Examkin

Sufficient Assumption

42 questions

All types42Multiple choice21Matching11Fill in the blank10
Question 21Question →

Ecologist: Any agricultural system that integrates deep-rooted perennial woody vegetation with livestock grazing significantly reduces nitrate leaching into local aquifers. Moreover, any farming method that significantly reduces nitrate leaching into local aquifers qualifies as an environmentally restorative practice. Therefore, every farm that implements rotational silvopastoral management qualifies as an environmentally restorative practice.

The ecologist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Every farm that implements rotational silvopastoral management integrates deep-rooted perennial woody vegetation with livestock grazing.

Answer

Every farm that implements rotational silvopastoral management integrates deep-rooted perennial woody vegetation with livestock grazing.
The argument establishes that integrating deep-rooted perennial woody vegetation with livestock grazing guarantees a reduction in nitrate leaching, which in turn guarantees qualification as an environmentally restorative practice. The conclusion introduces a new subject—farms implementing rotational silvopastoral management—and concludes they qualify as environmentally restorative. The statement that every farm implementing rotational silvopastoral management integrates deep-rooted perennial woody vegetation with livestock grazing provides the precise bridge needed to trigger the conditional chain and make the conclusion follow with 100% deductive certainty.

Step-by-Step Solution

1
Diagram the conditional premises provided in the stimulus.
Premise 1: Integrated woody vegetation + grazing -> Reduces nitrate leaching. Premise 2: Reduces nitrate leaching -> Environmentally restorative practice. Combined premise chain: Integrated woody vegetation + grazing -> Environmentally restorative practice.
Establishing the existing deductive chain clarifies what conditions are already proven to guarantee the outcome.
2
Analyze the conclusion to identify the missing concept and inferential gap.
Conclusion: Rotational silvopastoral management -> Environmentally restorative practice. The new subject introduced in the conclusion is 'rotational silvopastoral management'.
A sufficient assumption must provide a 100% deductive bridge connecting the new term in the conclusion to the existing premise chain.
3
Determine the required sufficient assumption to complete the deduction.
The statement 'Rotational silvopastoral management -> Integrated woody vegetation + grazing' completes the chain: Rotational silvopastoral management -> Integrated woody vegetation + grazing -> Reduces nitrate leaching -> Environmentally restorative practice.
Plugging this link into the premises fully guarantees the truth of the conclusion.

Key Concept

Sufficient Assumption in Conditional Syllogisms
Estimated Time:1m 15s
Question 22Question →

Environmental Policy Analyst: Any geothermal power station that utilizes closed-loop supercritical fluid extraction achieves an operational thermal efficiency exceeding forty percent. Furthermore, no geothermal facility operating at an efficiency exceeding forty percent qualifies for regional groundwater conservation credits unless it reinjects all extracted mineral condensates into deep sub-surface basalt formations. The North Ridge geothermal facility was recently awarded regional groundwater conservation credits. Therefore, the North Ridge facility does not utilize closed-loop supercritical fluid extraction.

The environmental policy analyst's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: The North Ridge geothermal facility does not reinject all extracted mineral condensates into deep sub-surface basalt formations.

Answer

The assumption that the North Ridge geothermal facility does not reinject all extracted mineral condensates into deep sub-surface basalt formations.
The argument contains a conditional gap between receiving conservation credits and not using supercritical fluid extraction. The premises establish that supercritical extraction requires efficiency exceeding forty percent, and that any facility exceeding forty percent efficiency that receives credits must reinject all extracted mineral condensates into basalt formations. Given that the North Ridge facility received these credits, assuming that it does not reinject all condensates into basalt formations logically necessitates that its efficiency cannot exceed forty percent (by modus tollens). Because its efficiency does not exceed forty percent, it cannot utilize closed-loop supercritical fluid extraction. Thus, the conclusion is deductively guaranteed.

Step-by-Step Solution

1
Analyze the premises and symbolize the formal conditional relationships in the argument.
Premise 1: Supercritical Extraction →\rightarrow Thermal Efficiency >40%> 40\%. Premise 2: Thermal Efficiency >40%> 40\% AND Conservation Credits →\rightarrow Basalt Reinjection. Premise 3: North Ridge received Conservation Credits.
Deconstructing the argument into formal logic isolates the exact inferential gap between the premises and the conclusion.
2
Determine what intermediate condition is required to reach the conclusion via contrapositive reasoning.
Conclusion to prove: North Ridge does NOT have Supercritical Extraction. By the contrapositive of Premise 1 (NOT Thermal Efficiency >40%→> 40\% \rightarrow NOT Supercritical Extraction), we need to establish that North Ridge does NOT have Thermal Efficiency >40%> 40\%.
A sufficient assumption must provide the missing premise that, combined with existing premises, deductively forces the intermediate and final conclusions.
3
Connect the credit status of North Ridge to the negation of the high-efficiency condition.
By Premise 2, if a facility has Thermal Efficiency >40%> 40\% and receives Conservation Credits, it MUST perform Basalt Reinjection. The contrapositive states: If a facility receives Conservation Credits and does NOT perform Basalt Reinjection, it CANNOT have Thermal Efficiency >40%> 40\%.
Since North Ridge received Conservation Credits, supplying the premise that it does NOT perform Basalt Reinjection forces the conclusion that its efficiency is not >40%> 40\%, which in turn proves it does not use Supercritical Extraction.

Key Concept

Sufficient Assumption in Conditional Reasoning Chains
Estimated Time:1m 30s
Question 23Question →

Archivist: Any parchment document treated with nano-cellulose spray creates an airtight molecular barrier. Furthermore, any document that possesses an airtight molecular barrier resists microbial ink erosion. Since the fourteenth-century guild charter was treated with nano-cellulose spray, it is certain to be approved for permanent display in the main rotunda.

The archivist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Every parchment document that resists microbial ink erosion is approved for permanent display in the main rotunda.

Answer

Every parchment document that resists microbial ink erosion is approved for permanent display in the main rotunda.
The argument establishes that the charter was treated with nano-cellulose spray, which guarantees an airtight molecular barrier, which in turn guarantees that it resists microbial ink erosion. The conclusion asserts that the charter will be approved for permanent display. The statement establishing that every parchment document that resists microbial ink erosion is approved for permanent display creates a complete, unbroken deductive chain: Charter → Nano-cellulose → Airtight Barrier → Resists Erosion → Approved for Display.

