Must Be True Questions

61 questions

Question 1Question →

According to the municipal zoning code, any city planner who approves the designation of a High-Density Residential Zone (HDRZ) in a given neighborhood must first complete a Comprehensive Traffic Impact Study (CTIS) for that neighborhood. Completing a CTIS requires that the planner consult with both the Regional Transit Authority and the neighborhood's local association. However, formal consultation with a neighborhood's local association is impossible if that neighborhood lacks a legally registered civic charter. Currently, none of the neighborhoods located within the historic Westside district possess a legally registered civic charter.

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

Show answer & explanation

Answer: No city planner has approved the designation of a High-Density Residential Zone in any neighborhood within the historic Westside district.

Answer

No city planner has approved the designation of a High-Density Residential Zone in any neighborhood within the historic Westside district.
The correct answer accurately reflects the contrapositive of the stimulus's logical chain. The text establishes that approving an HDRZ requires completing a CTIS, which requires consulting the local association. It also establishes that this consultation requires a civic charter. Because no neighborhood in the Westside district has a civic charter, it is impossible to consult their local associations. Consequently, a CTIS cannot be completed, meaning a city planner cannot approve an HDRZ there.

Step-by-Step Solution

1
Diagram the primary conditional statements provided in the municipal zoning rules.
HDRZ Approved → CTIS Completed → (Consult RTA AND Consult Local Association).
To establish the necessary prerequisites for a city planner to legally approve a high-density zone.
2
Diagram the restriction regarding neighborhood civic charters.
No Civic Charter → Local Association Cannot be Consulted.
To integrate the limiting condition into the logical framework.
3
Form the contrapositive logical chain combining all premises.
No Civic Charter → Local Association Cannot be Consulted → CTIS Cannot be Completed → HDRZ Cannot be Approved.
To determine the unavoidable consequences when a neighborhood lacks a civic charter.
4
Apply the specific factual premise about the Westside district to the contrapositive chain.
Westside Neighborhood → No Civic Charter → HDRZ Cannot be Approved.
To draw a definitive conclusion that must be true based entirely on the provided text.

Key Concept

Chaining conditional statements and applying the contrapositive to draw a guaranteed deduction.
Question 2Question →

Botanists studying a temperate rainforest have established that any fungal species producing the enzyme lignase can successfully break down mature hardwood. Furthermore, most fungal species inhabiting the rainforest's upper canopy produce lignase, though no upper-canopy fungal species can survive prolonged freezing temperatures. Interestingly, every fungal species capable of breaking down mature hardwood requires a highly humid microclimate to reproduce, unless that species is capable of surviving prolonged freezing temperatures.

Which of the following statements can be properly inferred from the information provided above?

Show answer & explanation

Answer: Most fungal species inhabiting the rainforest's upper canopy require a highly humid microclimate to reproduce.

Answer

Most fungal species inhabiting the rainforest's upper canopy require a highly humid microclimate to reproduce.
The correct answer is derived by chaining the provided facts. First, because most canopy fungi produce lignase, and all lignase producers break down hardwood, most canopy fungi break down hardwood. Second, we know absolutely no canopy fungi survive freezing. The final rule dictates that any fungus breaking down hardwood must require a humid microclimate, UNLESS it can survive freezing. Since the canopy fungi that break down hardwood cannot survive freezing, the 'unless' exception does not apply to them. Therefore, this majority group of canopy fungi must require a humid microclimate.

Step-by-Step Solution

1
Connect the 'most' quantifier to the first conditional rule.
Since most canopy species produce lignase, and all lignase producers break down hardwood, it follows that most canopy species break down hardwood.
This establishes a core characteristic (breaking down hardwood) that applies to the majority of the canopy species.
2
Analyze the restriction on canopy species regarding temperature.
No canopy species can survive prolonged freezing temperatures.
This establishes a universal negative characteristic for the entire canopy group.
3
Translate the 'unless' clause in the final premise into a standard conditional statement.
If a species breaks down hardwood AND cannot survive freezing temperatures, then it requires a highly humid microclimate.
The word 'unless' introduces a necessary condition negated. Thus, 'Requires Humid unless Survives Freezing' means 'If NOT Survives Freezing -> Requires Humid'.
4
Apply the conditional rule from Step 3 to the group identified in Steps 1 and 2.
Since most canopy species break down hardwood AND cannot survive freezing, most canopy species must require a highly humid microclimate.
The sufficient conditions for the final premise are entirely met by the majority of the canopy group.

Key Concept

Combining formal logic conditionals, 'unless' translations, and quantifier chaining.
Question 3Question →

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

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

Select all that apply

Show answer & explanation

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

Answer

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

Step-by-Step Solution

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

Key Concept

Drawing formal logic deductions by combining transitive conditional chains with proportion quantifiers (some/most).
Estimated Time:1m 45s
Question 4Question →

Under the revised maritime regulations, all commercial freight vessels operating within the Obsidian Strait are required to feature double-layered hulls. Furthermore, any vessel featuring a double-layered hull incurs a maintenance cost that is significantly higher than that of a standard single-hulled ship. According to recent shipping logs, most of the vessels currently operating within the Obsidian Strait are commercial freight vessels.

If all of the statements above are true, which one of the following can be logically inferred?

Show answer & explanation

Answer: Most of the vessels currently operating within the Obsidian Strait incur a maintenance cost that is significantly higher than that of a standard single-hulled ship.

