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Logical Reasoning

666 questions

All types666Multiple choice343Multiple select54True / False70Matching166Ordering18Fill in the blank10Short answer5
Question 261Question →

Health Policy Analyst: A five-year hospital study observed that patients assigned to rooms with large windows overlooking landscaped gardens requested 25 percent less pain medication following surgery than patients whose rooms overlooked brick walls. Therefore, exposure to natural scenery directly accelerates physiological recovery from surgical trauma, reducing the biological need for analgesic drugs.

Which of the following, if true, most seriously weakens the health policy analyst's argument?

Show answer & explanation

Answer: Hospital staff routinely assign patients recovering from minor, less invasive procedures to garden-view rooms while reserving brick-wall rooms for patients recovering from major surgeries.

Answer

The argument is most weakened by establishing that hospital staff routinely assign patients recovering from minor procedures to garden-view rooms and patients recovering from major surgeries to brick-wall rooms.
The correct answer demonstrates that the two patient cohorts were fundamentally dissimilar prior to room assignment. If patients undergoing less invasive procedures were placed in garden-view rooms, the 25 percent lower pain medication usage is directly explained by the less painful nature of their operations rather than any therapeutic effect of the scenery. This alternative explanation severs the causal link between the scenery and recovery rate.

Step-by-Step Solution

1
Identify the argument's premises and main conclusion
Premise: Patients in garden-view rooms requested 25% less pain medication post-surgery than those in brick-wall rooms. Conclusion: Exposure to natural scenery directly accelerates physiological recovery, thereby reducing biological pain medication need.
Deconstructing the argument isolates the author's logical leap from a correlation to a direct causal claim.
2
Identify the unstated assumption and logical vulnerability
The author assumes that the two patient groups were comparable in all relevant surgical aspects and that the visual scenery itself caused the disparity in medication requests.
Causal conclusions on the LSAT are vulnerable to alternate explanations, non-random group assignments, and confounding variables.
3
Evaluate the choices to find the statement that provides an alternative explanation for the disparity
Showing that patients with less severe surgeries were systematically placed in garden-view rooms accounts for the lower pain medication demand without attributing any curative power to the scenery.
Introducing an inherent difference in initial surgical severity between the groups breaks the proposed causal connection.

Key Concept

Alternative Explanations in Causal Reasoning
Estimated Time:1m 15s
Question 262Question →

Match each flawed argumentative excerpt on the left with the description on the right that most accurately identifies its primary reasoning vulnerability.

Click a left item, then click its matching right item

Items

Ecological Manager: The regional council resolved to preserve all 'viable' stands of old-growth timber in the valley. Because every timber stand surveyed can theoretically be harvested and sold on the commercial lumber market without incurring an operating deficit, every stand in the valley is financially viable and therefore protected under the council's preservation resolution.
Transit Planner: Every municipality that successfully lowered its downtown vehicular congestion by more than twenty percent over the past decade implemented an automated congestion-pricing cordon. Therefore, if our municipality implements an automated congestion-pricing cordon around the central business district, we are guaranteed to reduce downtown vehicular congestion by more than twenty percent.
Sports Biomechanist: A five-year longitudinal survey demonstrated that elite marathon runners who regularly perform high-velocity plyometric jump training report significantly fewer patellar tendon injuries than those who do not. Hence, incorporating high-velocity plyometric training into an endurance runner's weekly regimen directly prevents patellar tendon tissue degradation.
Marine Meteorologist: Each individual sensor component integrated into the newly deployed atmospheric monitoring buoy has an operational failure rate of less than one-tenth of one percent during severe oceanic storms. Consequently, the atmospheric monitoring buoy as an integrated system will almost certainly operate without any system failure during severe oceanic storms.

Matches

Show answer & explanation

Answer

The ecological manager excerpt matches the description of equivocation/shifting term meaning; the transit planner excerpt matches the confusion of necessary and sufficient conditions; the sports biomechanist excerpt matches the illicit leap from correlation to causation; and the marine meteorologist excerpt matches the composition error of attributing part-level reliability to the whole system.
Each pair correctly matches an argumentative excerpt to its primary abstract flaw: the ecological manager equivocates on the word 'viable'; the transit planner commits an illegal conditional reversal by treating a necessary prerequisite as a guarantee; the biomechanist confuses statistical correlation with direct causation; and the meteorologist commits the fallacy of composition by assuming system-level durability from individual component durability.

Step-by-Step Solution

1
Analyze the structural flaw in the ecological manager's statement.
The premise establishes a commercial definition of viable (economic solvency), but applies it to an ecological preservation mandate intended for biological viability. This shifts key terminology meaning between premise and conclusion.
Identifying equivocation requires isolating the term whose semantic scope changes across the argument's premises and conclusion.
2
Analyze the formal conditional structure in the transit planner's statement.
The premise states: 'Success -> Congestion Pricing Cordon'. The conclusion asserts: 'Congestion Pricing Cordon -> Success'. This treats a necessary condition as sufficient.
Mapping the conditional logic exposes an invalid reversal of necessary and sufficient conditions.
3
Analyze the causal inference in the sports biomechanist's statement.
A statistical correlation between plyometrics and reduced injuries is taken as definitive proof of direct physical prevention, ignoring third factors such as self-selection bias or unmeasured training variables.
Distinguishing between observational correlation and demonstrated causation is essential to identifying causal flaws.
4
Analyze the part-to-whole relationship in the marine meteorologist's statement.
The argument infers that an entire multi-component assembly is virtually failure-proof because each single component has a 0.1% failure rate, which overlooks cumulative system probability and interface failures.
Properties of individual parts do not transfer automatically to the aggregated whole.

