Examkin

Sufficient Assumption

31 questions

All types31Multiple choice17True / False8Matching6
Question 1Question →

Legal Scholar: A statute cannot be considered legitimately authoritative unless it reflects the deeply held moral convictions of the populace it governs. Reflecting such convictions necessitates that the legislative body drafting the statute be completely insulated from the financial influence of special interest groups. The recently enacted Corporate Accountability Act was drafted by a committee heavily financed by the very industries it seeks to regulate. Therefore, the Act will inevitably face widespread civil disobedience.

Which one of the following, if assumed, enables the legal scholar's conclusion to be properly drawn?

Show answer & explanation

Answer: No statute can avoid facing widespread civil disobedience unless it is legitimately authoritative.

Answer

The correct answer is the statement indicating that no statute can avoid facing widespread civil disobedience unless it is legitimately authoritative.
The argument's premises establish a conditional chain: if a statute is legitimately authoritative, it must reflect moral convictions, which in turn requires insulation from financial influence. Because the Corporate Accountability Act was drafted by a financially influenced committee, it fails the necessary condition for insulation. By applying the contrapositive, the Act cannot be legitimately authoritative. The conclusion then abruptly claims the Act will face widespread civil disobedience. To logically guarantee this conclusion, we need an assumption bridging the gap: if a statute is not legitimately authoritative, it will face civil disobedience. The correct option provides exactly this bridge using 'unless' conditional phrasing: 'cannot avoid civil disobedience' unless 'legitimately authoritative' translates to 'If it is not legitimately authoritative, it will face civil disobedience'.

Step-by-Step Solution

1
Map the conditional statements in the premises.
Legitimately Authoritative (LA) → Reflects Moral Convictions (RMC) → Insulated from Financial Influence (IFI).
To understand the chain of necessary conditions established by the legal scholar.
2
Apply the factual premise to the conditional chain.
The Corporate Accountability Act (CAA) was drafted by a heavily financed committee, meaning it is not insulated (~IFI). By contrapositive (~IFI → ~RMC → ~LA), the CAA is not legitimately authoritative (~LA).
To determine what can be proven about the Corporate Accountability Act using only the provided evidence.
3
Identify the logical gap between the inferred evidence and the main conclusion.
We have proven the CAA is not legitimately authoritative (~LA). The conclusion claims the CAA will face widespread civil disobedience (WCD). The gap is: ~LA → WCD.
A sufficient assumption must completely bridge the gap between what is proven and what is concluded.
4
Evaluate the options to find the one that establishes the necessary conditional bridge (~LA → WCD).
The phrase 'No statute can avoid WCD unless LA' translates logically to 'If ~LA, then WCD'. This matches the gap perfectly.
To ensure the selected option provides 100% deductive certainty for the conclusion.

Key Concept

Sufficient Assumption in Conditional Logic Chains
Question 2Question →

Cognitive Scientist: The established academic definition of genuine creative insight dictates that any entity capable of such insight must be able to synthesize disparate conceptual frameworks without relying on pre-programmed heuristics. The newly developed neural architecture, Synapse-X, operates exclusively by applying pre-programmed heuristics to massive datasets. Nevertheless, Synapse-X recently generated a novel urban infrastructure model that human engineers universally acclaimed as highly innovative. Therefore, the established academic definition of genuine creative insight must be fundamentally flawed.

Which one of the following, if assumed, allows the cognitive scientist's conclusion to be properly drawn?

Show answer & explanation

Answer: Any entity that generates an urban infrastructure model acclaimed as highly innovative by human engineers is capable of genuine creative insight.

Answer

The assumption stating that any entity generating an acclaimed innovative urban infrastructure model is capable of genuine creative insight.
The correct answer bridges the logical gap between the premise and the conclusion. To prove the definition (Genuine Creative Insight requires NOT relying on heuristics) is flawed, we need a counterexample. The stimulus gives us Synapse-X, which relies on heuristics and generated an acclaimed model. By assuming that generating such a model guarantees Genuine Creative Insight, we prove Synapse-X has Genuine Creative Insight despite relying on heuristics. This creates a perfect counterexample, making the conclusion 100% logically valid.

Step-by-Step Solution

1
Deconstruct the established academic definition provided in the premise into formal logic.
Genuine Creative Insight (GCI) -> NOT relying on pre-programmed heuristics.
To understand the rule the argument claims is flawed, we must translate it into a formal conditional statement.
2
Identify the logical requirements needed to prove the argument's conclusion.
To definitively prove the definition is flawed, the argument must establish a counterexample: an entity that possesses GCI but DOES rely on pre-programmed heuristics.
A universal conditional rule is proven false only when an instance meets its sufficient condition but fails its necessary condition.
3
Analyze the evidence provided about the subject, Synapse-X.
Synapse-X relies exclusively on pre-programmed heuristics (meeting the necessary condition failure), and it generated a model acclaimed as highly innovative.
This establishes half of the counterexample. We know Synapse-X relies on heuristics. Now we need the missing link to prove it actually possesses GCI.
4
Identify the Sufficient Assumption that completes the logical chain.
We must link Synapse-X's action (generating the highly innovative model) to the required classification (Genuine Creative Insight).
If generating the innovative model guarantees GCI, then Synapse-X has GCI. This completes the counterexample and guarantees the conclusion is 100% valid.

Key Concept

To prove a universal conditional definition is flawed, an argument must establish a valid counterexample that meets the sufficient condition but fails the necessary condition. In sufficient assumption questions, the correct answer often provides the missing logical link to guarantee that such a counterexample exists.
Question 3Question →

Historian: No social movement can achieve lasting institutional change unless it secures the active support of political elites. Securing the active support of political elites, however, invariably requires a movement to demonstrate a willingness to engage in incremental policy compromises. The newly formed Vanguard Coalition is explicitly committed to the complete dismantling of the current political establishment. Therefore, the Vanguard Coalition will fail to achieve lasting institutional change.

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

Show answer & explanation

Answer: No movement that is explicitly committed to the complete dismantling of the current political establishment is willing to engage in incremental policy compromises.