Answer

Most of the vessels currently operating within the Obsidian Strait incur a maintenance cost that is significantly higher than that of a standard single-hulled ship.
The stimulus establishes a formal logic chain: all commercial freight vessels in the Obsidian Strait must have double-layered hulls, and all vessels with double-layered hulls incur higher maintenance costs. By combining these premises, we can deduce that all commercial freight vessels in the Obsidian Strait incur higher maintenance costs. Furthermore, the text establishes that most of the vessels currently operating in the Strait are commercial freight vessels. If most of the vessels in the Strait belong to a category that universally incurs higher maintenance costs, it must logically follow that most vessels in the Strait incur higher maintenance costs.

Step-by-Step Solution

1
Analyze the conditional statements provided in the stimulus.
Premise 1: If a commercial freight vessel operates in the Obsidian Strait, it has a double-layered hull. Premise 2: If a vessel has a double-layered hull, it has higher maintenance costs.
To establish the formal logical rules governing the scenario.
2
Combine the conditional premises into a logical chain.
If a commercial freight vessel operates in the Obsidian Strait, it incurs higher maintenance costs.
Transitive property of formal logic (A implies B, and B implies C; therefore A implies C).
3
Apply the quantifier statement to the logical chain to determine the necessary inference.
Since 'most' vessels operating in the Strait are commercial freight vessels, and 'all' of those incur higher maintenance costs, it follows that 'most' vessels in the Strait must incur higher maintenance costs.
To deduce a final truth by applying a universal rule to a majority subgroup.

Key Concept

Combining formal conditional logic chains with quantifier statements ('most') to draw a valid necessary inference.
Estimated Time:1m 30s
Question 5Question →

Under the new environmental directives, any regional municipality that enacts a comprehensive water conservation protocol must either increase its baseline utility rates or secure a federal sustainability grant. A municipality is eligible to secure a federal sustainability grant only if it demonstrates a verifiable reduction in agricultural runoff. However, municipalities situated in the historically drought-prone Arid Basin region are strictly prohibited by state mandate from increasing their baseline utility rates. The municipality of Oakhaven, which is situated in the Arid Basin region, has recently enacted a comprehensive water conservation protocol.

Which of the following must be true on the basis of the statements above?

Show answer & explanation

Answer: Oakhaven has demonstrated a verifiable reduction in agricultural runoff.

Answer

The correct inference is that Oakhaven has demonstrated a verifiable reduction in agricultural runoff.
The correct answer accurately synthesizes the conditional statements provided in the stimulus. Because Oakhaven enacted the protocol, it is required to either increase its utility rates or secure a grant. Since state law prohibits Arid Basin municipalities from increasing rates, Oakhaven is left with only one option: securing the grant. Securing the grant inherently requires a verifiable reduction in agricultural runoff, meaning Oakhaven must have met this requirement.

Step-by-Step Solution

1
Map the first conditional rule.
Enact protocol → Increase rates OR Secure grant.
To establish the required consequences for any municipality enacting the protocol.
2
Map the second conditional rule regarding grants.
Secure grant → Demonstrate reduction in runoff.
To identify the necessary condition for receiving a federal grant.
3
Apply the geographic constraint to Oakhaven.
Oakhaven is in the Arid Basin, so it cannot increase its baseline utility rates.
To eliminate one of the two possible outcomes of enacting the protocol.
4
Chain the logic together for Oakhaven.
Oakhaven enacted the protocol, but cannot increase rates. Therefore, it must secure a grant. To secure a grant, it must demonstrate a reduction in runoff.
To derive the final valid inference that must be true.

Key Concept

Chaining Conditional Statements and Eliminating Alternatives
Question 6Question →

Under the revised corporate governance code, a board of directors can legally dismiss a chief executive officer only if the board achieves a supermajority vote. Furthermore, a supermajority vote is possible only when at least one independent director concurs with the board's executive directors. According to a recent audit, most companies in the Capstone Investment portfolio have boards consisting entirely of executive directors. However, any company in the Capstone Investment portfolio that has restated its quarterly earnings this year has legally dismissed its chief executive officer.

Which of the following logically follows from the information above?

Show answer & explanation

Answer: Most companies in the Capstone Investment portfolio have not restated their quarterly earnings this year.

Answer

Most companies in the Capstone Investment portfolio have not restated their quarterly earnings this year.
The correct answer accurately combines the stimulus's formal logic chain with its central quantifier. The text establishes that restating earnings requires dismissing a CEO, and dismissing a CEO requires an independent director on the board. Therefore, any company that restates earnings must have an independent director (Restating Earnings -> Independent Director). Because we are told that 'most' Capstone Investment companies lack independent directors (their boards are 'entirely' executive), we can securely apply the contrapositive: most of these companies lack a necessary condition for restating earnings, and therefore, most have not restated their earnings.

Step-by-Step Solution

1
Map the conditional relationships provided in the first two sentences.
Dismissing a CEO requires a supermajority (Dismiss CEO -> Supermajority). A supermajority requires an independent director (Supermajority -> Independent Director).
Establishing the formal logic chain allows us to identify necessary conditions. Transitivity means: Dismiss CEO -> Independent Director.
2
Map the conditional relationship in the final sentence.
Restating earnings requires dismissing the CEO (Restate Earnings -> Dismiss CEO).
Connecting this to our previous chain gives us the full logical sequence: Restate Earnings -> Dismiss CEO -> Independent Director.
3
Apply the quantifier provided in the third sentence to the full conditional chain.
Most Capstone companies have boards entirely consisting of executive directors, meaning they lack an independent director. By contrapositive (~Independent Director -> ~Dismiss CEO -> ~Restate Earnings), most Capstone companies cannot have restated their earnings.
If a necessary condition (Independent Director) is missing for the majority of a group, then the sufficient conditions (Dismissing CEO, Restating Earnings) must also be absent for the majority of that group.