Key Concept

Identifying Formal, Semantic, Causal, and Compositional Flaws in Logical Reasoning Arguments
Estimated Time:2m 30s
Question 263Question →

Complete the statement with the appropriate word or phrase to make the argument's conclusion follow logically.

Fill in the blanks below

Premise: Any employee who completes the advanced data analysis workshop is eligible for promotion to senior analyst.
Conclusion: Therefore, Marcus is eligible for promotion to senior analyst.

The conclusion follows logically if it is assumed that Marcus the advanced data analysis workshop.
Show answer & explanation

Answer

completed (or has completed)
The premise establishes a universal conditional relationship: completing the advanced data analysis workshop guarantees eligibility for promotion. To deductively prove that Marcus is eligible for promotion, we must establish that Marcus meets the trigger condition. Therefore, assuming that Marcus completed the workshop logically guarantees the truth of the conclusion.

Step-by-Step Solution

1
Identify the stated premise and the conclusion
Premise: Completes workshop implies eligible for promotion. Conclusion: Marcus is eligible for promotion.
Deconstructing the argument isolates the sufficient condition and the necessary outcome.
2
Identify the missing logical bridge needed to guarantee the conclusion
The argument requires establishing that Marcus satisfies the sufficient condition (completing the workshop).
Under Modus Ponens, if the conditional statement 'If P, then Q' is true, establishing P guarantees Q.
3
Fill in the blank with the required condition
Assuming Marcus 'completed' (or 'has completed') the workshop guarantees the conclusion with 100% deductive certainty.
Connecting Marcus directly to the sufficient condition closes the inferential gap completely.

Key Concept

Sufficient Assumption and Conditional Deduction
Question 264Question →

Consider the following argument:

Ecologist: Many urban municipalities are replacing high-pressure sodium streetlights with broad-spectrum white LED lamps to reduce electricity costs. Over the past two years, surrounding agricultural zones near cities adopting LEDs reported a 20 percent decline in the nocturnal pollination of night-blooming crops by moths. Because white LEDs emit substantial short-wavelength blue light, which is known to disorient adult moths and suppress foraging activity, the switch to white LEDs is the direct cause of this agricultural pollination decline.

Statement: The finding that agricultural zones surrounding these cities simultaneously introduced a broad-spectrum chemical treatment targeting nocturnal insect populations, if true, weakens the ecologist's argument.

Show answer & explanation

Answer: True

Answer

True, because introducing a plausible alternative cause for the pollination decline directly weakens the ecologist's causal conclusion.
The evaluated statement is correct (True) because a standard method of weakening a causal claim is to provide an alternate cause for the observed effect. The ecologist concludes that urban LED lighting caused the agricultural pollination decline. Demonstrating that the agricultural zones themselves introduced an insect-targeting chemical treatment during the same period provides an independent explanation for the reduced moth population and pollination activity, substantially weakening the ecologist's conclusion.

Step-by-Step Solution

1
Isolate the conclusion and the supporting evidence in the stimulus.
Conclusion: The switch to white LEDs is the direct cause of the 20 percent decline in nocturnal crop pollination. Evidence: White LEDs emit blue light known to disorient moths, and the decline coincided with the LED rollout over the past two years.
Accurately identifying the structural core of the argument is required before assessing any potential weakening effect.
2
Identify the unstated assumption and the vulnerability of the causal reasoning.
The ecologist assumes that no other factor introduced during the same two-year window accounts for the reduced moth activity in the agricultural zones.
Causal conclusions on the LSAT are inherently vulnerable to alternate explanations for the observed phenomenon.
3
Assess the impact of the supplementary statement on the author's conclusion.
If agricultural zones introduced an insecticidal chemical treatment at the same time, this treatment offers a direct, alternate reason for the decline in moth pollination independent of urban lighting.
Providing an alternative cause directly undermines the claim that urban LEDs were the sole or direct cause, confirming the statement is True.

Key Concept

Weakening a causal argument by introducing an alternative explanation for the observed effect
Estimated Time:1m 0s
Question 265Question →

Marine archaeologists preserving waterlogged wooden artifacts adhere to several strict conservation protocols:

- Any waterlogged artifact recovered from a marine environment that contains iron fasteners undergoes chemical desulfurization before polyethylene glycol (PEG) impregnation.
- A waterlogged artifact is freeze-dried only if it has successfully completed PEG impregnation.
- Every artifact that undergoes chemical desulfurization is treated with an alkaline neutralizing bath.
- No artifact recovered from a marine environment that is treated with an alkaline neutralizing bath exhibits post-drying structural warping.

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: Any waterlogged artifact recovered from a marine environment that contains iron fasteners does not exhibit post-drying structural warping.; Any waterlogged marine artifact that exhibits post-drying structural warping does not contain iron fasteners.

Answer

The statements guaranteeing that a waterlogged marine artifact with iron fasteners does not exhibit post-drying structural warping, and that any waterlogged marine artifact exhibiting post-drying structural warping does not contain iron fasteners, must both be true.
The premises form an unbroken deductive chain: any marine artifact with iron fasteners must undergo desulfurization, every desulfurized artifact receives an alkaline bath, and no marine artifact receiving an alkaline bath exhibits warping. Thus, such an artifact cannot warp. By contrapositive logic, if a marine artifact does warp, it cannot have had iron fasteners.

