Tüm alıştırma soruları

If $n$ is a real number, is $n$ an integer?

(1) $n^2 - 3n$ is an integer.
(2) $n^2 + 5n$ is an integer.

An urban transit authority conducted a comprehensive survey of all commuter rail passengers traveling on Line X during peak morning hours. The survey established that every passenger who traveled with a monthly pass completed their journey in under 45 minutes. The survey also determined that 30 percent of all morning peak passengers on Line X did not travel with a monthly pass, and that no passenger without a monthly pass completed their journey in under 30 minutes.

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

Conservators at a prominent museum have long maintained that installing centralized precision-humidity control systems in historic buildings is essential for preventing the degradation of centuries-old wooden panel paintings. However, a recent study of vintage panel deterioration shows no significant difference in structural decay between paintings housed in high-tech climate-controlled rooms and those kept in traditional buildings with simple passive ventilation. Because wooden panels naturally adjust to gradual seasonal fluctuations without suffering stress fractures, the costly replacement of traditional ventilation systems with complex environmental controls is an unnecessary expenditure for preserving these artworks.

Which of the following best describes the roles played by the two bolded statements in the argument?

Passage:
During the late nineteenth century, the North American timber industry experienced a rapid transition from river-driven log drives to specialized rail transport. Early river drives relied heavily on seasonal spring freshets—periods of high water caused by snowmelt—to flush timber downstream to coastal sawmills. Consequently, timber operations remained idle throughout the winter and late summer, leaving capital equipment underutilized for nearly seven months each year. In contrast, the implementation of narrow-gauge logging railways allowed timber syndicates to harvest and haul logs continuously regardless of weather conditions or river volume. Although railway construction demanded substantial initial capital outlay, the resulting year-round operations significantly lowered fixed costs per unit of lumber produced. Furthermore, year-round harvesting enabled sawmills to supply urban construction markets during winter months when timber prices historically peaked due to seasonal shortages, thereby capturing substantial market premiums that easily offset the debt service on railway infrastructure.

Statement: Based on the passage, timber syndicates that adopted narrow-gauge logging railways were able to offset their infrastructure debt service in part by selling lumber during months when market prices were elevated due to seasonal supply shortages.

Executive board members at a major technology firm maintain that purchasing comprehensive cybersecurity insurance is an unnecessary expense, contending that internal cash reserves are sufficient to absorb potential breach penalties. However, recent empirical studies demonstrate that the indirect financial damage of a major breach—including reputational harm and lost customer lifetime value—routinely exceeds a firm’s total liquid reserves by several orders of magnitude. Furthermore, insurance underwriters require continuous security audits that proactively identify software vulnerabilities before exploit incidents occur. Therefore, relying exclusively on internal financial reserves to manage enterprise cyber risk is an unsound management strategy.

In the argument given, the two boldfaced portions play which of the following roles?

To curb local air pollution, urban planners have advocated that the city municipal authority mandate all commercial delivery fleets to adopt zero-emission vehicles by the end of the decade. Industry representatives oppose the plan, claiming that the substantial capital expenditure required will bankrupt smaller logistics firms and disrupt urban supply chains. However, this objection relies on an incomplete picture of the policy package. The municipal authority has pledged to finance the installation of free fleet-charging hubs and provide low-interest loans specifically tailored for small operators. Consequently, the implementation of the mandate will not trigger the widespread failure of small logistics businesses.

In the argument given, the two boldfaced portions play which of the following roles?

For over a century, economic historians viewed medieval merchant guilds primarily as rent-seeking cartels designed to restrict competition, artificially inflate prices, and secure legal monopolies from local sovereigns. This traditional consensus, heavily influenced by classical economic theory, posited that guilds generated deadweight losses that stifled urban commercial expansion until Enlightenment-era market liberalization dismantled their institutional grip. However, in the late twentieth century, revisionist scholars challenged this view, arguing that guilds emerged primarily to solve severe information asymmetries and enforcement problems inherent to long-distance trade. According to this institution-focused framework, guilds provided crucial public goods—such as contract enforcement across political jurisdictions, quality verification for traded merchandise, and collective diplomatic bargaining leverage against predatory rulers who might otherwise confiscate foreign merchants' property.