Key Concept

Chaining Conditional Statements with Quantifiers
Question 7Question →

A corporation cannot be listed on the Apex Exchange unless it has undergone a comprehensive environmental audit. Only corporations that employ a dedicated sustainability officer can undergo a comprehensive environmental audit. No corporation that primarily manufactures synthetic plastics employs a dedicated sustainability officer. Furthermore, any corporation that qualifies for a municipal tax abatement either primarily manufactures synthetic plastics or fails to generate over ten million dollars in annual revenue.

Based on the information provided, any corporation listed on the Apex Exchange that qualifies for a municipal tax abatement fails to generate over ten million dollars in annual revenue.

Show answer & explanation

Answer: True

Answer

The statement is logically valid and therefore True.
The correct answer is True. By diagramming the premises, we derive the chain: Listed → Audit → Officer → Not Plastics. Therefore, any listed corporation cannot manufacture synthetic plastics. The stimulus also establishes: Abatement → Plastics OR Not Over 10M Revenue. If a corporation is both listed AND receives the abatement, it is automatically disqualified from the 'Plastics' option due to being listed. Therefore, by disjunctive syllogism, it must fulfill the only remaining option: failing to generate over ten million dollars in annual revenue. The statement is an undeniably valid deduction.

Step-by-Step Solution

1
Translate the first three premises into conditional logic chains.
Listed → Audit; Audit → Officer; Plastics → ~Officer.
Identifying the formal logic relationships is required to find connections between the terms.
2
Connect the individual conditions into a single transitive chain.
Listed → Audit → Officer → ~Plastics.
Combining the rules reveals the ultimate constraint placed on any corporation listed on the Apex Exchange.
3
Diagram the disjunctive premise concerning the tax abatement.
Abatement → (Plastics OR ~Over 10M Revenue).
The 'either...or' language establishes a necessary condition containing two distinct possibilities.
4
Apply the derived rules to the specific group mentioned in the statement: corporations that are both listed and receive the abatement.
Because they are listed, they must be ~Plastics. Because they receive the abatement, they must be (Plastics OR ~Over 10M Revenue).
To evaluate the statement, we must synthesize the conditions applying to this intersection of groups.
5
Utilize disjunctive syllogism to resolve the abatement condition.
Since the 'Plastics' option is impossible for listed corporations, the only remaining valid condition is '~Over 10M Revenue'.
When a necessary condition requires at least one of two options to be true, proving one false guarantees the other must be true.

Key Concept

Formal logic synthesis using transitive conditional chains, contrapositives, and disjunctive syllogism.
Question 8Question →

According to the regional agricultural board, any farmer in the valley who cultivates heirloom tomatoes must implement comprehensive pest-management protocols. Any farmer who implements comprehensive pest-management protocols is automatically disqualified from receiving the basic organic certification. Furthermore, recent records show that at least some farmers who received the newly established sustainability grant also qualified for the basic organic certification.

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

Show answer & explanation

Answer: At least some farmers who received the newly established sustainability grant do not cultivate heirloom tomatoes.

Answer

At least some farmers who received the newly established sustainability grant do not cultivate heirloom tomatoes.
The correct answer accurately combines the logical premises. First, we know that growing heirloom tomatoes requires comprehensive pest-management, which in turn prevents a farmer from getting the basic organic certification. Therefore, no farmer who grows heirloom tomatoes gets the certification. We also know that some farmers with the sustainability grant did get the certification. Because they got the certification, they cannot be farmers who grow heirloom tomatoes. Thus, at least some farmers with the grant do not cultivate heirloom tomatoes.

Step-by-Step Solution

1
Diagram the first conditional statement.
Cultivates heirloom tomatoes (HT) -> Implement comprehensive pest-management (CPM).
To establish the baseline logical relationship for farmers growing heirloom tomatoes.
2
Diagram the second conditional statement and connect it to the first.
CPM -> Disqualified from basic organic certification (~BOC). Therefore, HT -> ~BOC.
Transitive property of conditional logic allows chaining statements with a shared term.
3
Diagram the third statement involving the quantifier 'some'.
Sustainability grant (SG) <-Some-> Qualifies for basic organic certification (BOC).
To integrate the quantified factual premise with the conditional chain.
4
Combine the 'some' statement with the contrapositive of the conditional chain.
Since SG <-Some-> BOC, and the contrapositive of the chain is BOC -> ~HT, it must be true that SG <-Some-> ~HT.
When 'Some A are B' and 'All B are C', it logically follows that 'Some A are C'.

Key Concept

Chaining Conditional Statements with Quantifiers
Question 9Question →

Any infrastructure project that utilizes synthetic materials must pass a secondary safety inspection. Furthermore, no project that passes a secondary safety inspection is completed within its original budget. Every project managed by the transit authority utilizes synthetic materials, and some projects managed by the transit authority are funded by state bonds. Finally, only projects that incorporate sustainable design are funded by state bonds.

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

Show answer & explanation

Answer: At least one project that incorporates sustainable design fails to be completed within its original budget.