Step-by-Step Solution

1
Symbolize the conditional relationships established in the stimulus.
(Marine and Iron) implies Desulfurization; Freeze-dried implies Completed PEG; Desulfurization implies Alkaline Bath; (Marine and Alkaline Bath) implies No Warping.
Formalizing the premises clarifies the multi-step conditional pathways.
2
Chain the relevant conditional statements together.
(Marine and Iron) leads to Desulfurization, which leads to Alkaline Bath, which in a marine artifact ensures No Warping. Therefore, (Marine and Iron) implies No Warping.
Connecting sufficient and necessary links yields a valid composite deduction.
3
Derive the contrapositive of the valid chain.
The contrapositive of '(Marine and Iron) implies No Warping' is '(Marine and Warping) implies Not Iron'.
The contrapositive of any valid conditional statement is always logically equivalent and must also be true.

Key Concept

Conditional Chaining and Contrapositive Deduction
Estimated Time:1m 30s
Question 266Question →

In the Northern Cascade mountain range, any high-elevation forest plot that sustains a breeding population of northern spotted owls contains old-growth Douglas fir trees. Every forest plot containing old-growth Douglas fir trees has a canopy closure rate of at least 70 percent. However, no forest plot with a canopy closure rate of at least 70 percent permits the rapid proliferation of sun-loving invasive thistle species. In last year's ecological survey of the region, Plot K was found to have a rapid proliferation of sun-loving invasive thistle species.

If the statements above are true, which one of the following must also be true on the basis of them?

Show answer & explanation

Answer: Plot K does not sustain a breeding population of northern spotted owls.

Answer

Plot K does not sustain a breeding population of northern spotted owls.
The stimulus provides a three-step conditional rule: sustaining breeding spotted owls requires old-growth Douglas firs, which require a canopy closure of at least 70 percent, which in turn prevents rapid thistle proliferation. Taking the contrapositive of this entire chain demonstrates that any plot exhibiting rapid thistle proliferation cannot sustain breeding spotted owls. Since Plot K has rapid thistle proliferation, it strictly follows that Plot K does not sustain a breeding population of northern spotted owls.

Step-by-Step Solution

1
Formalize the conditional relationships provided in the stimulus.
Breeding Spotted Owls →\rightarrow Old-Growth Douglas Firs →\rightarrow Canopy Closure ≥70%→\ge 70\% \rightarrow No Rapid Thistle Proliferation.
Mapping the premises into standard formal logic allows for unambiguous chaining of sufficient and necessary conditions.
2
Derive the contrapositive of the full conditional chain.
Rapid Thistle Proliferation →\rightarrow Canopy Closure <70%→< 70\% \rightarrow No Old-Growth Douglas Firs →\rightarrow No Breeding Spotted Owls.
The contrapositive of any valid conditional relationship is logically equivalent and must also be true.
3
Apply the specific factual observation regarding Plot K to the contrapositive chain.
Plot K has rapid thistle proliferation, which deductively proves that Plot K cannot sustain a breeding population of northern spotted owls.
Executing modus tollens with the confirmed existence of thistles in Plot K guarantees the conclusion.

Key Concept

Deductive Conditional Chaining and Contrapositive Inference
Estimated Time:1m 15s
Question 267Question →

Under the Orbital Spaceflight Authority's safety regulations, any commercial satellite operator granted a low-Earth orbit constellation license is required to equip every deployed operational unit with an autonomous collision-avoidance thruster. An autonomous collision-avoidance thruster is approved for operational deployment only if it has passed cryogenic propellant validation. Furthermore, no propulsion mechanism that passes cryogenic propellant validation relies on single-phase chemical ignition. Last year, the Orbital Dynamics Consortium was granted a low-Earth orbit constellation license, and several of its proprietary propulsion units relied on single-phase chemical ignition.

If the statements above are true, which one of the following must be true?

Show answer & explanation

Answer: None of the Orbital Dynamics Consortium’s proprietary propulsion units that rely on single-phase chemical ignition are approved for operational deployment as autonomous collision-avoidance thrusters.

Answer

None of the Orbital Dynamics Consortium’s proprietary propulsion units that rely on single-phase chemical ignition are approved for operational deployment as autonomous collision-avoidance thrusters.
The stimulus establishes a conditional chain: an autonomous collision-avoidance thruster receives approval for operational deployment only if it has passed cryogenic propellant validation, and any unit passing this validation cannot rely on single-phase chemical ignition (Approved -> Cryogenic Validation -> No Chemical Ignition). The contrapositive establishes that any unit relying on single-phase chemical ignition did not pass cryogenic validation and therefore cannot be approved for operational deployment as an autonomous collision-avoidance thruster (Chemical Ignition -> No Cryogenic Validation -> Not Approved). Thus, for the consortium's units that rely on single-phase chemical ignition, none can be approved.