Step-by-Step Solution

1
Analyze the premises and symbolize the conditional chain
Treated with nano-cellulose spray leads to an airtight molecular barrier, which in turn leads to resisting microbial ink erosion. The fourteenth-century guild charter received this spray, deductively establishing that the charter resists microbial ink erosion.
Identify the full extent of what the given premises formally prove before addressing the conclusion.
2
Isolate the conclusion and identify the deductive gap
Conclusion: The charter is certain to be approved for permanent display in the main rotunda. Deductive Gap: Resisting microbial ink erosion must guarantee approval for permanent display.
A sufficient assumption must provide a 100% deductive bridge from the established intermediate fact to the final conclusion.
3
Select the conditional statement that bridges the gap
The statement specifying that every parchment document that resists microbial ink erosion is approved for permanent display completes the syllogism.
Premise chain + [Resists microbial erosion → Approved for display] → Charter is approved for display.

Key Concept

Deductive bridge assumption in a multi-step conditional chain
Estimated Time:1m 15s
Question 24Question →

An architectural acoustician constructs a deductive argument evaluating a newly designed performance venue. Complete the argument by identifying the missing premise that guarantees the conclusion follows logically and necessarily.

Fill in the blanks below

Premise 1: Any performance venue with an unbuffered resonance frequency below 120 Hz produces low-frequency standing waves.
Premise 2: Every performance venue that produces low-frequency standing waves is unsuitable for recording vocal polyphony.
Missing Premise: The Lyceum Auditorium .
Conclusion: Therefore, the Lyceum Auditorium is unsuitable for recording vocal polyphony.
Show answer & explanation

Answer

has an unbuffered resonance frequency below 120 Hz
Establishing that the Lyceum Auditorium has an unbuffered resonance frequency below 120 Hz triggers the full conditional chain (Resonance < 120 Hz → Standing Waves → Unsuitable for Vocal Polyphony), thereby deductively guaranteeing the conclusion with 100% logical certainty.

Step-by-Step Solution

1
Analyze the formal structure of the explicit premises and the conclusion.
Premise 1 establishes: Unbuffered resonance below 120 Hz → Low-frequency standing waves. Premise 2 establishes: Low-frequency standing waves → Unsuitable for vocal polyphony. The conclusion states: Lyceum Auditorium → Unsuitable for vocal polyphony.
Deconstructing the argument into conditional terms isolates the chain of deduction already established by the speaker.
2
Combine the premises to establish the overarching conditional rule.
By hypothetical syllogism: Unbuffered resonance below 120 Hz → Unsuitable for vocal polyphony.
Linking the two premises reveals the sufficient condition required to trigger the final necessary outcome.
3
Identify the deductive bridge required to reach the conclusion regarding the Lyceum Auditorium.
To reach the conclusion that the Lyceum Auditorium is unsuitable for recording vocal polyphony via modus ponens, the Lyceum Auditorium must satisfy the antecedent of the chain: it must have an unbuffered resonance frequency below 120 Hz.
A sufficient assumption must provide a 100% deductive guarantee of the conclusion when added to the existing premises.

Key Concept

Sufficient Assumption Deductive Chain Linking
Estimated Time:1m 15s
Question 25Question →

For each of the incomplete arguments in the left column, select the missing premise from the right column that, if assumed, allows the argument's conclusion to be properly drawn.

Click a left item, then click its matching right item

Items

Any coin minted with Laurion lead-silver isotope ratios was produced during the Athenian maritime hegemony. The hoard excavated at Sounion contains only coins that carry owl iconographic stamps. Therefore, the coins in the Sounion hoard were produced during the Athenian maritime hegemony.
Any planetary body exhibiting atmospheric phosphine in chemical disequilibrium without volcanic sulfur dioxide undergoes active biochemical methanogenesis. Spectroscopic scans of exoplanet Kepler-186f reveal significant atmospheric phosphine in chemical disequilibrium. Thus, Kepler-186f undergoes active biochemical methanogenesis.
Any subterranean aquifer with rapid conduit-dominated flow paths fails to filter microplastic particulates. Subterranean aquifers situated in dolomitic karst bedrock invariably feature rapid conduit-dominated flow paths. Hence, municipal wells drawing from the Edwards reservoir cannot produce water free of microplastics.

Matches

Show answer & explanation

Answer

Argument 1 matches with the statement that all owl-stamped coins have Laurion isotope ratios; Argument 2 matches with the statement that Kepler-186f lacks atmospheric volcanic sulfur dioxide; Argument 3 matches with the statement that Edwards reservoir wells draw from aquifers in dolomitic karst bedrock.
Each correctly matched premise supplies the precise missing link needed to complete a valid deductive chain: connecting the subject of the premise to the sufficient condition of the governing rule.

Step-by-Step Solution

1
Isolate the premise-to-conclusion gap in each argument.
Argument 1 requires a link from owl iconographic stamps to Laurion isotope ratios; Argument 2 requires confirming the negative conjunct of the conditional antecedent (lack of volcanic sulfur dioxide); Argument 3 requires linking the Edwards reservoir wells to dolomitic karst bedrock.
Sufficient assumptions must bridge the missing logical step such that Premises + Assumption strictly entail the Conclusion.
2
Evaluate candidate assumptions for exact deductive sufficiency.
Each matched premise provides a 100% guaranteed logical bridge closing the inferential gap for its corresponding argument without introducing invalid conditional reversals.
A sufficient assumption must guarantee the truth of the conclusion completely under formal deductive logic.

Key Concept

Sufficient Assumption
Estimated Time:2m 0s
Question 26Question →

Botanist: Any alpine plant that undergoes early budburst without a corresponding increase in foliar cuticle thickness will suffer extensive cellular necrosis if exposed to unseasonal late-spring freezes. Furthermore, any plant that suffers extensive cellular necrosis from late-spring freezes will experience a reduction in lifetime seed viability below the replacement threshold unless it can activate dormant meristem tissue. Southern dwarf willows invariably undergo early budburst in response to early-season warming, yet they completely lack dormant meristem tissue. Therefore, if unseasonal late-spring freezes occur in their habitat, southern dwarf willows will experience a reduction in lifetime seed viability below the replacement threshold.