Answer

The correct answer states that at least one project that incorporates sustainable design fails to be completed within its original budget.
The correct option is provable by connecting multiple formal premises. We know that some transit authority projects are funded by state bonds, and because ONLY projects with sustainable design receive state bonds, those specific transit projects must incorporate sustainable design. Furthermore, every transit project utilizes synthetic materials and thus passes a secondary safety inspection, which guarantees they are not completed within budget. Therefore, there exists at least one project (the state-bond-funded transit project) that incorporates sustainable design and is not completed within its original budget.

Step-by-Step Solution

1
Map the universal conditional chain starting from the transit authority.
Transit Authority -> Synthetic Materials -> Secondary Safety Inspection -> NOT Completed Within Budget.
This establishes that every single project managed by the transit authority ultimately fails to be completed within its original budget.
2
Translate the 'only' statement into a standard conditional.
The phrase 'only projects that incorporate sustainable design are funded by state bonds' translates to: State Bonds -> Sustainable Design.
The word 'only' modifies the necessary condition, meaning sustainable design is required for state bond funding.
3
Link the 'some' statement to the established conditions.
We are told: Transit Authority <-some-> State Bonds. Using the translation from Step 2, this means: Transit Authority <-some-> Sustainable Design.
Because some transit projects are funded by state bonds, and all state bond projects have sustainable design, at least some transit projects must have sustainable design.
4
Synthesize the overlapping groups to find the final necessary truth.
From Step 3, there is an intersecting group of projects that are both Transit Authority AND Sustainable Design. From Step 1, ALL Transit Authority projects go over budget. Therefore, this intersecting group of Sustainable Design projects must also go over budget.
Any characteristic that applies to ALL transit authority projects must also apply to the subset of transit authority projects that incorporate sustainable design.

Key Concept

Must Be True Questions
Question 10Question →

Under recently enacted financial statutory guidelines, every institution acting as a primary market maker is subject to strict liquidity stress tests. Any institution subject to strict liquidity stress tests is required to hold a minimum reserve of sovereign treasury bonds. Furthermore, no institution that is required to hold a minimum reserve of sovereign treasury bonds is permitted to engage in unregulated proprietary trading. Most institutions that act as primary market makers are currently categorized by regulators as systemically important. However, it is a matter of public record that some institutions categorized as systemically important do engage in unregulated proprietary trading.

Based on the information provided above, which of the following must be true?

Show answer & explanation

Answer: At least one institution categorized as systemically important is not permitted to engage in unregulated proprietary trading.

Answer

At least one institution categorized as systemically important is not permitted to engage in unregulated proprietary trading.
The correct answer synthesizes the conditional chain with a quantifier statement to yield a mathematically certain deduction. The stimulus establishes that all primary market makers must take stress tests, which requires holding treasury bonds, which in turn forbids unregulated proprietary trading. Therefore, all primary market makers are forbidden from unregulated proprietary trading. The text also states that most primary market makers are systemically important. Since more than half of primary market makers are systemically important, and absolutely every primary market maker is forbidden from proprietary trading, those specific overlapping institutions must be systemically important and forbidden from proprietary trading. This guarantees that at least one systemically important institution is not permitted to engage in unregulated proprietary trading.

Step-by-Step Solution

1
Map the conditional rules applying to primary market makers (PMM).
PMM → Strict Liquidity Stress Tests (SLST) → Minimum Reserve of Treasury Bonds (MRTB) → NOT permitted to engage in Unregulated Proprietary Trading (~UPT).
To establish the full chain of mandatory constraints acting upon any institution acting as a primary market maker.
2
Simplify the conditional chain to connect the first sufficient condition to the final necessary condition.
If an institution is a primary market maker, it is categorically forbidden from engaging in unregulated proprietary trading (PMM → ~UPT).
To make the overarching relationship between the start and end variables explicit for easier synthesis with the quantifier statements.
3
Integrate the 'most' quantifier statement with the deduced conditional rule.
We are given that 'Most PMMs are Systemically Important (SI)'. Since we know absolutely all PMMs are forbidden from UPT (PMM → ~UPT), it follows that those specific PMMs that are systemically important are also forbidden from UPT.
Because the 'most' quantifier guarantees an overlap of at least one institution (more than half), and the universal rule applies to all PMMs within that overlap.
4
Formulate the final necessary deduction based on the intersection established.
There must be at least one institution that is both systemically important and forbidden from engaging in unregulated proprietary trading.
This exactly matches the logical deduction that 'some systemically important institutions are not permitted to engage in unregulated proprietary trading', which is 100% provable from the text.

Key Concept

Synthesizing conditional logic chains with existential and majoritarian quantifiers.
Question 11Question →

According to the city's updated zoning laws, every new building constructed in the downtown district must include a green roof. Furthermore, any building that includes a green roof is automatically eligible for a municipal tax discount. The Apex Tower is a new building that was recently constructed in the downtown district.

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

Select all that apply

Show answer & explanation

Answer: The Apex Tower is eligible for a municipal tax discount.; Any new building constructed in the downtown district is eligible for a municipal tax discount.

Answer

The statements that must be true are that the Apex Tower is eligible for a municipal tax discount, and that any new building constructed in the downtown district is eligible for a municipal tax discount.
The stimulus establishes a chain of conditional logic: New Downtown Building -> Green Roof -> Tax Discount. The correct statements perfectly track this logic by correctly linking the first condition to the last (any new downtown building gets the discount) and correctly applying it to the specific example of the Apex Tower.