Step-by-Step Solution

1
Map the conditional statements from the stimulus into formal logical relationships.
Approved Autonomous Thruster -> Passed Cryogenic Validation -> Does NOT Rely on Single-Phase Chemical Ignition.
Establishing the chain of necessary conditions allows for rigorous deduction across multiple premises.
2
Derive the contrapositive of the full conditional chain.
Relies on Single-Phase Chemical Ignition -> Failed/Did Not Pass Cryogenic Validation -> NOT Approved for Operational Deployment as an Autonomous Collision-Avoidance Thruster.
The contrapositive of any valid conditional chain is logically equivalent to the original chain.
3
Apply the factual premises regarding the Orbital Dynamics Consortium to the deduced contrapositive.
Since several proprietary propulsion units rely on single-phase chemical ignition, none of those specific units can be approved for operational deployment as autonomous collision-avoidance thrusters.
Direct instantiation of a known fact into a valid contrapositive guarantees the truth of the conclusion.

Key Concept

Conditional Logic Chaining and Contrapositive Deduction
Estimated Time:1m 45s
Question 268Question →

Food Safety Inspector: To be certified as artisanal sourdough bread under the regional culinary registry, a bakery must use a naturally fermented sourdough culture rather than commercially packaged baker's yeast. The Old Mill Bakery prepares all of its bread loaves exclusively with a wild sourdough starter that is naturally fermented. Therefore, the bread produced by The Old Mill Bakery will definitely be certified as artisanal sourdough bread by the regional culinary registry.

Which one of the following most accurately describes a flaw in the food safety inspector's reasoning?

Show answer & explanation

Answer: assumes that meeting a necessary requirement for an official status is enough on its own to secure that status

Answer

assumes that meeting a necessary requirement for an official status is enough on its own to secure that status
The argument establishes that utilizing a naturally fermented sourdough culture is a necessary condition for receiving certification ('must use'). From the fact that The Old Mill Bakery satisfies this requirement, the inspector concludes that certification is guaranteed. This erroneously treats a requirement that is merely necessary as though it were sufficient on its own to ensure certification.

Step-by-Step Solution

1
Break down the stimulus into its structural components (premises and conclusion).
Premise 1: Certification as artisanal sourdough requires using a naturally fermented culture (Certification -> Naturally Fermented Culture). Premise 2: The Old Mill Bakery uses a naturally fermented wild starter. Conclusion: The Old Mill Bakery will definitely be certified.
Isolating premises from the conclusion is necessary to pinpoint where the logical leap occurs.
2
Analyze the conditional relationship between the requirement and the outcome.
Natural fermentation is stated as a mandatory prerequisite ('must use'), making it a necessary condition. However, there may be other mandatory criteria (such as flour standards, baking procedures, or hygiene protocols) that must also be satisfied.
Distinguishing necessary conditions from sufficient conditions exposes the underlying fallacy in the deduction.
3
Match the identified flaw with the option that describes it accurately.
The argument treats fulfilling a necessary condition as if it were sufficient to guarantee the outcome.
The correct answer must accurately capture this specific conditional flaw without introducing unrelated fallacies.

Key Concept

Mistaking a Necessary Condition for a Sufficient Condition (Conditional Reversal)
Estimated Time:1m 15s
Question 269Question →

A wildlife sanctuary reported a 40 percent decline in the local songbird population over the past two years, coinciding with the arrival of feral cats in the preserve. Because feral cats are known predators of small birds, sanctuary managers concluded that predation by the cats is the direct cause of this population decline.

Which of the following, if true, most seriously weakens the sanctuary managers' argument?

Show answer & explanation

Answer: A viral pathogen lethal to songbirds severely depleted avian populations across the entire geographical region over the past two years, including in preserves with no feral cats.

Answer

The statement introducing a widespread viral pathogen affecting songbird populations across areas with and without cats provides an alternate explanation, thereby weakening the causal conclusion.
The correct answer provides an alternate explanation for the songbird decline. Showing that songbird numbers fell just as sharply in adjacent preserves without feral cats strongly suggests that a regional factor, such as a pathogen, was responsible rather than predation by the cats.

Step-by-Step Solution

1
Identify the argument's premises and main conclusion.
Premise: Songbird population dropped by 40% over two years as feral cats arrived. Conclusion: Predation by feral cats directly caused the decline.
Weaken questions require targeting the logical bridge between stated premises and the conclusion.
2
Identify the underlying logical vulnerability.
The author presumes a correlation implies causation, overlooking potential external factors that could independently cause the decline.
Causal conclusions in logical reasoning are vulnerable to viable alternate causes.
3
Evaluate the answer choices for new information that severs the causal link.
Evidence of an overarching viral outbreak across the entire region demonstrates that the bird population declined even where feral cats were absent.
An alternate cause operating independently of the suspected factor directly undermines the proposed causal connection.

Key Concept

Causal Reasoning and Alternative Explanations
Estimated Time:1m 0s
Question 270Question →

All botanists employed at the state arboretum have specialized certification in rare flora preservation. Anyone who possesses specialized certification in rare flora preservation is authorized to collect plant specimens in the protected nature reserve. Clara is a botanist employed at the state arboretum.

If the statements above are true, which one of the following must also be true?

Show answer & explanation

Answer: Clara is authorized to collect plant specimens in the protected nature reserve.

Answer

Clara is authorized to collect plant specimens in the protected nature reserve.
The stimulus establishes a direct transitive conditional chain: being a botanist at the arboretum guarantees holding the rare flora certification, and holding that certification guarantees authorization to collect specimens in the nature reserve. Because Clara is a botanist at the arboretum, she necessarily possesses the certification and therefore must be authorized to collect specimens.