The botanist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Southern dwarf willows do not develop increased foliar cuticle thickness when they undergo early budburst.

Answer

The statement that southern dwarf willows do not develop increased foliar cuticle thickness when they undergo early budburst guarantees the conclusion.
The correct response supplies the precise missing premise needed to complete the conditional syllogism. Premise 1 states that early budburst combined with a lack of foliar cuticle increase leads to necrosis during a freeze. Premise 2 states that necrosis combined with a lack of dormant meristem tissue leads to sub-replacement seed viability. The stimulus states that southern dwarf willows experience early budburst and lack dormant meristems. By establishing that southern dwarf willows do not increase foliar cuticle thickness during early budburst, every necessary condition in the chain is satisfied when a freeze occurs, making the conclusion deductively valid.

Step-by-Step Solution

1
Deconstruct the formal conditional chain in the premises
Premise 1 establishes: (Alpine Plant + Early Budburst + No Cuticle Increase + Freeze) -> Cellular Necrosis. Premise 2 establishes: (Cellular Necrosis + No Dormant Meristems) -> Seed Viability Below Replacement. Factual evidence confirms southern dwarf willows undergo early budburst and lack dormant meristems.
Mapping the explicit conditional statements reveals the exact logical gap required to bridge the premises to the conclusion.
2
Identify the inferential gap between the conditional triggers and the conclusion
To reach the conclusion that a freeze guarantees seed viability falling below the replacement threshold, the condition for Cellular Necrosis must be fully satisfied. We know southern dwarf willows undergo early budburst, but we are not told whether they experience an increase in foliar cuticle thickness.
If southern dwarf willows develop increased cuticle thickness, the first conditional rule would not trigger cellular necrosis, leaving the conclusion unproven.
3
Select the assumption that completely closes the deductive gap
Assuming that southern dwarf willows do not develop increased foliar cuticle thickness when undergoing early budburst completes the antecedent of Premise 1 upon exposure to a freeze, which guarantees cellular necrosis and consequently drives seed viability below replacement.
A sufficient assumption must guarantee that the premises 100% logically entail the conclusion without exception.

Key Concept

Sufficient Assumption in Deductive Conditional Chains
Estimated Time:2m 0s
Question 27Question →

Urban Planner: Any historic district redevelopment proposal that mandates permeable stone pavements will significantly reduce seasonal urban stormwater runoff. Furthermore, every redevelopment proposal that significantly reduces seasonal urban stormwater runoff helps lower downstream municipal infrastructure costs. Therefore, any historic district redevelopment proposal that mandates permeable stone pavements will be granted expedited zoning authorization by the city council.

The conclusion of the urban planner's argument follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Every historic district redevelopment proposal that helps lower downstream municipal infrastructure costs will be granted expedited zoning authorization by the city council.

Answer

Every historic district redevelopment proposal that helps lower downstream municipal infrastructure costs will be granted expedited zoning authorization by the city council.
The argument establishes a conditional chain: Mandating Permeable Pavements implies Reduced Runoff, which implies Lower Downstream Costs. The conclusion asserts that Mandating Permeable Pavements implies Expedited Zoning Authorization. The statement that every proposal lowering downstream infrastructure costs receives expedited zoning authorization bridges Lower Downstream Costs directly to Expedited Zoning Authorization, thereby guaranteeing the conclusion 100% deductively.

Step-by-Step Solution

1
Diagram the conditional premise chain established in the stimulus.
Mandating permeable stone pavements guarantees reduced stormwater runoff, which in turn guarantees lowered downstream municipal infrastructure costs.
Combining the premises yields a unified conditional chain connecting permeable stone pavements directly to lowered downstream infrastructure costs.
2
Identify the conclusion and isolate the logical gap between the premises and the conclusion.
The conclusion claims that mandating permeable stone pavements guarantees expedited zoning authorization by the city council.
The premise chain establishes that permeable pavements lead to lower downstream costs, but the conclusion introduces the new concept of expedited zoning authorization.
3
Formulate the sufficient bridge assumption that completes the deductive syllogism.
Any proposal that lowers downstream municipal infrastructure costs must guarantee expedited zoning authorization by the city council.
Connecting the end of the premise chain directly to the conclusion's predicate deductively guarantees that any proposal mandating permeable pavements will receive expedited zoning authorization.

Key Concept

Sufficient Assumption / Deductive Conditional Bridging
Estimated Time:1m 15s
Question 28Question →

Ethics Analyst: Any algorithmic underwriting model that evaluates borrower risk primarily through secondary transaction data inevitably relies on unverified behavioral proxies. Furthermore, any underwriting model that relies on unverified behavioral proxies fails to satisfy the regulatory threshold for fair lending practices. Thus, any algorithmic underwriting model adopted by sovereign credit unions will fail to satisfy the regulatory threshold for fair lending practices.

The ethics analyst's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Every algorithmic underwriting model adopted by sovereign credit unions evaluates borrower risk primarily through secondary transaction data.

Answer

Every algorithmic underwriting model adopted by sovereign credit unions evaluates borrower risk primarily through secondary transaction data.
The correct answer provides the precise sufficient condition needed to validly bridge the argument's premises to its conclusion. The argument establishes that evaluating risk via secondary transaction data leads to unverified behavioral proxies, which in turn leads to failing the fair lending threshold. Assuming that all sovereign credit union models evaluate risk via secondary transaction data establishes a complete conditional chain from sovereign credit union models directly to regulatory failure.

Step-by-Step Solution

1
Isolate the premises and conclusion and formalize the conditional statements.
Premise 1: Model using secondary transaction data -> Relies on unverified behavioral proxies. Premise 2: Relies on unverified behavioral proxies -> Fails fair lending threshold. Combined Premise Chain: Model using secondary transaction data -> Fails fair lending threshold. Conclusion: Model adopted by sovereign credit unions -> Fails fair lending threshold.
Deconstructing the argument into symbolic logic clarifies the exact inferential gap.
2
Identify the missing link required to make the conclusion follow deductively.
The subject of the conclusion ('Model adopted by sovereign credit unions') is not connected to the sufficient condition of Premise 1 ('Model using secondary transaction data'). The required bridge is: Model adopted by sovereign credit unions -> Model using secondary transaction data.
A sufficient assumption must close 100% of the inferential gap so that Premises + Assumption logically necessitate the Conclusion.
3
Evaluate the answer choices to locate the statement providing this exact conditional link.
The statement specifying that every algorithmic underwriting model adopted by sovereign credit unions evaluates borrower risk primarily through secondary transaction data perfectly connects the left side of the conclusion to the established premise chain.
This completes the deductive chain: Sovereign credit union model -> Secondary transaction data -> Unverified behavioral proxies -> Fails fair lending threshold.