Step-by-Step Solution

1
Analyze the first conditional premise.
If a building is new and in the downtown district, then it must include a green roof.
To establish the initial condition required by the zoning laws.
2
Analyze the second conditional premise and chain it to the first.
If a building includes a green roof, then it is eligible for a tax discount. Therefore, if a building is new and in the downtown district, it is eligible for a tax discount.
To form a logical chain that connects the building's location and age directly to the tax discount.
3
Apply the factual premise to the logical chain.
The Apex Tower is a new building in the downtown district, so it must have a green roof, meaning it is eligible for a tax discount.
To determine the necessary outcomes for the specific subject mentioned in the stimulus.

Key Concept

Logical chaining of conditional statements and application to specific cases.
Question 12Question →

Under the new municipal zoning code, any neighborhood designated as a Transit-Oriented District must allow for high-density residential development. Furthermore, a neighborhood cannot be designated as a Transit-Oriented District unless it currently contains at least one active light-rail station. The code also specifies that any neighborhood allowing for high-density residential development is required to allocate at least 15 percent of its new housing units for low-income residents. The Historic Southside neighborhood recently had its only active light-rail station permanently decommissioned.

Which of the following must be true on the basis of the statements above?

Show answer & explanation

Answer: Any neighborhood that is not required to allocate at least 15 percent of its new housing units for low-income residents cannot be designated as a Transit-Oriented District.

Answer

Any neighborhood that is not required to allocate at least 15 percent of its new housing units for low-income residents cannot be designated as a Transit-Oriented District.
The stimulus provides two key conditional statements that can be connected: 'Transit-Oriented District -> high-density residential' and 'high-density residential -> 15 percent low-income'. Linking these statements creates the deduction: 'Transit-Oriented District -> 15 percent low-income'. The correct answer is the logical contrapositive of this deduction: if a neighborhood is not required to allocate 15 percent for low-income housing, it cannot be a Transit-Oriented District.

Step-by-Step Solution

1
Diagram the conditional statements provided in the stimulus.
1) TOD -> HDR
2) TOD -> ALRS (Contrapositive: ~ALRS -> ~TOD)
3) HDR -> 15% LI
4) Historic Southside -> ~ALRS
Translating text into formal logic makes it easier to track relationships and avoid traps.
2
Chain the conditional statements together where possible.
Combining premises 1 and 3 (TOD -> HDR and HDR -> 15% LI) yields the logical chain: TOD -> HDR -> 15% LI. Therefore, TOD -> 15% LI.
Connecting premises reveals hidden logical inferences that must be true.
3
Form the contrapositive of the new logical chain.
The contrapositive of (TOD -> 15% LI) is (~15% LI -> ~TOD).
Correct answers in 'Must Be True' questions are frequently the contrapositive of a chained inference.
4
Evaluate the information about the Historic Southside neighborhood.
Since Historic Southside has no active light-rail station (~ALRS), it cannot be a TOD (~TOD). No further valid deductions can be made about its high-density development or low-income housing.
This confirms that options making claims about Historic Southside's high-density development are likely testing illegal negation.

Key Concept

Conditional Logic Chaining and Contrapositives
Question 13Question →

All amphibians that inhabit the alpine tundra rely on the nectar of the *Saxifraga* plant during their larval stage. Most species that rely on *Saxifraga* nectar during their larval stage are capable of surviving sub-zero temperatures. Furthermore, any species capable of surviving sub-zero temperatures possesses elevated levels of blood glucose.

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

Select all that apply

Show answer & explanation

Answer: Most species that rely on the nectar of the *Saxifraga* plant during their larval stage possess elevated levels of blood glucose.; Any species that does not possess elevated levels of blood glucose is not capable of surviving sub-zero temperatures.

Answer

The correct statements are that most species relying on the nectar possess elevated blood glucose, and that any species lacking elevated blood glucose cannot survive sub-zero temperatures.
The correct statements are derived from valid logical rules. One is proven by chaining a 'most' premise directly into an 'all' premise, establishing that most nectar-reliant species possess elevated blood glucose. The other is proven by correctly forming the contrapositive of the final premise, establishing that lacking elevated blood glucose guarantees a species cannot survive sub-zero temperatures.

Step-by-Step Solution

1
Diagram the formal logic presented in the stimulus.
1. Alpine Tundra Amphibians -> Rely on Saxifraga Nectar. 2. Rely on Saxifraga Nectar -[most]-> Survive Sub-zero Temperatures. 3. Survive Sub-zero Temperatures -> Elevated Blood Glucose.
Mapping conditional and quantified statements clarifies the relationships and allowable deductions.
2
Evaluate combined logical inferences based on the diagram.
By linking statements 2 and 3, we can deduce that since most nectar-reliant species survive sub-zero temperatures, and ALL species that survive sub-zero temperatures possess elevated blood glucose, most nectar-reliant species must possess elevated blood glucose.
Chaining a 'most' statement with an 'all' statement yields a valid 'most' deduction.
3
Form contrapositives of the absolute conditional statements.
Contrapositive of 1: Do not rely on Saxifraga nectar -> Not an Alpine Tundra Amphibian. Contrapositive of 3: No elevated blood glucose -> Cannot survive sub-zero temperatures.
Contrapositives are always logically equivalent to the original conditional statements and are frequently tested in Must Be True questions.
4
Evaluate the given choices against the deduced truths to identify the correct answers.
The choice stating most nectar-reliant species possess elevated blood glucose matches our chained inference. The choice stating species without elevated blood glucose cannot survive sub-zero temperatures matches the contrapositive of statement 3.
Comparing choices to mathematically proven deductions ensures we select only the statements that are 100% supported by the text.