Step-by-Step Solution

1
Map the conditional rules established by the premises
Rule 1: Employed as arboretum botanist entails holding rare flora certification. Rule 2: Holding rare flora certification entails being authorized to collect specimens in the reserve. Fact: Clara is employed as an arboretum botanist.
Establishing the formal conditional structure allows for valid transitive deduction.
2
Chain the conditional statements and apply them to the specific subject
Clara -> Arboretum Botanist -> Certified in Rare Flora Preservation -> Authorized to Collect Plant Specimens.
Deductive validity requires combining valid 'all' statements into a unified logical chain.
3
Identify the statement that must be true based strictly on this deductive chain
Clara is logically guaranteed to be authorized to collect plant specimens in the protected nature reserve.
On Must Be True questions, the correct answer is fully supported without assuming external facts.

Key Concept

Transitive conditional deduction in deductive reasoning
Estimated Time:45s
Question 271Question →

Forestry Researcher: Alpine birch trees infested with leaf-mining moths suffer significantly less winter frost injury than uninfested birch stands nearby. Because the larvae generate minute amounts of metabolic heat while burrowing inside leaf tissues during late autumn, this thermal output must directly shield the birch trees from extreme freezing temperatures during the subsequent winter months.

Which of the following, if true, most seriously undermines the forestry researcher's conclusion?

Show answer & explanation

Answer: Leaf-mining larvae cease feeding and drop into the subsoil to pupate weeks before the first winter freezes, at which time the infested birch trees shed all their leaves.

Answer

The argument is most weakened by demonstrating that the larvae leave the tree and the leaves are shed before winter arrives, meaning the larval metabolic heat cannot physically shield the trees from freezing temperatures during winter.
The correct response introduces evidence that severs the causal mechanism proposed by the author. If the larvae migrate into the subsoil to pupate and the birch trees shed all of their leaves weeks before the onset of freezing winter weather, then larval metabolic heat produced within leaf tissues cannot possibly be present to insulate or shield the tree branches from sub-zero winter temperatures.

Step-by-Step Solution

1
Analyze the argument structure and isolate premises and conclusion
Premises: Infested birch trees experience less winter frost damage than uninfested stands; larvae generate minute metabolic heat inside leaf tissue in late autumn. Conclusion: This larval thermal output directly shields the birch trees from extreme sub-zero temperatures during the subsequent winter.
Deconstructing the core argument reveals the specific causal link proposed by the researcher.
2
Identify the unstated assumption and logical gap
The researcher assumes that the heat generated inside leaves during late autumn continues to protect the tree throughout the sub-zero freezing periods of winter.
Evaluating the temporal relationship and physical mechanism highlights potential disconnects between late-autumn larval activity and mid-winter freeze protection.
3
Select the choice that breaks the proposed causal mechanism
The statement showing that larvae leave and leaves fall before winter freezes eliminates the physical presence of the heat source during the time protection is claimed to occur.
Severing the necessary temporal and physical link directly undermines the conclusion that larval heat shields the tree from winter freezes.

Key Concept

Causal Disconnect and Temporal Inconsistency in Weaken Questions
Estimated Time:1m 45s
Question 272Question →

Every manuscript in the municipal archive that was created before 1750 is stored in a climate-controlled vault. Any archive document stored in a climate-controlled vault requires written authorization from the head archivist to be accessed. Today, researcher Evelyn was granted access to a municipal archive document without written authorization from the head archivist.

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

Select all that apply

Show answer & explanation

Answer: The document accessed by Evelyn is not stored in a climate-controlled vault.; The document accessed by Evelyn was not created before 1750.

Answer

The statements establishing that the document accessed by Evelyn is not stored in a climate-controlled vault and that the document was not created before 1750 must both be true.
The stimulus establishes a transitive conditional chain: if a manuscript was created before 1750, it is kept in the vault; if it is in the vault, written authorization is required to access it. Modus tollens (contrapositive reasoning) dictates that if a document is accessed without written authorization, it cannot be in the vault, and consequently, it cannot have been created before 1750.

Step-by-Step Solution

1
Symbolize the conditional rules in the stimulus
Created before 1750 implies Stored in vault; Stored in vault implies Requires written authorization. Chained: Created before 1750 implies Requires written authorization.
Establishing the conditional relationships enables valid deductive inferences via modus tollens.
2
Apply the given factual premise to the conditional chain
Evelyn accessed a document with No written authorization, triggering the contrapositives: Not stored in vault, and Not created before 1750.
The negation of a necessary condition guarantees the negation of the sufficient condition.
3
Evaluate the choices against the deduced contrapositives
Identify the choices reflecting that the document is not in a vault and not created before 1750 as logically certain, while rejecting mistaken reversals, necessary-sufficient confusions, and unjustified universal claims.
Must Be True questions require strictly valid deductions with no unsupported assumptions.

Key Concept

Conditional logic chains and contrapositive deduction
Question 273Question →

Match each argument with the fundamental unstated assumption on which its conclusion logically depends.

Click a left item, then click its matching right item

Items

A museum attributed an unsigned seventeenth-century landscape painting to Artist X because the rare cobalt pigment used in the canvas sky was manufactured exclusively in Artist X's private studio. Therefore, Artist X must have painted this canvas.
To reduce peak-hour congestion on the main bridge, the city plans to double the bridge toll. Because this increase makes driving significantly more expensive than taking the commuter train, the policy will successfully decrease bridge traffic.
A workplace study found that office workers who took a 15-minute afternoon walk reported lower daily stress levels than workers who stayed at their desks. Therefore, taking an afternoon walk causes a reduction in daily workplace stress.

