All practice questions

In the early twentieth century, the foundational crisis of mathematics precipitated a stark ideological schism between L.E.J. Brouwer’s intuitionism and David Hilbert’s formalism. Brouwer contended that mathematics is a pure construct of the human mind; mathematical entities exist only insofar as they can be mentally constructed. Consequently, Brouwer rejected the principle of the excluded middle—the logical axiom asserting that any proposition is either true or false—in applications involving infinite sets. He argued that without a finite constructive proof, one cannot validly claim that either a proposition or its negation holds. Hilbert, conversely, sought to secure classical mathematics by axiomatizing it and proving its consistency using strictly finitary methods. For Hilbert, to excise the principle of the excluded middle from mathematics would be akin to "proscribing the telescope to the astronomer or to the boxer the use of his fists." To protect the classical edifice, Hilbert’s program treated complex mathematical statements as strings of symbols manipulated according to rigid syntactic rules, a gambit designed to insulate mathematics from the epistemological vulnerabilities that intuitionism exposed. Ultimately, Gödel’s incompleteness theorems demonstrated that no sufficiently powerful formal system could prove its own consistency, subverting Hilbert's primary ambition while simultaneously relying on the very non-constructive methodologies that Brouwer condemned.

Which of the following best describes the primary purpose for which the author quotes Hilbert’s comparison involving an astronomer’s telescope?

Most of the residential buildings in the downtown district were constructed before 1950. Furthermore, every building constructed before 1950 features cast-iron plumbing. Therefore, it must be true that most of the residential buildings in the downtown district feature cast-iron plumbing.

Which one of the following arguments exhibits a pattern of reasoning that is most parallel to that in the argument above?

Traditional narratives concerning the Scientific Revolution frequently emphasize the triumph of mechanistic philosophy over Aristotelian teleology, characterizing this paradigm shift as a decisive rejection of purpose-driven explanations in nature. According to this narrative, seventeenth-century natural philosophers uniformly sought to explain physical phenomena exclusively in terms of matter and motion. However, recent historiography complicates this picture by highlighting the persistent, albeit transformed, role of teleological reasoning even among the most prominent mechanists. Robert Boyle, for instance, championed the mechanical philosophy but simultaneously argued that identifying the 'ends' or purposes of biological structures was essential for natural theology and provided crucial heuristic guidance for anatomical investigations. Rather than abandoning teleology, Boyle and his contemporaries often relocated it: while they expunged intrinsic purpose from inanimate matter, they retained it as a design feature imposed by a rational Creator, thereby utilizing teleological language to describe complex biological systems without conceding ground to Aristotelian essentialism.

Based on the passage, which of the following inferences about seventeenth-century natural philosophy are most strongly supported? (Select all that apply)

Tech Journalist: A prominent internet commentator recently published a scathing review of the new Helios smartphone, arguing that its battery life is inadequate and its software is extremely buggy. However, this commentator is notorious across online forums for being an abrasive, ill-tempered individual who seems to take pleasure in being universally disliked. Because of the commentator's thoroughly unpleasant personality, we should completely disregard their critique of the Helios smartphone.

The tech journalist's argument is most vulnerable to criticism on the grounds that it

A comprehensive review of international corporate law firms over the past decade revealed a striking statistical anomaly: firms that officially adopted a heavily subsidized "sabbatical leave" program for their mid-level associates subsequently demonstrated a 30 percent higher rate of those associates being promoted to senior partner compared to firms without such programs. The analysts conducting the review concluded that the period of extended rest provided by the sabbaticals directly rejuvenates the associates, thereby enhancing their cognitive endurance and causing the increased rate of prestigious promotions.

Which of the following statements, if true, provide a valid alternative explanation for the observed correlation, thereby weakening the analysts' causal conclusion? (Select all that apply)

Agricultural researcher: A recent survey of farms in the drought-stricken Oakhaven region found that farms utilizing the newly developed MicroDrip irrigation system experienced, on average, a 25 percent lower rate of crop failure than farms using traditional overhead sprinklers. Since both systems draw water from the same dwindling regional reservoir, it is clear that the MicroDrip system delivers water to plant roots more efficiently than overhead sprinklers do.

Which of the following, if true, most seriously weakens the agricultural researcher's argument?

Analyze the deductive reasoning in the following practical scenarios. Pair each scenario with the abstract logical framework that correctly represents its method of deduction.

Museum Curator: For historical textiles to be preserved without degradation for over a century, they absolutely must be stored in climate-controlled environments with strictly regulated humidity. Because our institution recently secured the funding to install state-of-the-art humidity-control systems in all of our storage vaults, we can be confident that the historical textiles in our collection will not degrade over the next century.

Which of the following most accurately describes a flaw in the museum curator's reasoning?

Some organisms dwelling in the abyssal zone are bioluminescent. Since no bioluminescent organisms possess functioning chloroplasts, it follows that some organisms dwelling in the abyssal zone do not possess functioning chloroplasts.

Which of the following arguments exhibits a pattern of reasoning most logically similar to that exhibited by the argument above?