Key Concept

Chaining formal logic and forming contrapositives to determine valid deductions.
Question 14Question →

According to the planetary geology archives:

- Every meteorite classified as a Type C chondrite contains elevated levels of iridium.
- Any meteorite containing elevated levels of iridium is designated as a Class-1 research priority by the Astromaterials Board.
- No meteorite recovered from the Antarctic glacial surface is designated as a Class-1 research priority unless it is a newly discovered fragment that has not been previously cataloged.
- Some meteorites classified as Type C chondrites were recovered from the Antarctic glacial surface, and most of these are exceptionally well-preserved.

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

Select all that apply

Show answer & explanation

Answer: Every Type C chondrite recovered from the Antarctic glacial surface is a newly discovered fragment.; At least some exceptionally well-preserved meteorites contain elevated levels of iridium.

Answer

The correct statements are that every Type C chondrite recovered from the Antarctic glacial surface is a newly discovered fragment, and that at least some exceptionally well-preserved meteorites contain elevated levels of iridium.
Based on the rules, any Type C chondrite is a Class-1 priority. Therefore, any Type C chondrite from Antarctica is both from Antarctica and a Class-1 priority, which means it must be a newly discovered fragment. Additionally, because some Type C chondrites from Antarctica exist, and most of them are well-preserved, there is at least one well-preserved Type C chondrite. Since it is Type C, it must contain elevated levels of iridium.

Step-by-Step Solution

1
Map the universal conditional statements.
Type C -> Iridium -> Class-1 Priority. (Antarctic AND Class-1) -> Newly Discovered.
This establishes the strict logical chains required to evaluate absolute statements.
2
Analyze the quantified statements ('some' and 'most').
There exists a group of meteorites that are Type C and Antarctic. Most of this specific group are well-preserved.
Quantifiers provide the existential facts that interact with the universal rules.
3
Combine the existential facts with the universal chains.
The (Type C + Antarctic) meteorites must be Class-1 (since they are Type C). Because they are (Class-1 + Antarctic), they must be newly discovered. Thus, all (Type C + Antarctic) are newly discovered.
This guarantees the truth of the statement regarding Type C chondrites from Antarctica.
4
Derive inferences from the 'most' statement.
Since 'most' of the (Type C + Antarctic) group are well-preserved, at least one such meteorite exists. Because this meteorite is Type C, it contains iridium. Therefore, some well-preserved meteorites contain iridium.
This guarantees the truth of the statement regarding well-preserved meteorites.

Key Concept

Chaining Conditional Statements and Quantifier Logic
Question 15Question →

According to the recent interstellar survey of the Orionis sector:

All rogue planets detected in the outer ring possess a dense atmosphere of frozen methane. Any planet with a dense atmosphere of frozen methane reflects less than 5% of incident starlight. Most rogue planets detected in the outer ring have a core temperature below -200 degrees Celsius. Furthermore, no planet that reflects less than 5% of incident starlight is currently targeted for deep-core drilling.

Based strictly on the information above, which of the following statements must be true? (Select all valid deductions)

Select all that apply

Show answer & explanation

Answer: Every rogue planet detected in the outer ring is currently excluded from deep-core drilling targets.; Any planet that is targeted for deep-core drilling reflects 5% or more of incident starlight.

Answer

The correct deductions are that every rogue planet in the outer ring is excluded from deep-core drilling targets, and that any planet targeted for deep-core drilling reflects 5% or more of incident starlight.
The valid deductions rely on strict conditional logic. By chaining the premises, we find that being an outer ring rogue planet guarantees a frozen methane atmosphere, which guarantees reflecting less than 5% of starlight, which in turn guarantees exclusion from drilling targets. Therefore, any such rogue planet is excluded. Additionally, the contrapositive of the final premise dictates that if a planet IS targeted for drilling, it cannot reflect less than 5% of starlight (meaning it must reflect 5% or more).

Step-by-Step Solution

1
Map the primary conditional chain provided in the stimulus.
Rogue Planet in Outer Ring (RP) -> Frozen Methane (FM) -> Reflects < 5% Light (<5L).
This establishes the basic transitive relationship from the first two premises.
2
Add the final conditional premise to the chain.
RP -> FM -> <5L -> NOT Targeted for Drilling (~TD).
The final premise introduces a negative necessary condition based on the light reflection.
3
Evaluate the beginning and end of the completed conditional chain.
RP -> ~TD (If a planet is a rogue planet in the outer ring, it is not targeted for drilling).
This proves that the statement claiming every rogue planet in the outer ring is excluded from drilling targets must be logically true.
4
Form the contrapositive of the relationship between light reflection and drilling targets.
The original rule is: If <5L -> ~TD. The contrapositive is: If TD -> NOT <5L (meaning 5% or more).
This proves that the statement claiming any targeted planet reflects 5% or more starlight must be logically true.

Key Concept

Transitive conditional reasoning and contrapositive formation
Question 16Question →

Biologists studying deep-sea ecosystems have found that all species of tube worm native to the Abyssal Ridge rely exclusively on chemosynthetic bacteria for energy. Furthermore, any organism that relies exclusively on chemosynthetic bacteria for energy lacks a functional digestive tract. Recently, researchers have also documented that some species of tube worm native to the Abyssal Ridge form symbiotic relationships with bioluminescent fungi.