Answer

The statement that no movement explicitly committed to the complete dismantling of the current political establishment is willing to engage in incremental policy compromises.
The argument relies on formal conditional logic. Lasting Change -> Elite Support -> Willingness to Compromise. To prove the Vanguard Coalition will not achieve lasting change, we must trigger the contrapositive: Not Willing to Compromise -> No Elite Support -> No Lasting Change. Since the only premise given about the Vanguard Coalition is that they are committed to dismantling the establishment, we must assume that this commitment guarantees an unwillingness to compromise. The correct answer provides exactly this required link.

Step-by-Step Solution

1
Identify the conclusion and the premises.
Conclusion: The Vanguard Coalition will not achieve lasting institutional change. Premises: Achieving lasting change requires elite support, and elite support requires a willingness to compromise. Fact: The Vanguard Coalition is committed to dismantling the establishment.
Deconstructing the argument structure is the first step in finding the logical gap.
2
Chain the conditional premises together to find the required condition for the conclusion.
Lasting Change -> Elite Support -> Willingness to Compromise. The contrapositive is: NOT Willing to Compromise -> NO Elite Support -> NO Lasting Change. To prove the conclusion for the Vanguard Coalition, we must prove they are NOT willing to compromise.
Understanding the deductive chain reveals exactly what necessary condition the Vanguard Coalition must fail.
3
Identify the missing link between the facts about the Vanguard Coalition and the required condition.
We know the Vanguard Coalition is committed to dismantling the establishment. We need to prove they are NOT willing to compromise. Therefore, the missing assumption must connect these two: If a movement is committed to dismantling the establishment, it is NOT willing to compromise.
A sufficient assumption must completely bridge the gap between the given premises and the conclusion to provide 100% deductive certainty.

Key Concept

Sufficient Assumption / Formal Logic Bridging
Question 4Question →

Legal theorist: A legal statute that infringes on personal privacy is morally defensible only if it demonstrably prevents a severe public harm. The recent Cybersecurity Act clearly infringes on personal privacy. Therefore, the recent Cybersecurity Act is not morally defensible.

Which one of the following, if assumed, enables the legal theorist's conclusion to be properly drawn?

Show answer & explanation

Answer: The recent Cybersecurity Act does not demonstrably prevent a severe public harm.

Answer

The recent Cybersecurity Act does not demonstrably prevent a severe public harm.
The correct answer provides the exact logical trigger needed to complete the argument. The legal theorist states that preventing a severe public harm is a necessary condition for a privacy-infringing statute to be morally defensible. Because we already know the Cybersecurity Act infringes on privacy, proving that it fails to meet this single necessary condition definitively guarantees that it is not morally defensible.

Step-by-Step Solution

1
Analyze the conditional logic in the first premise.
Rule: If a statute infringes on privacy (IP) AND is morally defensible (MD), then it must prevent a severe public harm (PSH). Formally: (IP + MD) -> PSH.
Identifying the exact necessary and sufficient conditions is the first step in finding the deductive gap.
2
Identify the logical contrapositive of the established rule.
Contrapositive: If a statute does NOT prevent a severe public harm (~PSH), then it cannot be both privacy-infringing and morally defensible. Since it is already privacy-infringing, it must be NOT morally defensible (~MD).
The conclusion attempts to prove a negative (~MD). The contrapositive provides the pathway to prove that negative.
3
Evaluate the argument's provided facts against the contrapositive.
Fact: The Cybersecurity Act infringes on privacy (IP). Conclusion: The Act is not morally defensible (~MD).
This reveals the missing link. To trigger the contrapositive and force the ~MD conclusion, we must satisfy the ~PSH trigger condition.
4
Select the assumption that bridges the gap.
The necessary assumption to guarantee the conclusion is that the Cybersecurity Act does NOT prevent a severe public harm.
Assuming this definitively triggers the contrapositive chain, guaranteeing the conclusion with 100% logical certainty.

Key Concept

Bridging a deductive gap by providing the sufficient condition to trigger a contrapositive argument structure.
Question 5Question →

Botanist: Any plant species that thrives in highly alkaline soil must possess an extensive taproot system. The newly discovered Silene deserti thrives in highly alkaline soil. Therefore, Silene deserti must be capable of surviving prolonged periods of drought.

Statement: The assumption that 'any plant species capable of surviving prolonged periods of drought possesses an extensive taproot system' is sufficient to logically guarantee the botanist's conclusion.

Show answer & explanation

Answer: False

Answer

False
The statement is false because the provided assumption is an illegal reversal. To guarantee that Silene deserti can survive a drought, the assumption must state that having an extensive taproot (which we know the plant has) is sufficient to ensure survival during a drought. Instead, the statement claims that surviving a drought requires an extensive taproot, which completely fails to prove the botanist's conclusion.

Step-by-Step Solution

1
Identify the premises and the conclusion of the argument.
Premise 1: Thrives in alkaline soil guarantees an extensive taproot. Premise 2: Silene deserti thrives in alkaline soil. Conclusion: Silene deserti survives prolonged drought.
Deconstructing the argument is the first step in identifying any deductive gaps.
2
Determine the intermediate inference supported by the premises.
Because Silene deserti thrives in alkaline soil, it can be logically deduced that it possesses an extensive taproot system.
This establishes exactly what is already proven about Silene deserti before attempting to validate the final conclusion.
3
Identify the logical gap between the intermediate inference and the final conclusion.
The argument establishes that the plant has an extensive taproot, but concludes it can survive droughts. The required sufficient assumption must bridge this gap: Extensive taproot guarantees survival during prolonged drought.
A sufficient assumption must guarantee the conclusion based entirely on the existing premises.
4
Evaluate the proposed assumption in the statement.
The statement proposes: Surviving prolonged drought guarantees an extensive taproot. This is the reverse of what is mathematically needed.
Reversing the necessary and sufficient conditions fails to guarantee the conclusion.

Key Concept

Identifying Illegal Reversals in Sufficient Assumptions
Question 6Question →

Financial theorist: A financial market is robust only if it is capable of withstanding severe liquidity shocks and maintains transparent trading protocols. The novel commodities exchange, Aetherion, utilizes decentralized anonymous ledgers. Because this feature completely precludes the maintenance of transparent trading protocols, it follows that Aetherion's underlying economic model must be inherently unstable.