Matches

Show answer & explanation

Answer

The painting attribution argument matches the assumption that no other painter obtained the exclusive pigment; the bridge toll argument matches the assumption that cost influences commuter transit choices; and the workplace study argument matches the assumption that walking workers were not already less prone to stress.
Each pair correctly matches an argument to an unstated premise required for the reasoning to hold. For the painting attribution, ruling out third-party access to the exclusive pigment is required to conclude the artist personally painted it. For the toll policy, commuter sensitivity to financial cost is necessary for a price hike to change travel habits. For the workplace walking study, ruling out baseline selection bias is required to establish a causal relationship between walking and lower stress.

Step-by-Step Solution

1
Isolate the conclusion and evidence for each argument on the left.
Identified the core inferential gap in each scenario: exclusive material to specific artist, increased toll cost to behavior change, and observed correlation to direct causation.
A necessary assumption must bridge the gap between the stated premises and the conclusion.
2
Apply the Negation Test to candidate assumptions.
Negating each matched assumption directly destroys the validity of its corresponding conclusion.
If an argument's conclusion collapses when a statement is negated, that statement is strictly necessary to the argument.

Key Concept

Necessary Assumption and the Negation Test
Estimated Time:1m 30s
Question 274Question →

Every deep-sea research probe deployed into the Hadal zone that operates below 7,000 meters requires a titanium-composite pressure hull. No probe equipped with a titanium-composite pressure hull can utilize standard acoustic telemetry for real-time surface communication. Any probe that cannot utilize standard acoustic telemetry must record its observational telemetry locally onto solid-state optical drives unless it is tethered directly to a fiber-optic surface buoy. Last season, the Mariana Oceanic Survey deployed six autonomous, untethered probes into the Hadal zone, all of which operated at a depth of 8,200 meters throughout their missions. Furthermore, some probes deployed by the survey last season suffered complete failure of their external imaging sensors.

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

Select all that apply

Show answer & explanation

Answer: All six autonomous probes deployed by the Mariana Oceanic Survey last season recorded their observational telemetry locally onto solid-state optical drives.; Any Hadal zone probe that successfully utilizes standard acoustic telemetry for real-time surface communication does not operate below 7,000 meters.

Answer

The statements asserting that all six autonomous probes recorded telemetry locally onto solid-state optical drives and that any Hadal zone probe utilizing standard acoustic telemetry does not operate below 7,000 meters must both be true.
Both correct statements are logically inescapable deductions. The first follows from chaining the depth threshold to the hull requirement, to the absence of acoustic telemetry, and finally to local optical recording given that the probes were untethered. The second is the strict contrapositive of the initial conditional chain: standard acoustic communication guarantees the absence of a titanium pressure hull, which in turn guarantees that the probe does not operate below 7,000 meters in the Hadal zone.

Step-by-Step Solution

1
Diagram the formal conditional premises from the stimulus.
Operating below 7,000 m in Hadal zone -> Titanium hull -> No standard acoustic telemetry -> (Tethered to fiber-optic buoy OR Local solid-state optical recording).
Establishing explicit conditional relationships allows deductive chaining and contrapositive derivations.
2
Apply the specific case of the six Mariana Oceanic Survey probes.
Operating at 8,200 m (> 7,000 m) means all 6 had titanium hulls, which means none could use standard acoustic telemetry. Because they were untethered, all 6 must have recorded locally onto solid-state optical drives.
Applying the conditional chain to the factual scenario proves the first valid deduction.
3
Derive the contrapositive chain for probes utilizing standard acoustic telemetry.
Utilizes standard acoustic telemetry -> No titanium hull -> Does not operate below 7,000 m in the Hadal zone (operates at 7,000 m or shallower).
A valid contrapositive inference is logically guaranteed to be true whenever the original conditional premises are true.
4
Evaluate and eliminate distractors based on quantifier shifts and logical fallacies.
Statements committing conditional reversal, illegitimate quantifier escalation from 'some' to 'every', and unwarranted exclusivity claims are invalid.
Deductive validity requires strict conformity to established premises without scope broadening.

Key Concept

Multi-premise conditional chaining, contrapositive derivation, and strict quantifier boundaries
Question 275Question →

Transportation Director: Six months after our municipal transit authority installed high-definition surveillance cameras across central bus terminals, reported pickpocketing incidents decreased by 35 percent. Because the cameras were mounted in prominent, well-marked locations, it is clear that potential thieves were deterred by the visible likelihood of being recorded.

Statement: If it is true that transit authorities also doubled the deployment of uniformed foot-patrol officers across the central terminals throughout the same six months, this fact weakens the Transportation Director's argument.

Show answer & explanation

Answer: True

Answer

True
The evaluation is true because the supplementary fact introduces an unaddressed confounding variable (doubled uniformed patrol presence) that occurred over the identical time interval, offering a strong alternative explanation for the drop in crime and thereby weakening the director's causal inference.