Which of the following must be true based on the statements above?

Show answer & explanation

Answer: At least some organisms that form symbiotic relationships with bioluminescent fungi lack a functional digestive tract.

Answer

At least some organisms that form symbiotic relationships with bioluminescent fungi lack a functional digestive tract.
The correct answer accurately synthesizes the premises. The stimulus establishes a chain: all Abyssal Ridge tube worms rely on chemosynthetic bacteria, and anything relying on chemosynthetic bacteria lacks a functional digestive tract. This means every Abyssal Ridge tube worm lacks a functional digestive tract. We are also told that some Abyssal Ridge tube worms form symbiotic relationships with bioluminescent fungi. These specific tube worms, therefore, have both traits: they have the symbiotic relationship AND they lack a functional digestive tract. Thus, it must be true that at least some organisms with this symbiotic relationship lack a functional digestive tract.

Step-by-Step Solution

1
Identify the conditional statements (the 'all' and 'any' premises).
1. Native to Abyssal Ridge -> Rely on chemosynthetic bacteria. 2. Rely on chemosynthetic bacteria -> Lacks functional digestive tract.
Mapping absolute conditional relationships is the first step in deduction.
2
Chain the conditional statements together.
Native to Abyssal Ridge -> Lacks functional digestive tract.
Since relying on chemosynthetic bacteria is the necessary condition in the first premise and sufficient in the second, they can be linked.
3
Incorporate the overlapping 'some' statement.
Some species native to the Abyssal Ridge form symbiotic relationships with bioluminescent fungi.
Quantifier statements ('some') provide specific instances where the general conditional rules apply.
4
Combine the 'some' statement with the chained conditional rule.
Because those 'some' tube worms are native to the Abyssal Ridge, they must lack a functional digestive tract. Therefore, some organisms with bioluminescent fungi relationships lack a functional digestive tract.
Whatever characteristics apply to all members of a group must also apply to any specific subset of that group.

Key Concept

Must Be True Questions
Estimated Time:1m 30s
Question 17Question →

An analysis of international sovereign wealth funds (SWFs) reveals that any SWF prioritizing renewable energy investments divests entirely from fossil fuel derivatives. Furthermore, every SWF that divests entirely from fossil fuel derivatives reports a lower short-term yield than the market average. Currently, most SWFs managed by independent trustee boards prioritize renewable energy investments. Interestingly, some SWFs that report a lower short-term yield than the market average nonetheless maintain an AAA institutional credit rating. No SWF that maintains an AAA institutional credit rating is subject to mandatory quarterly parliamentary audits.

Which one of the following conclusions can be properly drawn from the information above?

Show answer & explanation

Answer: Most sovereign wealth funds managed by independent trustee boards report a lower short-term yield than the market average.

Answer

Most sovereign wealth funds managed by independent trustee boards report a lower short-term yield than the market average.
This conclusion is deductively valid by combining a 'most' premise with a chain of universal premises. The stimulus establishes that most independent boards prioritize renewables, and every fund that prioritizes renewables ultimately reports a lower yield. If most of group X is in group Y, and all of group Y is in group Z, it logically guarantees that most of group X is in group Z.

Step-by-Step Solution

1
Map the formal logic relationships provided in the stimulus.
1. Prioritize Renewable -> Divest Fossil Fuels. 2. Divest Fossil Fuels -> Lower Yield. 3. Independent Board -[most]-> Prioritize Renewable. 4. Lower Yield -[some]- AAA Rating. 5. AAA Rating -> NO Parliamentary Audits.
Tracking conditional statements and quantifiers (all/any/every, most, some) is essential for evaluating valid deductions.
2
Chain the absolute (universal) conditional statements together.
Since Prioritize Renewable -> Divest Fossil Fuels, and Divest Fossil Fuels -> Lower Yield, we can combine these to form a longer chain: Prioritize Renewable -> Lower Yield.
Transitive properties of formal logic allow us to connect conditional chains to find implicit universal truths.
3
Combine the universal chain with the 'most' quantifier statement.
We know Independent Board -[most]-> Prioritize Renewable. We also know Prioritize Renewable -> Lower Yield. Therefore, we can deduce: Independent Board -[most]-> Lower Yield.
In formal logic, 'Most A are B' combined with 'All B are C' guarantees that 'Most A are C'.
4
Evaluate the answer choices against the deduced relationships.
The deduction 'Independent Board -[most]-> Lower Yield' perfectly matches one of the options. The other choices feature logical fallacies such as illegal reversals, illegal negations, or reliance on outside information.
A valid inference must be 100% provable from the text without any external assumptions.

Key Concept

Chaining Quantifiers and Conditionals (Most A are B + All B are C = Most A are C)
Question 18Question →

According to the revised aviation safety guidelines, any commercial aircraft operating in polar regions must be equipped with dual-band thermal radar. Furthermore, any aircraft equipped with dual-band thermal radar undergoes rigorous cryogenic calibration every six months. Skyways Airlines recently announced that its entire fleet of cargo planes undergoes rigorous cryogenic calibration every six months.

Statement: Based on the information provided, it must be true that Skyways Airlines operates its cargo planes in polar regions.

Show answer & explanation

Answer: False

Answer

False. The proposed statement is not a valid deduction because it relies on an illegal reversal of the conditional premises.
The conclusion drawn in the statement relies on a classic formal logic error. The premises establish a one-way chain: operating in polar regions requires cryogenic calibration. We are told Skyways Airlines undergoes cryogenic calibration. However, we cannot read a conditional statement backward. It is entirely possible that aircraft operating in other regions also undergo cryogenic calibration for different reasons. Thus, it is not logically required that Skyways operates in polar regions, making the 'must be true' claim false.