Read the following passage excerpt:

"Historians have long debated the primary catalyst for the Industrial Revolution. Traditionalists argue that technological innovations, such as the steam engine, were the singular driving force, pointing to the rapid increase in manufacturing output. However, a growing group of revisionist historians contends that economic and legal institutions, such as property rights and patent laws, were the true catalysts, as they created the necessary environment for innovation to thrive. While the traditionalists correctly identify the immediate mechanisms of change, their view is too narrow. Conversely, the revisionists overstate the role of institutions, ignoring that these laws often lagged behind technological realities. A more comprehensive understanding requires recognizing that technological advancements and institutional frameworks functioned in a symbiotic feedback loop, mutually reinforcing one another."

To achieve the primary purpose of advocating for a symbiotic model of historical change, the author employs a specific rhetorical progression. Arrange the following rhetorical steps in the chronological sequence they appear in the passage.

Identify the precise logical error committed in each argument below. Pair the arguments on the left with their corresponding abstract flaw descriptions on the right.

Recent excavations at the ancient city of Oxtotitlán revealed a striking correlation: the neighborhoods with the highest concentration of imported luxury ceramics also contained the highest number of clay tablets detailing unpaid financial debts owed by the residents of those households. The lead historian concludes that the exorbitant cost of acquiring these luxury ceramics drove the residents of these neighborhoods into severe debt.

The reasoning in the historian's argument is most vulnerable to criticism on the grounds that it...

Read the following passage, in which the sentences are numbered.

[1] In the mid-twentieth century, the New Critics transformed literary analysis by insisting that a text must be evaluated solely as a self-contained aesthetic object, divorced from its historical context. [2] Contemporary historicist scholars, however, frequently condemn this formalism for imposing an ideological sterility upon literature, arguing that ignoring sociopolitical contexts strips works of their moral resonance. [3] While these contemporary critiques accurately identify the limitations of attempting to isolate a text from its era, they fundamentally misapprehend the New Critics' actual legacy. [4] Ultimately, the enduring significance of the New Critical movement resides not in its flawed theoretical premise of the autonomous text, but rather in its creation of a rigorous, standardized methodology of close reading that even its most ardent historicist detractors unknowingly depend upon. [5] By establishing precise analytical tools for examining paradox and tension within a text, the New Critics forged a methodological infrastructure that makes all sophisticated modern literary analysis possible. [6] Indeed, when modern historicists analyze how a nineteenth-century novel subverts contemporary political ideologies through its use of subtle irony, they are directly employing the very mechanical tools the New Critics invented. [7] The pervasive nature of this methodological reliance demonstrates that the analytical vocabulary of New Criticism has completely transcended the theoretical framework that originally birthed it.

Based on the passage, which sentence explicitly states the author's main point? (Enter the sentence number)

Read the following passage excerpt regarding constitutional interpretation methodologies. Match each cited detail or phrase from the passage to its primary rhetorical function in the author's argument.

Recent shifts in constitutional originalism have seen scholars increasingly adopt corpus linguistics—the computational analysis of vast databases of historical texts—to ascertain the 'original public meaning' of constitutional provisions. Proponents argue this empirical turn rescues originalism from the subjective, cherry-picked historical anecdotes that long plagued intentionalist approaches. By aggregating thousands of linguistic usages from the Founding era, corpus linguistics purports to offer an objective frequency of meaning. However, critics note that this methodological pivot merely displaces the interpretive dilemma rather than resolving it. While corpus data might reveal the statistical dominance of a particular usage in everyday parlance, it cannot dictate whether a constitutional framer employed a term in its most common sense or in a specialized, perhaps legally distinct, register. Furthermore, the reliance on extant historical databases inevitably biases the analysis toward the literate, propertied classes whose writings were preserved, systematically muting marginalized voices of the era and thus skewing the supposed 'public' meaning.

City Planner: The community board's proposal to rezone the waterfront district should be rejected. The board's chairperson owns a significant amount of commercial property just outside the proposed rezoning area, so she stands to benefit financially if development is restricted along the waterfront.

Statement: The city planner's argument is logically flawed because it rejects the community board's recommendation strictly by pointing out the chairperson's vested financial interest, ignoring the actual viability of the rezoning plan itself.

Read the following passage.

For over a century, the prevailing consensus within paleoanthropology held that Neanderthals were cognitively impoverished relative to early *Homo sapiens*. This view, rooted primarily in early, flawed reconstructions of Neanderthal skeletal remains, posited that our hominin cousins lacked the neurological architecture necessary for symbolic thought, complex language, and sophisticated social organization. Consequently, the rapid replacement of Neanderthals by anatomically modern humans upon the latter’s arrival in Europe was historically explained as an inevitable triumph of superior cognitive flexibility over brute strength.

However, a cascade of recent archaeological discoveries has begun to systematically dismantle this deeply entrenched narrative. Excavations in the Iberian Peninsula have unearthed cave paintings that definitively predate the arrival of *Homo sapiens* in the region, indicating that Neanderthals were engaging in non-utilitarian, symbolic expression tens of thousands of years earlier than previously assumed. Furthermore, the discovery of eagle talons bearing deliberate cut marks, interpreted as jewelry, along with complex multi-component adhesive tools, suggests a level of planning and abstract representation that is highly advanced.