Which one of the following is an assumption that, if true, allows the financial theorist's conclusion to be properly drawn?

Show answer & explanation

Answer: Every financial market that is not robust has an inherently unstable economic model.

Answer

Every financial market that is not robust has an inherently unstable economic model.
The argument establishes that maintaining transparent trading protocols is a necessary condition for a market to be robust (Robust -> Transparent). It then tells us Aetherion cannot maintain transparent protocols. By the contrapositive, Aetherion is not robust. The author concludes that Aetherion's economic model is inherently unstable. To completely bridge the gap, we must link the established fact (Aetherion is not robust) to the conclusion (Aetherion is inherently unstable). The statement 'Every financial market that is not robust has an inherently unstable economic model' perfectly supplies this bridge.

Step-by-Step Solution

1
Map the formal logic of the first premise.
Robust -> Capable of withstanding shocks AND Maintains transparent protocols.
The phrase 'only if' introduces necessary conditions for a market to be considered robust.
2
Evaluate the facts provided about Aetherion.
Aetherion utilizes decentralized anonymous ledgers, which means it DOES NOT maintain transparent trading protocols (~Transparent).
The stimulus explicitly states that the ledgers completely preclude maintaining transparent protocols.
3
Draw an intermediate conclusion about Aetherion.
Because Aetherion fails a necessary condition for robustness (~Transparent), Aetherion is not robust (~Robust).
Applying the contrapositive of the first premise (~Transparent OR ~Capable of withstanding shocks -> ~Robust).
4
Identify the logical gap to the main conclusion.
The argument concludes Aetherion is inherently unstable. The gap is between the deduced fact '~Robust' (or '~Transparent') and the conclusion 'Inherently unstable'.
A sufficient assumption must provide a 100% guaranteed bridge from the premises to the final conclusion.
5
Formulate the required bridge and select the matching option.
The assumption 'If ~Robust, then Inherently unstable' (~Robust -> Unstable) perfectly completes the logical chain.
Combining the rule '~Robust -> Unstable' with the established fact 'Aetherion is ~Robust' deductively proves the conclusion.

Key Concept

Conditional Logic Bridges
Estimated Time:2m 0s
Question 7Question →

Every painting acquired by the city museum before 1900 is considered part of the permanent collection. Therefore, every painting acquired by the museum before 1900 must be displayed on the first floor of the building.

Which one of the following, if assumed, enables the argument's conclusion to be properly drawn?

Show answer & explanation

Answer: Every painting that is part of the permanent collection must be displayed on the first floor of the building.

Answer

The correct assumption is that every painting that is part of the permanent collection must be displayed on the first floor of the building.
The argument provides the premise (A -> B) and draws the conclusion (A -> C). To make this logically valid, we must bridge the gap between B and C with the rule (B -> C). The correct answer explicitly provides this missing rule: if a painting is in the permanent collection, it must be displayed on the first floor.

Step-by-Step Solution

1
Identify the argument's premise.
If a painting was acquired before 1900, it is part of the permanent collection (Acquired Before 1900 -> Permanent Collection).
This establishes the starting condition of the logic chain.
2
Identify the argument's conclusion.
If a painting was acquired before 1900, it must be displayed on the first floor (Acquired Before 1900 -> First Floor).
This is the final destination the author is trying to prove.
3
Find the logical gap between the premise and the conclusion.
The argument leaps from 'Permanent Collection' in the premise to 'First Floor' in the conclusion without connecting them.
For the conclusion to be 100% guaranteed, there must be no unconnected terms.
4
Formulate the necessary bridge to guarantee the conclusion.
We must state that anything in the permanent collection must go to the first floor (Permanent Collection -> First Floor).
Chaining 'Acquired Before 1900 -> Permanent Collection' with 'Permanent Collection -> First Floor' deductively yields 'Acquired Before 1900 -> First Floor'.

Key Concept

Sufficient Assumption conditional chaining
Question 8Question →

Philosopher: A political doctrine cannot be considered genuinely egalitarian unless it categorically repudiates the concept of inherited executive authority, except in systems where the exercise of such authority is entirely symbolic. The foundational charters of the Valesian Order establish a governance model predicated on inherited executive authority. Consequently, the Valesian charters fail to offer a genuinely egalitarian political doctrine.

Which one of the following, if assumed, enables the philosopher's conclusion to be properly drawn?

Show answer & explanation

Answer: No governance model predicated on inherited executive authority restricts the exercise of that authority to entirely symbolic functions.

Answer

The correct assumption is that no governance model predicated on inherited executive authority restricts the exercise of that authority to entirely symbolic functions.
The philosopher's rule states that to be genuinely egalitarian, a doctrine must EITHER repudiate inherited authority OR possess authority that is entirely symbolic. The Valesian charters do not repudiate inherited authority. Therefore, to validly conclude that they are definitively not egalitarian, we must assume they also fail the second condition (i.e., their authority is not entirely symbolic). The correct statement provides a universal rule that any model with inherited authority (which the Valesian charters have) inherently fails to be entirely symbolic. This closes the logical gap and forces the conclusion to be 100% true.

Step-by-Step Solution

1
Map the formal logic of the philosopher's primary principle.
Genuinely Egalitarian -> Repudiates Inherited Authority OR Authority is Entirely Symbolic.
The phrase 'cannot be... unless... except when' creates a compound necessary condition. A doctrine must meet at least one of those two conditions to be considered egalitarian.
2
Analyze the application of the principle to the Valesian Order.
The Valesian charters establish inherited authority, meaning they fail the 'Repudiates Inherited Authority' condition.
The stimulus states the charters are 'predicated on inherited executive authority.'
3
Identify the logical gap leading to the conclusion.
The author concludes the charters are NOT egalitarian. For this to be definitively true, the charters must also fail the second necessary condition: their authority must NOT be entirely symbolic.
If the Valesian authority were entirely symbolic, it could still theoretically be egalitarian under the philosopher's rule. We must eliminate this possibility to guarantee the conclusion.
4
Evaluate the correct assumption.
The statement 'No governance model predicated on inherited executive authority restricts... to entirely symbolic functions' translates to: Inherited Authority -> NOT Entirely Symbolic.
Because the Valesian charters have inherited authority, this assumption guarantees their authority is not entirely symbolic, failing both necessary conditions and strictly proving they are not egalitarian.