Step-by-Step Solution

1
Diagram the first conditional premise.
Polar Region → Dual-Band Thermal Radar.
The word 'any' introduces a sufficient condition. If an aircraft operates in polar regions, it is logically required to have the radar.
2
Diagram the second conditional premise.
Dual-Band Thermal Radar → Cryogenic Calibration.
Again, 'any' indicates that having the radar is sufficient to guarantee the aircraft undergoes the calibration.
3
Combine the conditional premises into a chain.
Polar Region → Dual-Band Thermal Radar → Cryogenic Calibration.
Transitive logic allows us to connect the common term to deduce the overarching rule: Polar Region → Cryogenic Calibration.
4
Evaluate the new factual information about Skyways Airlines against the established conditional chain.
We know Skyways Cargo Planes → Cryogenic Calibration. This matches the necessary condition of our chain.
To determine what 'must be true', we must see if the factual premise forces a logical deduction.
5
Determine if the statement is a logically valid deduction.
The statement concludes that Skyways operates in polar regions. This deduction is invalid.
Affirming the necessary condition (calibration) does not prove the sufficient condition (polar operation). Therefore, it does not have to be true that Skyways operates in polar regions.

Key Concept

Evaluating conditional reasoning chains and identifying illegal reversals (affirming the consequent).
Question 19Question →

All atmospheric circulation models that accurately predict jet stream anomalies incorporate data on sudden stratospheric warmings (SSWs). Furthermore, any circulation model that incorporates data on SSWs must account for mesospheric wind shear, unless it relies strictly on historical tropospheric temperature gradients. Interestingly, while most atmospheric circulation models developed by the Coriolis Institute incorporate data on SSWs, none of the models developed by the Coriolis Institute account for mesospheric wind shear.

Based on the statements above, which one of the following must also be true?

Show answer & explanation

Answer: Most atmospheric circulation models developed by the Coriolis Institute rely strictly on historical tropospheric temperature gradients.

Answer

Most atmospheric circulation models developed by the Coriolis Institute rely strictly on historical tropospheric temperature gradients.
The stimulus establishes that if a model incorporates SSW data, it must do at least one of two things: account for mesospheric wind shear or rely strictly on historical tropospheric temperature gradients. We are told that most Coriolis Institute models incorporate SSW data, which means this 'majority group' of models is subject to the rule. Since we are also told that NO Coriolis models account for mesospheric wind shear, this majority group cannot fulfill that half of the requirement. Therefore, to satisfy the rule, every model in this majority group must rely strictly on historical tropospheric temperature gradients. Thus, it must be true that most Coriolis models rely strictly on historical gradients.

Step-by-Step Solution

1
Translate the first premise into formal logic.
Accurately predict jet stream -> Incorporate SSW data.
This establishes the necessary condition for accurate jet stream prediction.
2
Translate the second premise (the 'unless' statement) into formal logic.
Incorporate SSW data -> Account for mesospheric wind shear OR Rely strictly on historical gradients.
In conditional logic, 'unless' indicates a necessary alternative; if the first condition isn't met, the second must be.
3
Map the specific characteristics of Coriolis Institute models.
Most Coriolis models -> Incorporate SSW data. No Coriolis models -> Account for mesospheric wind shear.
This applies the general rules to a specific subset of models mentioned in the stimulus.
4
Synthesize the rules to deduce the inevitable conclusion.
The majority of Coriolis models that incorporate SSW data MUST rely strictly on historical gradients, because they cannot fulfill the other half of the 'unless' condition.
Combining a disjunctive necessary condition (A or B) with the negation of one element (not A) forces the remaining element (must be B) to be true.

Key Concept

Conditional Logic with Quantifiers and 'Unless' Formulation
Question 20Question →

If a frog species inhabits the upper canopy of the rainforest, it must have specialized toe pads. Any frog species that has specialized toe pads is capable of adhering to wet leaves. The blue-legged tree frog is a frog species that inhabits the upper canopy of the rainforest.

Which of the following must be true on the basis of the statements above?

Show answer & explanation

Answer: The blue-legged tree frog is capable of adhering to wet leaves.

Answer

The blue-legged tree frog is capable of adhering to wet leaves.
The stimulus provides a direct chain of conditional reasoning: Canopy → Toe Pads → Adhere to Wet Leaves. Since we are explicitly told that the blue-legged tree frog is a canopy species, it triggers this entire chain, guaranteeing that it can adhere to wet leaves.

Step-by-Step Solution

1
Identify the conditional relationships presented as facts in the stimulus.
Inhabits upper canopy → Has specialized toe pads. Has specialized toe pads → Capable of adhering to wet leaves.
Mapping the conditional logic is the most reliable way to find deductions that are mathematically certain.
2
Chain the conditional statements together using their shared term.
Inhabits upper canopy → Capable of adhering to wet leaves.
The transitive property of logic allows us to connect the first sufficient condition directly to the final necessary condition.
3
Apply the specific factual premise to the logical chain.
Because the blue-legged tree frog satisfies the sufficient condition (inhabits upper canopy), the necessary condition (capable of adhering to wet leaves) must apply to it.
This guarantees a 100% provable inference, which is required for 'Must Be True' questions.

Key Concept

Must Be True Questions
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