Key Concept

Sufficient Assumption Deductive Bridging
Estimated Time:2m 0s
Question 29Question →

Complete the archaeometrist's formal deductive argument by identifying the missing premise that logically guarantees the conclusion.

Fill in the blanks below

Premise 1: Any ancient ceramic shard containing trace crystalline zircon was fired at temperatures exceeding 900°C.
Premise 2:
Conclusion: Therefore, every artifact unearthed at the Oakhaven kiln complex was fired at temperatures exceeding 900°C.
Show answer & explanation

Answer

Every artifact unearthed at the Oakhaven kiln complex contains trace crystalline zircon
The argument requires a deductive bridge connecting the subject of the conclusion ('every artifact unearthed at the Oakhaven kiln complex') to the sufficient condition of Premise 1 ('ancient ceramic shard containing trace crystalline zircon'). By establishing that all Oakhaven artifacts contain trace crystalline zircon, the chain becomes: Oakhaven Artifact → Contains Trace Zircon → Fired Exceeding 900°C. This 100% guarantees the truth of the conclusion via hypothetical syllogism.

Step-by-Step Solution

1
Isolate the conclusion and formalize its conditional terms
The conclusion asserts: If an artifact was unearthed at the Oakhaven kiln complex, then it was fired at temperatures exceeding 900°C (Oakhaven Artifact → Fired >900°C).
Establishing the target conditional statement reveals what logical outcome must be derived from the premises.
2
Analyze the given premise to map the existing deductive link
Premise 1 states: If a ceramic shard contains trace crystalline zircon, then it was fired at temperatures exceeding 900°C (Contains Trace Zircon → Fired >900°C).
Determining the existing conditional chain identifies the intermediate predicate and isolates the inferential gap.
3
Bridge the gap between the subject of the conclusion and the antecedent of Premise 1
Connecting 'Oakhaven Artifact' to 'Contains Trace Zircon' creates a valid hypothetical syllogism: Oakhaven Artifact → Contains Trace Zircon → Fired >900°C.
A sufficient assumption must fully guarantee that the conclusion necessarily follows when added to the premises.

Key Concept

Sufficient Assumption in Conditional Deductive Chains
Estimated Time:1m 15s
Question 30Question →

Cognitive Ethologist: Ravens in subarctic habitats reliably adjust their food-caching strategies depending on whether they were observed by dominant conspecifics, which demonstrates intentional deception. Any animal that exhibits intentional deception must have the capacity for second-order mental representation. Therefore, subarctic ravens possess a theory of mind.

The cognitive ethologist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Any animal that has the capacity for second-order mental representation possesses a theory of mind.

Answer

The argument's conclusion is logically guaranteed by assuming that any animal having the capacity for second-order mental representation possesses a theory of mind.
The argument establishes a linear conditional chain: subarctic ravens adjust caching strategies, which proves intentional deception, which in turn proves the capacity for second-order mental representation. The conclusion introduces a new concept ('possesses a theory of mind'). The statement that any animal with the capacity for second-order mental representation possesses a theory of mind seamlessly bridges the final link of the premises directly to the conclusion, ensuring deductive validity.

Step-by-Step Solution

1
Analyze the premises and decompose the argument into conditional steps.
Premise 1 establishes: Observed caching adjustment → Intentional deception. Premise 2 establishes: Intentional deception → Capacity for second-order mental representation. Chaining these gives: Subarctic ravens → Capacity for second-order mental representation.
Deconstructing premises reveals the exact logical chain established by the author.
2
Identify the conclusion and locate the inferential gap.
Conclusion: Subarctic ravens → Possess a theory of mind. The gap lies between 'Capacity for second-order mental representation' and 'Possess a theory of mind'.
Sufficient assumption questions require finding the exact missing premise that completes the formal deduction.
3
Formulate the required sufficient bridge statement.
Capacity for second-order mental representation → Possess a theory of mind.
Adding this universal conditional statement completes the deductive chain: Subarctic ravens → Caching adjustment → Intentional deception → Second-order mental representation → Theory of mind.

Key Concept

Sufficient Assumption in Formal Conditional Logic
Estimated Time:1m 15s
Question 31Question →

Match each incomplete argument on the left with the sufficient assumption on the right that logically guarantees its conclusion. Which sufficient assumption properly completes each argument?

Click a left item, then click its matching right item

Items

Argument 1:
Premise: Any environmental mitigation policy that relies on voluntary corporate compliance inevitably fails to produce verifiable reductions in particulate emissions.
Conclusion: Thus, the municipal clean air initiative will fail to qualify for federal regulatory subsidies.
Argument 2:
Premise: Any biomedical clinical trial that utilizes synthetic control groups rather than randomized human controls cannot establish statistical equivalence across diverse subpopulations.
Conclusion: Thus, the experimental immunotherapy protocol should not receive expedited regulatory approval.
Argument 3:
Premise: Any algorithmic judicial sentencing tool that optimizes solely for recidivism reduction disproportionately weighs prior arrest records over severity of conviction.
Conclusion: Thus, the state correctional board's automated sentencing model systematically violates statutory parity mandates.

Matches

Show answer & explanation

Answer

Argument 1 matches with the assumption linking voluntary compliance and lack of verifiable emission reductions to federal subsidy disqualification; Argument 2 matches with the assumption linking synthetic control groups and lack of statistical subpopulation equivalence to expedited approval denial; Argument 3 matches with the assumption linking single-metric recidivism optimization and prior arrest weighting to violations of statutory parity mandates.
Each correct pairing provides the precise missing subject instantiation and universal conditional rule required to close the inferential gap between the argument's stated premise and its definitive conclusion. When the matched statement is added to the premise set, the conclusion follows with absolute deductive certainty.