These findings strongly challenge the notion of human cognitive uniqueness during the Middle Paleolithic. Ultimately, the emerging archaeological record necessitates a fundamental revision of the traditional evolutionary paradigm: rather than being a cognitively deficient evolutionary dead-end, Neanderthals possessed symbolic and technological capacities that were largely comparable to those of early modern humans.

While some conservative scholars maintain that these artifacts represent isolated instances of acculturation—arguing that Neanderthals merely mimicked the behaviors of encroaching modern humans without grasping their underlying symbolic significance—this counterargument struggles to explain the chronological precedence of the Neanderthal artifacts. As dating techniques become more precise, it becomes increasingly untenable to dismiss Neanderthal cognitive parity as a mere artifact of cross-species imitation.

Which one of the following most accurately expresses the main point of the passage?

Linguist: An analysis of isolated indigenous languages reveals a striking pattern: languages that lack distinct grammatical markers for the future tense are overwhelmingly spoken by communities that exhibit exceptionally high savings rates and long-term economic stability. It has been hypothesized that the structure of a language shapes its speakers' worldview. Our findings confirm this hypothesis: by forcing speakers to grammatically treat the future as equivalent to the present, these languages subconsciously compel their speakers to prioritize future needs, thereby fostering economic prudence.

Which one of the following most accurately describes a flaw in the linguist's reasoning?

Proponents of the strict propertization of trademarks often invoke the specter of the 'tragedy of the commons'—the depletion of shared resources through uncoordinated individual action—to justify granting perpetual exclusivity over commercial signs and symbols. Yet this theoretical extension founders on a categorical conflation of rivalrous material assets with non-rivalrous informational goods. While an overgrazed pasture is empirically degraded by collective overuse, a widely appropriated cultural symbol does not fracture or diminish in its capacity to convey meaning; on the contrary, its semantic resonance frequently proliferates precisely through unconstrained circulation. Consequently, to marshal the logic of environmental exhaustion in defense of semantic monopoly is to fundamentally misapprehend the mechanics of cultural capital.

The author references 'an overgrazed pasture' primarily in order to

While musicological historiography frequently frames the advent of musical modernism as a progressive destabilization of tonal hierarchy—a syntactic trajectory culminating in serialism—this narrative often obscures a parallel, arguably more profound ontological rupture: the transvaluation of silence. For classical and romantic composers, silence functioned teleologically as acoustic punctuation; it was an exclusionary void demarcating structural units of articulated sound. In contrast, certain late nineteenth-century Symbolist composers reconceptualized silence not as an absence, but as a primary material substance possessing its own intrinsic density. This paradigm shift, however, provoked a severe methodological crisis regarding musical orthography. Because the inherited notational grammar was optimized exclusively to map pitch coordinates and chronometric duration, it possessed no endogenous mechanism for articulating the qualitative textures of silence. Consequently, composers were compelled to parasitize existing expressive diacritics—such as *fermatas* and phrasing slurs—merely to indicate the psychological weight of a pause. Yet, this reliance on a profoundly sound-centric notational scaffolding inevitably compromised the ontological autonomy these composers sought to grant to silence, systematically anchoring the 'silent' substance to the acoustic vectors that immediately preceded and followed it.

Which one of the following statements regarding the "inherited notational grammar" is most strongly supported by the passage?

Legal scholars have long debated the boundaries of the "public trust doctrine," a common law principle holding that certain natural resources are preserved for public use and cannot be fully privatized. Traditionally, this doctrine was strictly confined to navigable surface waters and tidal lands. In recent years, however, driven by the escalating crisis of aquifer depletion and the sluggish pace of legislative action, some environmental advocates have forcefully argued for extending the public trust doctrine to encompass groundwater. These advocates contend that because groundwater and surface water are hydrologically inextricably linked—often functioning as a single, unified system—the legal protections historically afforded to one must logically extend to the other.

While this hydrological reality is undeniable, the push to subject groundwater to the public trust doctrine is fundamentally misguided. Extending the doctrine in this manner would not only generate profound legal uncertainty regarding established property rights, but it would also empower courts to make complex, ad hoc hydrological policy decisions that they are inherently ill-equipped to handle. The overarching goal of sustainable aquifer management is indeed imperative, yet achieving it through the retroactive application of a rigid common law doctrine is a clumsy approach that threatens widespread economic disruption.

Therefore, rather than attempting to shoehorn groundwater into the historical confines of the public trust doctrine, policymakers must recognize that aquifer conservation is best achieved through comprehensive, forward-looking statutory regimes. Such legislative frameworks, unlike piecemeal judicial decrees rooted in the public trust, can be meticulously tailored to balance the intricate ecological realities of groundwater systems with the profound economic reliances of current water users.

Which one of the following most accurately expresses the central thesis of the passage?