Step-by-Step Solution

1
Identify the conclusion and underlying causal logic of the argument.
The director concludes that visible surveillance cameras caused the 35 percent reduction in pickpocketing.
Weaken questions require identifying the specific link between the evidence and the main conclusion.
2
Evaluate how the supplementary statement impacts the author's causal claim.
The statement introduces a confounding variable: a doubled presence of uniformed officers during the exact same timeframe and location.
An alternative cause explains the observed outcome without attributing it to the author's proposed cause.
3
Determine whether providing an alternative explanation weakens the argument.
Because the alternative explanation directly reduces the likelihood that the cameras alone caused the decrease, it weakens the argument, making the statement true.
In logical reasoning, demonstrating that another concurrent factor could account for the effect weakens a causal inference.

Key Concept

Undermining a causal conclusion through an alternative explanatory cause
Question 276Question →

Match each flawed argument excerpt on the left with the description on the right that most accurately identifies its primary reasoning vulnerability.

Click a left item, then click its matching right item

Items

Archaeologist: Every fossil site in the eastern basin that preserves intact hominid footprints also contains extensive volcanic ash layers. Since the newly excavated site at Omo Valley contains extensive volcanic ash layers, it must preserve intact hominid footprints.
Health Economist: Recent public health surveys indicate that adults who regularly take dietary supplements visit physicians less frequently than those who do not. Therefore, taking dietary supplements directly prevents medical illnesses that would require clinical care.
Art Historian: The renowned architect argues that the ancient ceremonial palace was designed around precise celestial alignments. However, this architect was recently investigated for fabricating archival records, so her hypothesis regarding the palace must be false.
Materials Scientist: Each individual composite ceramic tile used in the spacecraft's thermal protection shield is capable of withstanding temperatures exceeding 3,000 degrees Celsius without degradation. Thus, the entire thermal shield system assembled from these tiles will maintain structural integrity at that temperature.

Matches

Show answer & explanation

Answer

The archaeologist's argument matches the description of treating a necessary condition as sufficient; the health economist's argument matches inferring causation from correlation; the art historian's argument matches directing criticism at the source rather than the claim; and the materials scientist's argument matches inferring that a whole system possesses a property of its individual parts.
Each flawed argument exhibits a classic formal or informal reasoning vulnerability: (1) The archaeologist's argument treats the presence of volcanic ash, which is merely a necessary correlate for footprint preservation, as a sufficient condition to conclude footprints exist. (2) The health economist's argument leaps from an observed statistical association between supplement use and fewer physician visits to an unverified causal claim. (3) The art historian's argument rejects a claim by attacking the past honesty of the person proposing it rather than testing the claim's merits. (4) The materials scientist's argument commits a composition fallacy by assuming an assembled system automatically retains the thermal properties of its constituent individual tiles.

Step-by-Step Solution

1
Analyze the archaeologist's argument structure.
Premise: Preserves footprints → Contains volcanic ash. Observation: Omo Valley has volcanic ash. Conclusion: Omo Valley has footprints. This is an invalid conditional reversal.
Identify the logical flaw committed when moving from a necessary condition to a guaranteed outcome.
2
Analyze the health economist's argument structure.
Premise: Taking supplements correlates with fewer doctor visits. Conclusion: Taking supplements directly prevents illness. This assumes correlation proves causation.
Identify the vulnerability of deriving a direct causal mechanism from observational survey data.
3
Analyze the art historian's argument structure.
Premise: The architect who formulated the hypothesis has fabricated records. Conclusion: The hypothesis is false. This attacks the source rather than the claim.
Identify the ad hominem flaw where source credibility is substituted for evaluating substantive evidence.
4
Analyze the materials scientist's argument structure.
Premise: Each individual tile can withstand 3,000 degrees Celsius. Conclusion: The entire assembled shield will maintain structural integrity at 3,000 degrees Celsius. This commits a part-to-whole (composition) fallacy.
Identify the structural error of transferring properties of parts to the aggregate whole without justification.

Key Concept

Flaw in the Reasoning: Identifying formal conditional errors, causal fallacies, ad hominem attacks, and errors of composition
Estimated Time:1m 30s
Question 277Question →

At the Crestview Municipal Library, every employee who manages the archival collection has completed advanced cataloging training. In addition, no employee who has completed advanced cataloging training is permitted to perform public front-desk duties during morning shifts.

If the statements above are true, which of the following must also be true?

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Answer: No employee at the Crestview Municipal Library who manages the archival collection is permitted to perform public front-desk duties during morning shifts.

Answer

No employee at the Crestview Municipal Library who manages the archival collection is permitted to perform public front-desk duties during morning shifts.
The statement that no employee who manages the archival collection is permitted to perform morning front-desk duties follows directly from chaining the two premises: any archive manager must have completed advanced cataloging training, and anyone who has completed that training is barred from working the morning front desk.

Step-by-Step Solution

1
Identify and symbolize the first conditional premise.
Manage Archive → Completed Advanced Training
The statement establishes that managing the archival collection guarantees that advanced cataloging training has been completed.
2
Identify and symbolize the second conditional premise.
Completed Advanced Training → NOT Permitted Morning Front-Desk Duties
The universal negative rule establishes that having completed advanced training excludes an employee from morning front-desk duties.
3
Chain the conditional statements together deductively.
Manage Archive → Completed Advanced Training → NOT Permitted Morning Front-Desk Duties, which yields: Manage Archive → NOT Permitted Morning Front-Desk Duties
Transitive property of conditional logic yields the guaranteed deduction.