Step-by-Step Solution

1
Isolate the premise, conclusion, and inferential gap in each argument
Each argument contains an ungrounded subject instantiation and a missing conditional linkage connecting the intermediate predicate to the final conclusion predicate.
Sufficient assumptions must bridge all new or disconnected conceptual terms from the premises directly into the conclusion.
2
Construct the required deductive bridge formula for each argument
For Argument 1: [Initiative → Voluntary Compliance] and [No Verifiable Reductions → No Subsidies]. For Argument 2: [Protocol → Synthetic Controls] and [No Statistical Equivalence → No Expedited Approval]. For Argument 3: [Model → Recidivism Optimization] and [Disproportionate Arrest Weighting → Parity Violation].
Adding these premises creates unbroken chains of formal conditionals that force the truth of each respective conclusion.
3
Align each argument with its corresponding full-coverage assumption
Each argument maps directly and uniquely to the statement providing both subject instantiation and the required universal conditional link.
No other pairing provides the necessary conceptual or formal alignment to render the conclusion 100% deductively valid.

Key Concept

Sufficient Assumption in Formal Deductive Chains
Estimated Time:2m 0s
Question 32Question →

An astrobiologist constructs a formal deductive argument to establish the habitability potential of a planetary body. Complete the argument by identifying the missing premise that logically and deductively guarantees the truth of the conclusion.

Fill in the blanks below

Premise 1: Every marine hydrothermal system that exhibits active serpentinization produces continuous alkaline fluid emissions.
Premise 2: The benthic floor of the Kraken Mare basin exhibits active serpentinization.
Premise 3: Any geological formation that produces continuous alkaline fluid emissions is .
Conclusion: Therefore, the benthic floor of the Kraken Mare basin is viable for prebiotic amino acid synthesis.
Show answer & explanation

Answer

The missing premise must establish that producing continuous alkaline fluid emissions is sufficient to make a geological formation viable for prebiotic amino acid synthesis.
The argument establishes two links: the benthic floor of Kraken Mare exhibits active serpentinization (KM -> AS), and active serpentinization produces continuous alkaline fluid emissions (AS -> AFE), which yields the intermediate deduction that the benthic floor of Kraken Mare produces alkaline fluid emissions (KM -> AFE). To guarantee the conclusion that the benthic floor is viable for prebiotic amino acid synthesis (KM -> PAAS), the missing premise must provide a 100% deductive bridge from alkaline fluid emissions to viability for prebiotic amino acid synthesis (AFE -> PAAS).

Step-by-Step Solution

1
Isolate and diagram the explicit premises and conclusion.
Premise 1: Active Serpentinization (AS) -> Alkaline Fluid Emissions (AFE). Premise 2: Kraken Mare Benthic Floor (KM) -> Active Serpentinization (AS). Conclusion: Kraken Mare Benthic Floor (KM) -> Viable for Prebiotic Amino Acid Synthesis (PAAS).
Mapping the conditional chain reveals the formal inferential gap between the established intermediate term and the target conclusion predicate.
2
Chain the existing premises together.
KM -> AS and AS -> AFE yield the combined valid sub-inference: KM -> AFE (The benthic floor of Kraken Mare produces continuous alkaline fluid emissions).
This establishes what is already proven about the subject of the conclusion before adding any new assumption.
3
Determine the conditional bridge required to reach the conclusion 100% deductively.
We have KM -> AFE, and we must reach KM -> PAAS. The required sufficient bridge is AFE -> PAAS (Any formation that produces continuous alkaline fluid emissions is viable for prebiotic amino acid synthesis).
Connecting the intermediate characteristic (AFE) directly to the conclusion property (PAAS) completes a fully valid hypothetical syllogism.

Key Concept

Sufficient Assumption conditional bridging (Hypothetical Syllogism)
Question 33Question →

Archivist: Any digital archiving project that utilizes proprietary file formats will eventually require format migration to maintain public accessibility. However, migrating complex digital records across different formats invariably introduces some data degradation. Therefore, no archiving project that maintains perfect record fidelity can utilize proprietary file formats.

The archivist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Any digital archiving project that introduces data degradation fails to maintain perfect record fidelity.

Answer

The argument's conclusion follows logically if it is assumed that any digital archiving project that introduces data degradation fails to maintain perfect record fidelity.
The premises establish a direct conditional sequence: using proprietary file formats requires format migration, which in turn invariably introduces data degradation. Thus, any project using proprietary file formats will introduce data degradation. The conclusion asserts that no project maintaining perfect record fidelity can use proprietary formats (i.e., maintaining perfect fidelity requires avoiding proprietary formats). The missing link is that introducing data degradation is strictly incompatible with maintaining perfect record fidelity. The statement that any archiving project that introduces data degradation fails to maintain perfect record fidelity provides this exact bridge, making the argument deductively valid.

Step-by-Step Solution

1
Isolate the premises and conclusion in the stimulus
Premise 1: Proprietary formats lead to format migration. Premise 2: Format migration introduces data degradation. Chain: Proprietary formats lead to data degradation. Conclusion: Perfect record fidelity requires avoiding proprietary formats (or proprietary formats preclude perfect record fidelity).
Deconstructing the formal conditional statements reveals the exact logical structure of the argument.
2
Identify the inferential gap between the combined premises and the conclusion
The premises establish that proprietary formats cause data degradation, while the conclusion asserts that proprietary formats are incompatible with perfect record fidelity. The missing link must connect 'introducing data degradation' to 'failing to maintain perfect record fidelity'.
A sufficient assumption must close the logical gap completely so that the premises plus the assumption deductively guarantee the conclusion.
3
Select the bridge premise that 100% deductively guarantees the conclusion
Assuming that introducing data degradation guarantees a failure to maintain perfect record fidelity completes the chain: Proprietary formats → Data degradation → No perfect record fidelity.
Taking the contrapositive (Perfect record fidelity → No data degradation → No proprietary formats) proves the conclusion is necessarily true.

Key Concept

Sufficient Assumption in Formal Conditional Logic
Estimated Time:1m 15s
Question 34Question →

Ecologist: Any wetlands conservation initiative that permanently elevates local water tables prevents the microbial decomposition of subterranean peat. Preventing the microbial decomposition of subterranean peat guarantees that a wetland will not release methane into the atmosphere. The wetlands conservation project in the Millford Basin will permanently elevate local water tables. Thus, the Millford Basin project will contribute to a net decrease in atmospheric greenhouse gas concentrations.

The ecologist's conclusion follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Any wetland that does not release methane into the atmosphere contributes to a net decrease in atmospheric greenhouse gas concentrations.