Key Concept

Sufficient Assumptions with Compound Necessary Conditions
Question 9Question →

Legal Scholar: A legal framework is effective only if it continuously adapts to changing societal norms. Furthermore, a framework adapts to changing societal norms if and only if it grants judges broad interpretative discretion. Hence, any effective legal framework must grant judges broad interpretative discretion. Rigid statutory mandates, however, prevent a legal framework from granting judges broad interpretative discretion. Therefore, it is clear that any jurisdiction whose legal framework relies heavily on rigid statutory mandates will ultimately fail to sustain a prosperous economy.

Which one of the following, if assumed, allows the legal scholar's conclusion to be properly drawn?

Show answer & explanation

Answer: A jurisdiction can sustain a prosperous economy only if its legal framework is effective.

Answer

A jurisdiction can sustain a prosperous economy only if its legal framework is effective.
The argument's premises establish a continuous chain of logic: Rigid statutory mandates prevent broad discretion, which prevents adapting to norms, which ultimately means the framework is not effective. So, Rigid Mandates = Not Effective. The conclusion takes a leap, claiming Rigid Mandates = Not Prosperous. To make this conclusion logically bulletproof, we must assume that being 'Not Effective' mathematically guarantees being 'Not Prosperous' (Not Effective -> Not Prosperous). The correct answer provides the logical contrapositive of this exact rule: A prosperous economy requires an effective framework (Prosperous -> Effective). If this is assumed, the scholar's conclusion follows with absolute certainty.

Step-by-Step Solution

1
Map the conditional relationships in the premises.
Effective -> Adapts. Adapts <-> Grants Discretion. Rigid Mandates -> NOT Grants Discretion.
Formal logic mapping is required to see how the premises logically connect to one another.
2
Chain the premises together to find the intermediate deduction.
Since Rigid Mandates -> NOT Grants Discretion, and Effective -> Grants Discretion (via Adapts), it follows that Rigid Mandates -> NOT Effective.
This establishes exactly what we know about jurisdictions with rigid statutory mandates based solely on the provided evidence.
3
Identify the main conclusion and isolate the logical gap.
The main conclusion is: Rigid Mandates -> NOT Prosperous Economy. The gap is between the end of our premise chain ('NOT Effective') and the new term in the conclusion ('NOT Prosperous Economy').
A sufficient assumption must introduce a rule that seamlessly connects the established evidence to the new claim.
4
Formulate the required assumption and find its match in the options.
We need the rule 'NOT Effective -> NOT Prosperous Economy'. The contrapositive of this rule is 'Prosperous Economy -> Effective', which translates to 'A prosperous economy requires an effective framework'. This perfectly matches the correct option.
This bridge makes the conclusion 100% deductively valid, satisfying the task of a Sufficient Assumption question.

Key Concept

Sufficient Assumption conditional chaining and contrapositives
Question 10Question →

Macroeconomist: A national currency cannot achieve global reserve status unless its issuing central bank operates completely independent of short-term political pressures. Some analysts argue that the newly launched Solarian Credit will achieve global reserve status because it is backed by vast physical commodity reserves. However, any currency backed by vast physical commodity reserves inherently subjects its valuation to unpredictable global market fluctuations. Furthermore, no central bank can successfully prioritize long-term economic stability if its currency's valuation is subjected to such unpredictable market fluctuations. Therefore, the Solarian Credit cannot achieve global reserve status.

Which of the following, if assumed, enables the macroeconomist's conclusion to be properly drawn?

Show answer & explanation

Answer: Any central bank that operates completely independent of short-term political pressures is able to successfully prioritize long-term economic stability.

Answer

The statement that any central bank that operates completely independent of short-term political pressures is able to successfully prioritize long-term economic stability.
The macroeconomist's argument relies on a chain of formal logic that remains incomplete. To prove the Solarian Credit cannot achieve global reserve status, the first premise dictates we must prove it lacks independence from political pressure. The evidence provided only proves that the Solarian Credit's central bank cannot prioritize long-term economic stability (due to commodity backing causing market fluctuations). To bridge the gap, we must assume that an inability to prioritize long-term stability guarantees a lack of political independence. The correct answer states this exact rule in its contrapositive form: Any bank that IS independent MUST be able to prioritize long-term stability. If we add this rule, the Solarian Credit's inability to prioritize stability guarantees it lacks independence, which in turn guarantees it cannot achieve global reserve status.

Step-by-Step Solution

1
Map the required condition for the conclusion.
The conclusion is that the Solarian Credit will not achieve global reserve status. According to the first premise, the only stated way to prove this is to prove that its central bank is NOT completely independent of short-term political pressures.
Establishing the endpoint of the logical chain needed to mathematically guarantee the conclusion.
2
Map the chain of established premises regarding the Solarian Credit.
Solarian Credit -> Backed by commodities -> Subjected to market fluctuations -> Cannot successfully prioritize long-term economic stability.
Determines the furthest point we can reach using the explicit evidence provided in the stimulus.
3
Identify the logical gap.
The explicit chain ends at 'Cannot prioritize long-term stability'. The required trigger to prove the conclusion is 'Not independent of political pressures'. Therefore, the missing link is: 'If a bank cannot prioritize long-term stability, it is not independent of political pressures.'
A sufficient assumption must perfectly connect the end of the premise chain to the trigger for the conclusion.
4
Formulate the contrapositive of the missing link to find the correct answer.
The contrapositive of 'If it cannot prioritize stability, it is not independent' is exactly: 'If a bank is independent of political pressures, it must be able to successfully prioritize long-term economic stability.'
LSAT questions frequently present the correct sufficient assumption in its contrapositive form to test advanced formal logic translation.

Key Concept

Sufficient Assumption (Conditional Logic Chains and Contrapositives)
Estimated Time:2m 0s
Question 11Question →

Archaeologist: Any ancient civilization that possessed a centralized government was capable of organizing large-scale public works. Extensive excavations in the region historically inhabited by the Moradi civilization have revealed absolutely no evidence of monumental architecture, such as pyramids, large temples, or administrative palaces. Therefore, it is clear that the Moradi did not possess a centralized government.