Key Concept

Transitive conditional chaining and universal deductive deduction
Estimated Time:45s
Question 278Question →

Agricultural Advisor: A regional coffee farming cooperative recently reported that member farms using a newly introduced organic compost experienced a twenty percent decrease in crop-damaging beetle infestations compared to the previous year. Because no other new pest control products were distributed to these farms during that period, the cooperative's directors concluded that the compost itself produces compounds that actively repel these beetles.

Which of the following, if true, most seriously weakens the directors' argument?

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Answer: An unseasonable regional cold snap caused a similar decrease in beetle infestations on neighboring coffee farms that did not apply the compost.

Answer

The argument is most weakened by evidence that an unseasonable regional cold snap caused a similar decrease in beetle infestations on neighboring coffee farms that did not apply the compost.
The correct answer provides an alternative explanation for the observed reduction in beetles. By demonstrating that a regional cold snap caused an identical decrease on farms that never used the compost, it shows that the decline in beetle infestation was likely due to weather rather than any chemical property of the compost.

Step-by-Step Solution

1
Identify the premises and the main conclusion.
Premises: Farms using new compost had 20% fewer beetles, and no other new pest products were used. Conclusion: The compost itself produces compounds that repel beetles.
Isolating the argument structure reveals the causal inference made by the directors.
2
Identify the underlying assumption and logical vulnerability.
The directors assume that no external or environmental factor accounted for the drop in beetle numbers.
Causal claims based on simple before-and-after observations are vulnerable to alternative explanations.
3
Evaluate the choices to find the one that undermines the causal link.
Showing that untreated control farms experienced the same reduction due to cold weather demonstrates that the compost was not the cause.
Providing a plausible alternative cause that explains the observed correlation effectively weakens the argument.

Key Concept

Weaken a causal argument by providing an alternative explanation for an observed correlation
Estimated Time:50s
Question 279Question →

Botanist: In order for this rare species of orchid to bloom, it must be kept in an environment with high humidity. The greenhouse housing this specimen has maintained high humidity throughout the entire year. Therefore, this orchid will bloom.

Which one of the following most accurately describes the reasoning flaw in the botanist's argument?

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Answer: assumes that satisfying a prerequisite for blooming is enough to ensure that the orchid will bloom

Answer

The argument assumes that satisfying a prerequisite for blooming is enough to ensure that the orchid will bloom.
The botanist states that high humidity is a necessary condition ('in order for... it must be...'). However, satisfying a necessary condition does not guarantee the outcome. The author commits a classic error of conditional logic by treating a necessary condition as though it were sufficient to guarantee that the orchid will bloom.

Step-by-Step Solution

1
Identify the premises and conclusion of the argument
Premise 1: High humidity is required for the orchid to bloom (Blooming -> High Humidity). Premise 2: High humidity is present. Conclusion: The orchid will bloom.
Deconstructing the argument into formal components isolates the structural relationship between conditions.
2
Analyze the logical transition between premises and conclusion
The author affirms the necessary condition (humidity) and attempts to deduce that the sufficient condition (blooming) must occur.
Meeting a necessary requirement does not guarantee an outcome, because other necessary factors (e.g., proper sunlight, soil nutrients, temperature) might still be lacking.
3
Match the identified flaw with the correct description
The argument confuses a necessary condition (a prerequisite) with a sufficient condition (a guarantee).
Accurately identifying the formal logical fallacy resolves the question.

Key Concept

Mistaking a Necessary Condition for a Sufficient Condition
Estimated Time:50s
Question 280Question →

A university library recently replaced all of its older fluorescent ceiling lights with energy-efficient LED fixtures that emit a cooler, bluer spectrum of light. During the semester following the installation, the average number of hours students spent studying in the library each evening increased by thirty percent. The university administration concluded that the cooler light spectrum provided by the LED fixtures directly caused students to study for longer periods. Which one of the following is an assumption on which the university administration's argument depends?

Show answer & explanation

Answer: The increase in average evening study hours was not primarily the result of other changes made to the library during the same semester.

Answer

The argument depends on the assumption that the increase in average evening study hours was not primarily the result of other changes made to the library during the same semester.
The author infers a direct causal relationship from a chronological correlation (new lighting followed by longer study hours). For this causal conclusion to hold, the author must assume that other concurrent factors (such as extended facility hours, new tutoring programs, or changes in academic policies) were not the true primary cause of the increase. Logically negating this statement confirms that if other changes caused the increase, the administration's argument collapses.

Step-by-Step Solution

1
Identify the core premises and the conclusion
Premises: Fluorescent lights were replaced by cooler-spectrum LED fixtures, and subsequent average evening study hours rose by 30%. Conclusion: The cooler light spectrum directly caused the increase in study time.
Isolating the conclusion clarifies the specific causal leap made by the author.
2
Detect the unstated assumption bridging the premises to the conclusion
The author assumes that no confounding variable or alternative factor introduced during that same semester was responsible for the increase in study hours.
Causal conclusions always require ruling out plausible alternative causes that could fully account for the observed correlation.
3
Apply the Negation Test to verify necessity
Negating the statement gives: 'The increase in study hours WAS primarily the result of other changes made to the library during the same semester.' This directly shatters the conclusion that the lighting caused the increase.
A necessary assumption must fatally undermine the conclusion when logically negated.

Key Concept

Necessary Assumption: Defender Pattern (Ruling out alternative explanations for a causal conclusion)
Estimated Time:55s
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