Answer

Any wetland that does not release methane into the atmosphere contributes to a net decrease in atmospheric greenhouse gas concentrations.
The argument's premises establish that the Millford Basin project will permanently elevate water tables, which prevents peat decomposition, which in turn guarantees that the wetland will not release methane into the atmosphere. The conclusion asserts that the project will contribute to a net decrease in atmospheric greenhouse gas concentrations. The missing link is a rule stating that not releasing methane guarantees a contribution to a net decrease in atmospheric greenhouse gas concentrations. The credited option provides exactly this bridge, making the deductive chain 100% valid.

Step-by-Step Solution

1
Break down the premises into a conditional logic chain
Millford Basin project -> Permanently elevates water tables -> Prevents microbial decomposition of peat -> Will not release methane into the atmosphere.
Identify the exact endpoint established by the stated premises.
2
Identify the conclusion and locate the inferential gap
Conclusion: Millford Basin project -> Contributes to a net decrease in atmospheric greenhouse gas concentrations. Gap: [Does not release methane] -> [Contributes to a net decrease in atmospheric greenhouse gas concentrations].
A sufficient assumption must supply a universal rule connecting the premise endpoint to the new term in the conclusion.
3
Evaluate the choices for a complete 100% deductive link
The statement specifying that any wetland that does not release methane contributes to a net decrease in atmospheric greenhouse gas concentrations closes the gap entirely.
Adding this premise allows the conclusion to follow deductively with absolute certainty.

Key Concept

Sufficient Assumption Deductive Bridging
Estimated Time:1m 15s
Question 35Question →

Complete the formal deductive argument below by filling in the missing conditional bridge assumption so that the conclusion follows logically from the stated premises.

Fill in the blanks below

Premise 1: Any automated translation engine that lacks context-sensitive disambiguation produces semantic drift.
Premise 2: Any translation system that produces semantic drift fails the benchmark for diplomatic certification.
Missing Assumption: Any system that is prohibited from official treaty documentation.
Conclusion: Therefore, any automated translation engine that lacks context-sensitive disambiguation is prohibited from official treaty documentation.
Show answer & explanation

Answer

fails the benchmark for diplomatic certification
The premises establish a deductive chain from engines lacking context-sensitive disambiguation to producing semantic drift, and from semantic drift to failing the benchmark for diplomatic certification. To validly conclude that any engine lacking context-sensitive disambiguation is prohibited from official treaty documentation, the argument requires a conditional premise stating that failing the benchmark for diplomatic certification guarantees prohibition from official treaty documentation.

Step-by-Step Solution

1
Map the stated premises into a conditional logic chain
Premise 1: Lacks Context-Sensitive Disambiguation → Produces Semantic Drift. Premise 2: Produces Semantic Drift → Fails Benchmark for Diplomatic Certification. Linking them gives: Lacks Context-Sensitive Disambiguation → Fails Benchmark for Diplomatic Certification.
Determining the existing premise chain reveals the intermediate logical endpoint that must connect to the conclusion.
2
Identify the target conclusion predicate and isolate the inferential gap
The argument concludes: Lacks Context-Sensitive Disambiguation → Prohibited from Official Treaty Documentation.
The conclusion introduces a new predicate ('prohibited from official treaty documentation') that has not appeared in any premise.
3
Construct the sufficient bridge connecting the intermediate condition to the final predicate
Establishing that 'Any system that fails the benchmark for diplomatic certification is prohibited from official treaty documentation' closes the transitive gap completely (Lacks Disambiguation → Semantic Drift → Fails Benchmark → Prohibited).
Supplying this specific condition in the missing assumption guarantees that the conclusion follows with 100% deductive validity.

Key Concept

Sufficient Assumption conditional bridging
Estimated Time:1m 15s
Question 36Question →

Urban Planner: Any municipal zoning policy that restricts high-density commercial developments within transit corridors inadvertently reduces public transit ridership. Furthermore, no policy that reduces public transit ridership can effectively lower a city's net carbon emissions from passenger vehicles. Therefore, the municipal council's newly enacted downtown zoning policy will not effectively lower the city's net carbon emissions from passenger vehicles.

The conclusion of the urban planner's argument follows logically if which one of the following is assumed?

Show answer & explanation

Answer: The municipal council's newly enacted downtown zoning policy restricts high-density commercial developments within transit corridors.

Answer

The municipal council's newly enacted downtown zoning policy restricts high-density commercial developments within transit corridors.
The premises state that restricting high-density commercial developments within transit corridors reduces public transit ridership, and reducing ridership prevents a policy from effectively lowering net carbon emissions (R→D→∼ER \rightarrow D \rightarrow \sim E). The conclusion asserts that the newly enacted downtown zoning policy will not effectively lower net carbon emissions (P→∼EP \rightarrow \sim E). The correct answer provides the exact missing premise—that the new policy restricts high-density commercial developments within transit corridors (P→RP \rightarrow R)—which validly completes the deductive syllogism (P→R→D→∼EP \rightarrow R \rightarrow D \rightarrow \sim E).

Step-by-Step Solution

1
Analyze the premises and map out the conditional chain.
Premise 1 establishes: Restricting transit-corridor commercial development (RR) →\rightarrow Reduces transit ridership (DD). Premise 2 establishes: Reduces transit ridership (DD) →\rightarrow Does not effectively lower net carbon emissions (∼E\sim E). This forms the deductive chain: R→D→∼ER \rightarrow D \rightarrow \sim E, meaning R→∼ER \rightarrow \sim E.
Identifying the formal conditional relationships in the premises isolates what has already been proven.
2
Identify the conclusion and locate the inferential gap.
Conclusion: The newly enacted policy (PP) will not effectively lower net carbon emissions (P→∼EP \rightarrow \sim E). The premises prove that R→∼ER \rightarrow \sim E, but never establish that the new policy (PP) actually restricts transit-corridor commercial development (RR).
A sufficient assumption must provide the exact condition necessary to connect the subject of the conclusion to the chain of premises.
3
Select the assumption that bridges the subject of the conclusion to the initial sufficient condition.
Adding the premise P→RP \rightarrow R completes the chain: P→R→D→∼EP \rightarrow R \rightarrow D \rightarrow \sim E, rendering the conclusion logically necessary.
Connecting the new policy to the restriction condition guarantees that the negative outcome regarding carbon emissions must follow.