The archaeologist's conclusion is properly drawn if which one of the following is assumed?

Show answer & explanation

Answer: Any ancient civilization that was capable of organizing large-scale public works left behind evidence of monumental architecture.

Answer

The correct assumption is that any ancient civilization that was capable of organizing large-scale public works left behind evidence of monumental architecture.
The argument relies on connecting the evidence (no monumental architecture) to the conclusion (no centralized government). The premise states that a centralized government guarantees the capability for large-scale public works. To strictly guarantee the conclusion, we must prove the Moradi lacked this capability. The correct assumption provides the missing link: if any civilization capable of public works left behind monumental architecture, then the Moradi's lack of such architecture proves they were incapable of public works, thus perfectly proving they lacked a centralized government.

Step-by-Step Solution

1
Identify the premises and the conclusion of the argument.
Premise: Centralized Government -> Capable of Public Works. Evidence: Moradi -> NO Monumental Architecture. Conclusion: Moradi -> NO Centralized Government.
Deconstructing the argument into its conditional logic components is essential for identifying the missing link.
2
Determine the logical gap between the stated premises and the conclusion.
To prove NO Centralized Government, we must trigger the contrapositive of the premise, which requires proving NO Capability of Public Works. The evidence only establishes NO Monumental Architecture.
Identifying the exact deductive gap dictates what the sufficient assumption must provide to logically complete the argument.
3
Formulate the required sufficient assumption to bridge the gap.
The assumption must link the evidence to the required trigger: NO Monumental Architecture -> NO Capability of Public Works. The contrapositive of this is: Capable of Public Works -> Monumental Architecture.
A sufficient assumption must logically guarantee the conclusion, meaning it must complete the conditional chain perfectly without logical leaps.

Key Concept

Sufficient Assumption (Deductive Bridge)
Question 12Question →

The university has announced that any student who completes the advanced research seminar will be awarded a special graduation commendation. Therefore, we can be certain that every student majoring in history will be awarded this special graduation commendation.

Which one of the following, if assumed, enables the argument's conclusion to be properly drawn?

Show answer & explanation

Answer: Every student majoring in history completes the advanced research seminar.

Answer

The option stating that every student majoring in history completes the advanced research seminar.
The argument establishes a conditional rule in the premise: If a student takes the seminar, then they receive the commendation. The conclusion attempts to state: If a student is a history major, then they receive the commendation. To make this conclusion 100% logically valid, we must bridge the gap between being a history major and taking the seminar. The correct answer provides this exact bridge: If a student is a history major, then they take the seminar. This creates a perfect deductive chain.

Step-by-Step Solution

1
Identify the argument's core premise and main conclusion.
Premise: Completing the seminar guarantees the commendation. Conclusion: Majoring in history guarantees the commendation.
Isolating the formal structure of the argument is necessary to spot the missing logical link.
2
Determine the gap in the reasoning.
The argument jumps from the condition of 'majoring in history' to the trigger of 'completing the seminar' without connecting them.
The conclusion introduces a new group (history majors) that must be directly linked to the premise's trigger condition (completing the seminar).
3
Formulate the missing sufficient assumption.
The required assumption is that all history majors complete the advanced research seminar.
If all history majors take the seminar, and taking the seminar guarantees the commendation, then all history majors are mathematically guaranteed to receive the commendation.

Key Concept

Sufficient Assumption (Formal Logic Bridge)
Question 13Question →

Match each argument below with the sufficient assumption that logically guarantees its conclusion. Note that one assumption provided is an incorrect trap.

Click a left item, then click its matching right item

Items

The proposed highway expansion will increase traffic flow. Thus, the expansion should be approved.
The recently discovered compound contains carbon. Thus, the compound is organic.
The new novel was written by a Nobel laureate. Thus, it will win the book of the year award.
The manufacturing plant uses solar power. Thus, the plant is environmentally friendly.

Matches

Show answer & explanation

Answer

Highway expansion matches with 'increases traffic flow should be approved'; carbon compound matches with 'contain carbon are organic'; Nobel novel matches with 'written by a Nobel laureate will win'; solar plant matches with 'use solar power are environmentally friendly'.
Each correctly matched assumption follows the formal logic pattern: 'Premise -> Conclusion'. By establishing this universal rule, the fact provided in the premise becomes sufficient to definitively prove the conclusion.

Step-by-Step Solution

1
Analyze each argument to identify its stated premise and its final conclusion.
For example, in the first argument, Premise: 'will increase traffic flow', Conclusion: 'should be approved'.
Finding the structural components of the argument is the first step in identifying the missing logical gap.
2
Determine the required sufficient assumption by linking the premise directly to the conclusion.
The correct format for the assumption is 'If [Premise], then [Conclusion]'. For the first argument, this means 'If it increases traffic flow, it should be approved'.
A sufficient assumption mathematically guarantees the conclusion, completing the deductive bridge.
3
Match each argument with its corresponding 'If Premise, then Conclusion' statement from the available options.
The four correct statements directly link the provided premises to their respective conclusions without reversing the logic.
Reversing the logic (If Conclusion, then Premise) is a common trap and does not guarantee the conclusion.

Key Concept

Sufficient Assumption
Estimated Time:1m 0s
Question 14Question →

Consider the following argument:

Architect: A building cannot be considered a modernist masterpiece unless it prioritizes functional utility over ornamentation and utilizes industrial materials like steel or glass. The new municipal library clearly utilizes industrial materials, featuring a striking glass facade supported by a steel frame. Furthermore, its interior layout was strictly dictated by the practical requirements of storing and accessing books.
Therefore, the new municipal library is a modernist masterpiece.

Statement: The assumption 'Any building whose interior layout is strictly dictated by practical requirements prioritizes functional utility over ornamentation' is sufficient to logically guarantee the architect's conclusion.

Show answer & explanation

Answer: False

Answer

False
The correct answer is False because the original argument commits a flaw of conditional logic by treating necessary conditions as sufficient. While the proposed assumption successfully bridges a semantic gap to prove the library meets all necessary conditions, fulfilling necessary conditions is never logically sufficient to guarantee the conclusion.

