Passage B to determine its central argument.
Passage B argues that while monumental architecture originally fostered egalitarian cohesion through shared religious devotion, elites later co-opted this symbolic power to justify social stratification.
Identifying the core claims of the second text allows for cross-text comparison.
3
Identify claims that are central to the arguments of BOTH passages.
Both authors build their arguments around the premises that monumental structures held profound religious/cosmological significance, and that elites ultimately used this symbolic weight to naturalize social inequality.
The question specifically asks for shared central endorsements.
4
Evaluate the given options against the shared central claims.
The options regarding elites leveraging symbolic capital and the connection to cosmological convictions accurately reflect the shared central arguments. The other options either represent only one author's view, focus on a minor shared detail, or overstate the claims.
Systematic evaluation eliminates distractors based on viewpoint misattribution, overgeneralization, or confusing minor details with main points.

Key Concept

Identifying shared central claims and evaluating how differing authors integrate common premises into distinct overarching arguments.
Question 19Question →

Astrophysics engineers established the following operational parameters for orbital deep-space observatories:

• Every deep-space observation satellite equipped with a sub-kelvin bolometer array operates a multistage pulse-tube cryocooler.
• Any satellite operating a multistage pulse-tube cryocooler requires active vibration damping unless it maintains a passive magnetic levitation mount.
• No satellite requiring active vibration damping can perform continuous wide-field interferometry.
• Every satellite that maintains a passive magnetic levitation mount consumes auxiliary solar battery reserve power.

During its calibration phase, the Astraea deep-space observation satellite was equipped with a sub-kelvin bolometer array and successfully performed continuous wide-field interferometry.

If the statements above are true, which of the following statements must also be true? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: During its calibration phase, Astraea maintained a passive magnetic levitation mount.; During its calibration phase, Astraea consumed auxiliary solar battery reserve power.

Answer

During its calibration phase, Astraea maintained a passive magnetic levitation mount, and Astraea consumed auxiliary solar battery reserve power.
The stimulus establishes that Astraea possessed a sub-kelvin bolometer array (guaranteeing it operated a cryocooler) and performed continuous wide-field interferometry (guaranteeing it did not require active vibration damping). Operating the cryocooler without active damping is possible only if a passive magnetic levitation mount is maintained. Furthermore, maintaining such a mount guarantees the consumption of auxiliary solar battery reserve power. Therefore, both the statement that Astraea maintained a passive magnetic levitation mount and the statement that Astraea consumed auxiliary solar battery reserve power must be true.

Step-by-Step Solution

1
Deduce cryocooler operation from bolometer presence
Astraea operated a multistage pulse-tube cryocooler during calibration.
The first premise states that every satellite equipped with a sub-kelvin bolometer array operates a multistage pulse-tube cryocooler.
2
Deduce absence of active vibration damping from interferometry capability
Astraea did not require active vibration damping.
The third premise states that no satellite requiring active vibration damping can perform continuous wide-field interferometry. Since Astraea performed this interferometry, by contraposition it did not require active vibration damping.
3
Synthesize cryocooler operation and damping absence to deduce mounting mechanism
Astraea maintained a passive magnetic levitation mount.
The second premise states that operating a cryocooler requires active vibration damping unless a passive magnetic levitation mount is maintained. Since Astraea operated the cryocooler but did not require active damping, it must have maintained the passive mount.
4
Deduce power consumption from the mounting mechanism
Astraea consumed auxiliary solar battery reserve power.
The fourth premise states that every satellite maintaining a passive magnetic levitation mount consumes auxiliary solar battery reserve power.

Key Concept

Multi-premise conditional chaining and contrapositive deductive inference
Question 20Question →

Urban planners for the city of Oakhaven have established the following zoning regulations and observations: Any residential parcel zoned for high-density development must be located within 500 meters of a rapid transit station. Furthermore, if a parcel is located within 500 meters of a rapid transit station and is also zoned for commercial mixed-use, it automatically qualifies for a parking minimum exemption. Currently, no parcels zoned for high-density development qualify for a parking minimum exemption. Finally, most parcels zoned for commercial mixed-use in the downtown district are located within 500 meters of a rapid transit station.

Based on the information above, which of the following statements must be true? (Select all that apply)

Select all that apply

Show answer & explanation

Answer: No residential parcel zoned for high-density development is also zoned for commercial mixed-use.; At least some parcels located within 500 meters of a rapid transit station are not zoned for high-density development.

Answer

The statements that must be true are that no high-density parcel is commercial mixed-use, and that some transit-adjacent parcels are not high-density.
The correct statements reflect logical certainties derived directly from the text. First, because high-density parcels must be near transit, making them commercial mixed-use would trigger an exemption they explicitly do not have; thus, they cannot be commercial mixed-use. Second, because most downtown commercial mixed-use parcels are near transit, and we know they cannot be high-density, it guarantees that at least some transit-adjacent parcels are not high-density.

Step-by-Step Solution

1
Map the formal logic conditionals from the stimulus.
1: High-Density (HD) -> Near Transit (NT). 2: (NT + Commercial Mixed-Use (CMU)) -> Exemption (E). 3: HD -> ~E. 4: Downtown CMU -most-> NT.
Mapping the premises allows for precise deduction without relying on outside assumptions.
2
Combine premises 1, 2, and 3 to find overlapping conditions.
If a parcel is HD, it is NT. If it were also CMU, it would be NT + CMU, triggering E. But premise 3 says HD -> ~E.
Testing intersection of categories reveals impossible combinations.
3
Deduce the relationship between HD and CMU.
Because being both HD and CMU leads to a contradiction (qualifying for E and not qualifying for E), a parcel cannot be both. Thus, No HD is CMU.
Resolving the contradiction establishes the first objectively true statement.
4
Apply the new deduction to the proportional premise (premise 4).
Since Downtown CMU -most-> NT, there is at least one (in fact, many) NT parcel that is CMU. Since no CMU is HD, these specific NT parcels are not HD.
Combining a 'most' statement with a negative absolute statement yields a 'some are not' deduction.

Key Concept

Conditional Logic Chaining and Quantifier Intersections
Estimated Time:3m 0s
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