Key Concept

Sufficient Assumption (Conditional Chain Completion)
Estimated Time:1m 15s
Question 37Question →

Bioethicist: A clinical medical trial is ethically permissible only if it prioritizes patient welfare above the pursuit of scientific discovery. Furthermore, a trial prioritizes patient welfare only if its participants are not subjected to disproportionate physiological risks. Unfortunately, obtaining statistically robust efficacy data in early-stage oncology trials invariably requires administering drug dosages that approach maximum tolerated toxic thresholds. Consequently, none of the early-stage oncology trials currently underway at the Apex Research Institute are ethically permissible.

The conclusion drawn by the bioethicist follows logically if which one of the following is assumed?

Show answer & explanation

Answer: Every early-stage oncology trial currently underway at the Apex Research Institute involves obtaining statistically robust efficacy data, and the administration of drug dosages that approach maximum tolerated toxic thresholds inherently subjects participants to disproportionate physiological risks.

Answer

The correct assumption must perfectly bridge two distinct gaps: connecting the Apex trials to the necessity of obtaining robust data, and connecting the administration of toxic dosages to disproportionate physiological risks.
The argument requires a sufficient assumption to prove that all Apex trials are ethically impermissible. By establishing that all Apex trials involve obtaining robust data, we know they must administer near-toxic dosages (from the third premise). By further establishing that near-toxic dosages cause disproportionate physiological risks, the formal chain is complete: Apex trials -> robust data -> near-toxic dosages -> disproportionate risks -> not prioritizing welfare -> not ethically permissible. The correct answer provides both necessary bridges to make the conclusion 100% deductively valid.

Step-by-Step Solution

1
Map the conditional premises provided in the stimulus.
1) Ethically Permissible -> Prioritizes Welfare. 2) Prioritizes Welfare -> No Disproportionate Risks. 3) Obtaining Robust Data -> Administering Toxic Dosages.
Formalizing the logic reveals the established deductive chain. Combining 1 and 2 gives: Ethically Permissible -> No Disproportionate Risks. The contrapositive is: Disproportionate Risks -> Not Ethically Permissible.
2
Identify the core conclusion.
Apex Trials -> Not Ethically Permissible.
This is the final claim the bioethicist is trying to prove, marked by the indicator 'Consequently'.
3
Identify the missing logical links between the premises and the conclusion.
Gap 1: The argument assumes Apex trials are obtaining robust data (Apex Trials -> Obtaining Robust Data). Gap 2: The argument assumes administering toxic dosages constitutes a disproportionate physiological risk (Administering Toxic Dosages -> Disproportionate Risks).
Without these connections, the fact that Apex is conducting trials cannot trigger the rule about toxic dosages, nor can the toxic dosages trigger the rule about ethical permissibility.
4
Select the option that fully guarantees both missing links.
The correct option must formally state both required conditional relationships to make the argument 100% deductively valid.
A sufficient assumption must leave no logical ambiguity, entirely closing all gaps between the premises and the conclusion.

Key Concept

Formal Logic: Identifying Nested Conditional Gaps in Sufficient Assumption Questions
Question 38Question →

Paleoclimatologist: Validating any predictive model of rapid hemispheric glaciation necessitates either an uninterrupted stratigraphic record of deep-sea sediment cores or a precise quantification of atmospheric aerosol concentrations during the transition epoch. However, a precise quantification of these aerosol concentrations is strictly contingent upon the recovery of pristine ice cores from the corresponding period. Dr. Halley’s latest predictive model regarding the onset of the Younger Dryas anomaly has been conclusively validated. Yet, glaciological surveys confirm that all ice cores from the Younger Dryas transition epoch were irreparably contaminated by subsequent thermal maximums. Therefore, Dr. Halley must have been granted access to the classified geological archives held by the Nordic Subsea Consortium.

The conclusion drawn by the paleoclimatologist follows logically if which one of the following is assumed?

Show answer & explanation

Answer: The only existing uninterrupted stratigraphic records of deep-sea sediment cores for the Younger Dryas transition epoch are contained within the classified geological archives held by the Nordic Subsea Consortium.

Answer

The correct answer states that the only existing uninterrupted stratigraphic records of deep-sea sediment cores for the epoch are contained within the Nordic Subsea Consortium archives.
To guarantee the conclusion, we must bridge the gap between what we logically know and what the author concludes. We know Dr. Halley validated her model. Validation requires either sediment cores (USR) or aerosol quantification (PQA). Because pristine ice cores are unavailable, PQA is impossible. Therefore, Halley must have used USR. The author concludes she accessed the Nordic Subsea Consortium (NSC). To logically guarantee this conclusion, we must assume that anyone who has USR must have accessed the NSC. The correct answer provides this exact bridge by stating the only existing USR are in the NSC archives, meaning Halley could not have gotten them from any other source.

Step-by-Step Solution

1
Map the initial requirements for model validation.
Validation requires either an Uninterrupted Stratigraphic Record (USR) OR Precise Quantification of Aerosols (PQA).
The first sentence establishes a necessary condition containing a disjunction ('either... or...').
2
Map the requirement for precise quantification.
PQA requires Pristine Ice Cores (PIC).
The second sentence explicitly states that PQA is 'strictly contingent upon' the recovery of PIC.
3
Apply the factual premises regarding Dr. Halley's model and the state of the ice cores.
Halley's model is validated. However, no PIC exist for the epoch (~PIC).
The stimulus states her model 'has been conclusively validated' and that all ice cores 'were irreparably contaminated'.
4
Deduce what Dr. Halley must have possessed to validate her model.
By modus tollens, ~PIC means ~PQA. Since Validation requires USR OR PQA, and ~PQA is true, Halley MUST have possessed USR.
The deductive chain eliminates one of the two necessary conditions for validation, leaving the other as an absolute requirement.
5
Identify the logical gap between the deduced intermediate conclusion and the author's final conclusion.
We know Halley has USR. The author concludes Halley had access to the Nordic Subsea Consortium (NSC). Gap: USR -> NSC Access.
To logically guarantee the conclusion (Sufficient Assumption), we must find an answer choice that states having USR guarantees having access to the NSC.