Step-by-Step Solution

1
Diagram the conditional logic in the first sentence.
Modernist Masterpiece (MM) -> Prioritizes Functional Utility (PFU) AND Utilizes Industrial Materials (UIM).
The phrase 'cannot be considered... unless' introduces necessary conditions that must be placed on the right side of the conditional arrow.
2
Identify the premises regarding the specific subject (the municipal library).
The library has UIM (glass and steel) and its layout was dictated by practical requirements.
To map the evidence provided against the established conditional rules.
3
Analyze the proposed assumption to see what it adds.
The assumption 'Dictated by practical requirements -> PFU' establishes that the library definitely possesses PFU.
We must evaluate how this new premise changes the argument's validity.
4
Evaluate if the combined premises logically guarantee the conclusion.
With the assumption, we know the library has both PFU and UIM. The conclusion asserts the library is an MM. However, MM -> (PFU AND UIM). Fulfilling the necessary conditions does not guarantee the sufficient condition (MM).
A sufficient assumption must make the conclusion 100% deductively valid. Affirming the consequent commits a formal flaw, so the assumption is insufficient.

Key Concept

Distinguishing between necessary and sufficient conditions in formal logic, and recognizing that bridging a semantic premise gap cannot repair an underlying structural flaw.

Alternative Method

You can quickly eliminate the proposed assumption by looking purely at the logical structure rather than the meaning of the words. The first premise establishes the structure: A -> (B and C). The conclusion asserts A. Since the premises only establish the right side of the conditional, no assumption that merely reinforces the right side can ever prove the left side (A). A sufficient assumption must explicitly state that (B and C) -> A.
Estimated Time:2m 0s
Question 15Question →

Consider the following argument:

Only algorithms that undergo rigorous adversarial testing can successfully identify zero-day vulnerabilities. Furthermore, if an algorithmic system requires massive computational overhead, it cannot be deployed on edge devices. The newly developed 'Aegis' protocol is capable of identifying zero-day vulnerabilities. Therefore, the 'Aegis' protocol cannot be deployed on edge devices.

Statement: The assumption "Any algorithmic system that does not require massive computational overhead has not undergone rigorous adversarial testing" is sufficient to logically guarantee the argument's conclusion.

Show answer & explanation

Answer: True

Answer

True
The statement accurately identifies a sufficient assumption. The required logical bridge is 'Rigorous Testing →\rightarrow Massive Overhead'. The provided assumption is its valid contrapositive ('∼\sim Massive Overhead →\rightarrow ∼\sim Rigorous Testing'), which perfectly completes the deductive chain and guarantees the conclusion.

Step-by-Step Solution

1
Map the formal logic of the premises.
Identify Zero-Day →\rightarrow Rigorous Testing. Massive Overhead →\rightarrow Cannot Deploy on Edge. Aegis →\rightarrow Identify Zero-Day.
Translating the text into conditional relationships is necessary to find the structural gap in the argument.
2
Identify the conclusion and trace the existing logical chain.
Conclusion: Aegis →\rightarrow Cannot Deploy on Edge. Current chain: Aegis →\rightarrow Identify Zero-Day →\rightarrow Rigorous Testing.
This establishes what is known and what needs to be proven deductively.
3
Determine the required missing link.
We need to connect 'Rigorous Testing' to 'Cannot Deploy on Edge'. Since 'Massive Overhead' leads to 'Cannot Deploy on Edge', the required bridge is: Rigorous Testing →\rightarrow Massive Overhead.
A sufficient assumption must fill the exact deductive gap to guarantee the conclusion.
4
Evaluate the provided assumption against the required missing link.
The provided assumption is: Does not require massive overhead →\rightarrow Has not undergone rigorous testing (∼\sim Massive Overhead →\rightarrow ∼\sim Rigorous Testing). This is the logically equivalent contrapositive of the required bridge (Rigorous Testing →\rightarrow Massive Overhead).
A contrapositive functions identically to the original conditional statement, making the assumption completely sufficient.

Key Concept

Sufficient assumptions must provide absolute logical validity to the conclusion by supplying a missing deductive link. This missing link can be presented in its contrapositive form and remain entirely valid.
Question 16Question →

Match each argument with the sufficient assumption that logically guarantees its main conclusion.

Click a left item, then click its matching right item

Items

Only entities that synthesize proteins can be classified as alive. Prions consist solely of misfolded proteins and lack the cellular machinery to synthesize anything. Therefore, prions are incapable of biological evolution.
Expanding the public transit system requires significant increases in municipal funding. The upcoming referendum, if passed, will strictly cap property taxes. Consequently, if the referendum passes, the public transit system will not be expanded.
A valid legal contract requires mutual consideration. The agreement between the corporation and the intern involved the exchange of labor for experience, but no monetary compensation was provided. Thus, the agreement is not a valid legal contract.
Historically, revolutionary scientific theories are initially rejected by the academic establishment. Dr. Vance's new theory of quantum gravity has been warmly embraced by all major physics journals. Therefore, Dr. Vance's theory is incorrect.
The mayor's proposal will reduce traffic congestion in the downtown area. Any proposal that reduces traffic congestion will ultimately improve the city's air quality. Therefore, the city council will definitively approve the mayor's proposal.

Matches

Show answer & explanation

Answer

Argument 1 pairs with 'Only entities classified as alive...', Argument 2 pairs with 'Municipal funding cannot...', Argument 3 pairs with 'An agreement lacks...', Argument 4 pairs with 'No scientific theory is correct...', and Argument 5 pairs with 'The city council approves...'
Each correct pairing connects an argument to the specific conditional statement that logically bridges the gap between its premises and its conclusion. By translating the text into formal logic (e.g., identifying contrapositives or mapping conditional chains), each matched assumption provides the exact sufficient condition required to make its corresponding argument 100% deductively valid.

Step-by-Step Solution

1
Analyze the prion argument to isolate the missing logical link.
The premises prove prions are 'not alive'. The conclusion states they are 'incapable of evolution'. The required bridge is 'not alive -> incapable of evolution' or its contrapositive 'capable of evolution -> alive'.
Identifying the exact deductive gap is the first step in recognizing a sufficient assumption.
2
Analyze the referendum argument's conditional logic.
Premises: Expand -> Increase Funding. Referendum -> Capped Taxes. Conclusion: Referendum -> Not Expand. We must bridge 'Capped Taxes' to 'Not Increase Funding'.
Chaining conditional statements reveals precisely where the argument's logic breaks down.
3
Identify the missing trigger in the contract argument.
We need to prove the agreement lacks mutual consideration to invoke the rule that it is not a valid contract. The assumption must state that 'no monetary compensation' guarantees a 'lack of mutual consideration'.
Sufficient assumptions often serve to trigger a pre-existing conditional premise.
4
Evaluate the contrapositives in the scientific theory argument.
Vance's theory was not rejected, so it is not revolutionary. To conclude it is incorrect, we need 'Not revolutionary -> Incorrect'. This is the contrapositive of 'Correct -> Revolutionary' (No theory is correct unless it is revolutionary).
Translating 'unless' statements into standard 'if-then' conditional formatting is necessary to test validity.
5
Complete the causal/conditional chain for the mayor's proposal.
The premises lead to the fact that the proposal will improve air quality. To conclude approval, the assumption must state that improving air quality is sufficient to guarantee council approval.
Linking the final derived premise to the conclusion is the standard method for solving bridging assumption questions.

Key Concept

Identifying deductive gaps and supplying the exact formal logic conditional (or its contrapositive) that makes the conclusion 100% valid.
Question 17Question →

Match each flawed argument with the sufficient assumption that logically guarantees its conclusion. Consider contrapositives and conditional translations carefully.

Click a left item, then click its matching right item

Items

Argument 1: The proposed budget cuts will drastically reduce funding for the arts program. Therefore, the budget cuts will harm the intellectual development of the students.
Argument 2: To qualify as a historical landmark, a building must have been constructed before 1920. The abandoned textile mill was built in 1934. Thus, the mill cannot be exempted from the new property tax.
Argument 3: The novel's protagonist acts out of pure self-interest rather than a sense of moral duty. Hence, the novel cannot be classified as a traditional tragedy.
Argument 4: The governor's transit initiative relies heavily on privatized toll roads. Therefore, the initiative will disproportionately burden low-income commuters.

Matches

Show answer & explanation

Answer

Each argument must be matched with the assumption that perfectly bridges the gap between its premises and conclusion, often presented as a contrapositive or through advanced conditional terminology like 'unless' or 'only if'.
Each correct pair matches an argument with a missing logical link to the rule that perfectly bridges that gap. The matching assumptions utilize contrapositives and complex conditional phrasing (e.g., 'only if', 'unless') to state the required bridges logically.

Step-by-Step Solution

1
Analyze Argument 1's logical gap.
The gap is between reducing arts funding and harming intellectual development.
To guarantee the conclusion, we need a premise stating that reducing arts funding causes intellectual harm.
2
Identify the assumption for Argument 1.
The correct match is the statement that provides the contrapositive of the needed rule.
The statement 'If not harming development -> not reducing funding' is logically equivalent to 'If reducing funding -> harming development'.
3
Analyze Argument 2's structure.
Premise: Landmark -> Built before 1920. The mill is NOT built before 1920. Conclusion: The mill is NOT exempted.
The missing link must logically connect being exempted to being built before 1920.
4
Identify the assumption for Argument 2.
The matching assumption states 'Exempted -> Built before 1920'.
Since the mill fails the necessary condition (built before 1920), it cannot be exempted, perfectly guaranteeing the conclusion.
5
Analyze Argument 3's gap.
Premise: Protagonist acts out of self-interest. Conclusion: Not a traditional tragedy.
We need the rule 'Self-interest -> Not traditional tragedy'.
6
Identify the assumption for Argument 3.
The statement 'Traditional tragedy only if not self-interest' translates to 'Traditional tragedy -> Not self-interest'.
This is the contrapositive of the required premise, validating the argument.
7
Analyze Argument 4's gap and matching assumption.
Gap: Toll roads -> Burdens commuters. The match uses 'No X unless Y' format.
The statement 'No initiative relies on toll roads unless it burdens commuters' means 'If it relies on toll roads, it burdens commuters', which bridges the gap.

Key Concept

Sufficient Assumption Conditional Mapping
Question 18Question →

Read the following argument carefully:

A translation of a literary work can preserve the original text's aesthetic impact only if it abandons strict literal accuracy. Any translation that abandons strict literal accuracy necessarily introduces the translator's own cultural biases. Furthermore, the introduction of the translator's own cultural biases invariably distorts the original author's philosophical intent. Therefore, any algorithmic translation system designed to maximize fidelity to the original author's philosophical intent will fail to evoke an emotional response in its readers.

Evaluate the logical validity of the following claim:
The argument's conclusion logically follows if it is assumed both that any translation avoiding the distortion of the author's philosophical intent is one designed to maximize fidelity to that intent, and that failing to preserve a literary work's aesthetic impact guarantees a failure to evoke an emotional response in its readers.

Show answer & explanation

Answer: False

Answer

False
The statement is false. The argument requires us to prove that Maximizing Fidelity (MF) guarantees Failing to Evoke Emotion (FEE). The premises establish that Avoiding Distortion (~DI) guarantees Failing to Preserve Aesthetic (~PA). The second provided assumption correctly bridges the end of the chain (~PA → FEE). However, the first assumption states that Avoiding Distortion (~DI) guarantees Maximizing Fidelity (MF). This logically means ~DI leads to both MF and FEE. But to reach the conclusion, we must start at MF and reach FEE. Because we cannot trace the logic backward from MF to ~DI, the argument remains unproven.