Key Concept

Sufficient Assumption (Formal Logic and Disjunctive Syllogism)
Question 39Question →

Analyze the structural gaps in the following deductive arguments. Match each incomplete argument with the specific conditional premise (sufficient assumption) that, if added, would logically guarantee its conclusion.

Click a left item, then click its matching right item

Items

An artificial intelligence can engage in genuine ethical reasoning only if it can evaluate the semantic weight of counterfactual scenarios. However, evaluating such counterfactuals requires a self-referential internal architecture, a feature that all current large language models completely lack. Therefore, current large language models cannot be held morally culpable for any harmful instructions they generate.
A corporate entity is legally liable for punitive damages only if its executive board possessed prior, explicit knowledge of a product's defect. In the recent litigation against VertexCorp, it was conclusively proven that the executives had no such prior knowledge, as the defect was deliberately concealed by a supplier. Consequently, VertexCorp will not be forced to declare corporate bankruptcy.
A genetic intervention is considered ethically impermissible if it imposes irreversible risks on unconsenting future generations. Unlike germline editing, Procedure X-99 exclusively targets a patient's somatic cells, meaning it produces absolutely no heritable genetic modifications. Thus, Procedure X-99 must be classified as an ethically unproblematic therapeutic technique.
According to the current taxonomic framework, a celestial body is categorized as a major planet only if its gravitational dominance has cleared its orbital neighborhood of smaller planetesimals. Object Z-Prime is located within the outer Oort cloud, a region densely populated with primordial icy debris. From this, we can deduce that Object Z-Prime does not possess a differentiated internal structure.

Matches

Show answer & explanation

Answer

The arguments logically pair with the conditional statements that provide the exact missing deductive bridge: the AI argument pairs with the assumption requiring ethical reasoning for culpability; the Corporate argument pairs with the 'unless' statement about punitive damages; the Bioethics argument pairs with the contrapositive assumption about heritable modifications; and the Astrophysics argument pairs with the prerequisite assumption regarding major planets.
Each correct pairing takes the established factual conclusion from the argument's premises (e.g., LLMs cannot engage in ethical reasoning) and applies a universal conditional rule that uses that fact as a trigger to definitively prove the author's conclusion.

Step-by-Step Solution

1
Deconstruct the stimulus to isolate the premises from the conclusion, identifying the exact logical gap.
For the Bioethics argument, the premise proves 'No heritable modifications', while the conclusion introduces a new term: 'Ethically unproblematic'.
Sufficient assumptions must strictly link the evidence provided to the new terminology in the conclusion.
2
Translate the right-hand conditional statements into formal 'If-Then' notation to reveal their logical force.
The Corporate assumption 'Avoid bankruptcy unless legally liable' translates to 'If NOT legally liable -> Avoid bankruptcy'.
Complex indicators like 'unless', 'requires', and 'prerequisite' often obscure the true sufficient and necessary conditions.
3
Apply the contrapositive of the translated assumptions where necessary to match the flow of the argument.
The Astrophysics assumption 'Major planet is a prerequisite for differentiated structure' means 'If Differentiated -> Major Planet'. The contrapositive is 'If NOT Major Planet -> NOT Differentiated', which bridges the Astrophysics gap perfectly.
The correct answer in LSAT sufficient assumption questions is frequently presented in its contrapositive form to increase difficulty.

Key Concept

Sufficient Assumption Conditional Bridging and Contrapositives
Question 40Question →

Read the formal argument below and determine the exact missing premise that logically completes the deduction.

Fill in the blanks below

Cybersecurity Analyst: A decentralized network protocol can be considered fundamentally secure only if it prevents autonomous node spoofing. However, preventing autonomous node spoofing is mathematically impossible unless the cryptographic handshake strictly utilizes quantum-resistant hashes. Therefore, the recently deployed Omega-Mesh architecture cannot be considered fundamentally secure.

Complete the required sufficient assumption that guarantees the conclusion:
The architecture fails to strictly utilize quantum-resistant .
Show answer & explanation

Answer

The Omega-Mesh architecture fails to strictly utilize quantum-resistant hashes.
The argument requires a sufficient assumption to bridge the gap between a specific protocol (Omega-Mesh) and the conditions for fundamental security. By formalizing the premises, we establish a chain: Fundamentally Secure -> Prevents Node Spoofing -> Utilizes Quantum-Resistant Hashes. The conclusion states Omega-Mesh is NOT Fundamentally Secure. To mathematically guarantee this conclusion using all evidence, we must trigger the contrapositive of the entire chain: If a protocol does NOT utilize quantum-resistant hashes, it is NOT fundamentally secure. Therefore, assuming that the Omega-Mesh architecture fails to strictly utilize quantum-resistant hashes perfectly bridges the logical gap.

Step-by-Step Solution

1
Identify the main conclusion of the analyst's argument.
The conclusion is: The Omega-Mesh architecture cannot be considered fundamentally secure (Omega-Mesh -> ~Secure).
Isolating the conclusion identifies the specific claim that the sufficient assumption must definitively guarantee.
2
Formalize the first conditional premise regarding fundamental security.
Secure -> Prevents Node Spoofing. The phrase 'only if' introduces a necessary condition.
This establishes the first link in the logical chain of requirements for a secure protocol.
3
Formalize the second conditional premise regarding node spoofing.
Prevents Node Spoofing -> Utilizes Quantum-Resistant Hashes. The phrase 'impossible unless' translates to 'If not Hashes, then not Prevents Spoofing', which contraposes to: Prevents Spoofing -> Hashes.
This extends the logical chain to its final, most specific necessary condition.
4
Synthesize the complete premise chain and determine its contrapositive.
Combined chain: Secure -> Prevents Spoofing -> Hashes. Contrapositive chain: ~Hashes -> ~Prevents Spoofing -> ~Secure.
The contrapositive reveals the exact logical pathway required to force the negative conclusion (~Secure) demanded by the argument.
5
Identify the missing link that triggers the contrapositive chain for the specific subject.
To conclude that Omega-Mesh is not secure, we must assume that Omega-Mesh triggers the start of the contrapositive chain. Therefore, Omega-Mesh fails to utilize quantum-resistant hashes.
This assumption bridges the new subject in the conclusion (Omega-Mesh) to the established premise chain, flawlessly guaranteeing the outcome.

Key Concept

Sufficient Assumption - Formal Logic Chain and Contrapositive
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