Step-by-Step Solution

1
Diagram the conditional premises to establish the main deductive chain.
Preserve Aesthetic (PA) → Abandon Literal (AL) → Introduce Bias (IB) → Distort Intent (DI). Simplified: PA → DI.
Tracking formal conditional logic is necessary to evaluate exactly what the premises prove.
2
Determine the contrapositive of the main chain.
Not Distort Intent (~DI) → Not Preserve Aesthetic (~PA).
The conclusion deals with terms ('maximize fidelity' and 'fail to evoke emotion') that logically align with the negative versions of the premise terms.
3
Identify the exact logical gaps between the premises and the conclusion.
The conclusion claims: Maximize Fidelity (MF) → Fail to Evoke Emotion (FEE). We need to connect MF to ~DI, and ~PA to FEE.
A sufficient assumption must completely bridge the premises to the new terms in the conclusion in the correct direction.
4
Translate and evaluate the two assumptions provided in the statement.
Assumption 1: ~DI → MF (Any avoiding distortion is one maximizing fidelity). Assumption 2: ~PA → FEE (Failing to preserve guarantees failure to evoke).
We must test if these assumptions logically guarantee the conclusion when added to the premises.
5
Test if the assumptions complete the deductive chain.
We have ~DI → MF (Assumption 1) and ~DI → ~PA (Premises) → FEE (Assumption 2). This does NOT prove MF → FEE. The first assumption is backwards.
To prove MF → FEE, we needed MF → ~DI. Because the provided assumption is reversed, it fails to guarantee the conclusion.

Key Concept

Identifying illegal reversals within complex conditional chains and evaluating sufficient assumptions that must bridge multiple logical gaps.
Question 19Question →

Legal Scholar: A commercial agreement cannot be classified as a legally binding contract unless the agreement requires at least one of the participating parties to assume a verifiable financial risk. Under the terms of the recent agreement between Zenith Studios and a group of freelance animators, the animators agreed to forfeit their residual streaming rights, and in return, Zenith Studios promised to include the animators' names in the credits of all future sequels. Zenith's promise regarding the credits clearly does not require the studio to assume a verifiable financial risk. Therefore, the agreement between Zenith Studios and the animators is not a legally binding contract.

Which of the following, if assumed, allows the legal scholar's conclusion to be properly drawn?

Show answer & explanation

Answer: Forfeiting residual streaming rights does not require the freelance animators to assume a verifiable financial risk.

Answer

The statement asserting that forfeiting residual streaming rights does not require the freelance animators to assume a verifiable financial risk.
The argument relies on a conditional rule: a legally binding contract requires that *at least one* party assumes a verifiable financial risk. To properly deduce the conclusion that this specific agreement is *not* a contract, we must trigger the contrapositive of that rule by proving that *neither* party assumed such a risk. The stimulus explicitly states that Zenith Studios did not assume a risk. By adding the assumption that the animators also did not assume a risk (by forfeiting their streaming rights), it becomes definitively true that no party assumed a financial risk. This completely bridges the gap, triggering the rule and legally guaranteeing the conclusion.

Step-by-Step Solution

1
Identify the conclusion of the argument.
The conclusion is: 'the agreement between Zenith Studios and the animators is not a legally binding contract.'
This sets the target for what must be 100% logically proven by the premises plus the correct answer choice.
2
Deconstruct the conditional rule provided in the first sentence.
If Legally Binding Contract -> At least one party assumes Verifiable Financial Risk (VFR). The contrapositive is: If NO party assumes VFR -> NOT a Legally Binding Contract.
Understanding the formal logic of the rule is necessary to see exactly what conditions must be met to trigger the conclusion.
3
Analyze how the facts of the specific agreement apply to the rule.
The agreement involves two parties: Zenith Studios and the animators. The stimulus establishes that Zenith's contribution (credits) does not equal a VFR. However, the stimulus is silent on whether the animators' contribution (forfeiting rights) equals a VFR.
This reveals the missing logical link. The rule requires that 'at least one' party assumes a risk. Knowing only that Zenith didn't assume a risk is insufficient to prove the contract is invalid.
4
Formulate the assumption required to guarantee the conclusion.
To trigger the contrapositive and definitively prove the contract is not binding, we must assume the animators also did not assume a VFR. Therefore, forfeiting residual rights does not constitute a VFR.
Sufficient Assumption questions require an answer choice that, when added to the premises, makes the conclusion mathematically inescapable.

Key Concept

Sufficient Assumption (Bridging Deductive Gaps in Conditional Logic)
Question 20Question →

Urban Planner: A city cannot effectively revitalize its downtown commercial district unless it significantly expands its pedestrian-only zones. However, expanding pedestrian-only zones inevitably requires a comprehensive overhaul of the city's public transit routing. Therefore, Springfield's upcoming urban renewal initiative will fail to effectively revitalize its downtown commercial district.

Which one of the following, if assumed, allows the urban planner's conclusion to be properly drawn?

Show answer & explanation

Answer: Springfield's upcoming urban renewal initiative will not involve a comprehensive overhaul of the city's public transit routing.

Answer

The correct answer is the statement indicating that Springfield will not undertake a comprehensive overhaul of its public transit routing.
The argument relies on conditional logic: effectively revitalizing the downtown district requires expanding pedestrian-only zones, which in turn requires a comprehensive overhaul of public transit routing. This creates the logical chain: Revitalize → Expand Pedestrian Zones → Overhaul Transit. The urban planner's conclusion is that Springfield's initiative will fail to revitalize the district. To mathematically guarantee this conclusion, we need to establish the failure of one of the necessary conditions. The correct option provides the missing premise that Springfield will not comprehensively overhaul its transit routing. By applying the contrapositive (No Transit Overhaul → No Pedestrian Expansion → No Revitalization), this assumption strictly guarantees the planner's conclusion.

Step-by-Step Solution

1
Identify the core conditional logic in the premises.
Premise 1: Revitalize -> Expand Pedestrian Zones. Premise 2: Expand Pedestrian Zones -> Overhaul Transit Routing.
Mapping the conditional logic of the argument reveals the necessary conditions for a successful revitalization.
2
Chain the conditional premises together and identify the conclusion.
The chain is: Revitalize -> Overhaul Transit Routing. The conclusion is that Springfield will NOT revitalize.
Simplifying the conditional chain makes it easier to evaluate what is missing to mathematically prove the negative conclusion.
3
Determine what additional premise guarantees the conclusion.
To deduce that Springfield will not revitalize, we must trigger the contrapositive of the chain. Assuming that Springfield will NOT overhaul its transit routing triggers the contrapositive, definitively proving the conclusion.
A sufficient assumption must completely bridge the gap between the evidence and the conclusion with absolute logical certainty.

Key Concept

Sufficient Assumption in Conditional Reasoning
Page 1 / 2Next
Sufficient Assumption Practice Questions — LSAT | Examkin