Recently, a third wave of scholarship has sought to synthesize these opposing perspectives by examining the temporal evolution of guild functionality. These micro-historical analyses suggest that whether a guild acted predominantly as an efficiency-enhancing institution or a growth-inhibiting cartel depended largely on the maturity of surrounding state apparatuses. In the early medieval period, when centralized legal structures were rudimentary or non-existent, merchant guilds operated essentially as privatized governance systems that significantly reduced transaction costs and expanded trade volumes. However, as territorial states developed robust judicial systems and public enforcement mechanisms during the early modern era, the governance functions of guilds became redundant. Rather than dissolving voluntarily, mature guilds leveraged their accumulated wealth and institutional influence to lobby state authorities for statutory monopolies, effectively transitioning from growth-promoting institutions into rent-seeking cartels. Thus, the debate is not whether guilds were inherently efficient or predatory, but how shifting external institutional contexts transformed their economic impact over time.

Which of the following best describes the overall rhetorical plan of the passage?

For all non-zero real numbers $x$ and $y$ such that $x \neq y$, the Data Sufficiency Yes/No target question "Is $\frac{x}{y} + \frac{y}{x} > 2$?" is algebraically equivalent to the simplified target question "Is $xy > 0$?"

Consider the following argument: A regional hospital system plans to replace all traditional brass door handles across its facilities with handles coated in a novel antimicrobial polymer coating in order to reduce patient infection rates. Hospital administrators reason that because laboratory tests demonstrate the polymer kills 99 percent of surface bacteria within fifteen minutes of contact, installing these coated handles will significantly decrease the incidence of hospital-acquired infections.

True or False: Determining whether the routine chemical cleaning solutions used by hospital sanitation staff rapidly degrade the antimicrobial efficacy of the polymer coating upon contact constitutes a valid application of the Test of Variance for evaluating the validity of the administrators' argument.

If $x$ is a real number, is $x$ an integer?

(1) $x^2 + x$ is an integer.
(2) $x^3 + x^2$ is an integer.

To reduce annual operational expenditures, the municipal water authority of Oakhaven plans to install acoustic sensor networks along its underground pipeline grid. The authority reasons that because these sensors detect acoustic frequencies generated by micro-leaks long before water breaches the surface, maintenance crews can repair small pipe fractures early, thereby significantly lowering total water loss costs and expensive emergency excavation expenses.

Which of the following, if true, most seriously weakens the municipal water authority's argument?

[Tab 1: Cold-Chain Storage & Transport Protocol (2026 Revision)]
Pharmaceutical Logistics Regulatory Policy:
- Class 1 Biologics: Must be maintained at $2^\circ\text{C}$ to $8^\circ\text{C}$ during transit. Any temperature excursion above $8^\circ\text{C}$ lasting strictly more than 30 minutes triggers mandatory thermal quarantine. A $15\%$ surcharge is assessed on the shipment's base transport fee for quarantined items, unless the freight carrier holds a Tier-A Thermal Compliance Certification.
- Class 2 Biologics: Must be maintained below $-20^\circ\text{C}$. Any excursion above $-20^\circ\text{C}$ invalidates the shipment unless a secondary liquid nitrogen (LN2) backup system was logged active throughout the entire duration of the excursion.

[Tab 2: Q2 Carrier Audit Log (Apex Cargo Services)]
- Shipment #801: Class 1 Biologics; Base Transport Fee: $\$12,000$; Temp Excursion: Reached $10^\circ\text{C}$ for 45 minutes; Secondary LN2 Backup: N/A; Carrier Certification: Tier-B Thermal Compliance.
- Shipment #802: Class 2 Biologics; Base Transport Fee: $\$25,000$; Temp Excursion: Reached $-15^\circ\text{C}$ for 15 minutes; Secondary LN2 Backup: Logged Active; Carrier Certification: Tier-A Thermal Compliance.
- Shipment #803: Class 1 Biologics; Base Transport Fee: $\$18,000$; Temp Excursion: Reached $9^\circ\text{C}$ for 20 minutes; Secondary LN2 Backup: N/A; Carrier Certification: Tier-B Thermal Compliance.

Statement: Based on the provided protocol and carrier audit log, Shipment #801 is subject to a mandatory $\$1,800$ thermal surcharge, whereas Shipment #803 incurs no thermal surcharge.

If $x$ and $y$ are positive real numbers, is $x$ an integer?

(1) $x + y$ is an integer, and $x^2 + xy$ is an integer.
(2) $x - y$ is an integer, and $x^2 - y^2$ is an integer.

If $k$ is a positive real number, is $k$ an integer?

(1) $\sqrt{k}$ is an integer.
(2) $k^2 - 4k$ is an integer.

The table below details operational telemetry for eight municipal battery energy storage system (BESS) microgrid zones during 2025:

Consider the following three independent statements:

I. If the zones are sorted in ascending order by Battery Capacity (MWh), the median Peak Efficiency (%) of the lower half of the sorted zones is greater than $90.5\%$.
II. The average annual energy discharged per MWh of battery capacity across the three zones with the fewest unplanned maintenance hours is strictly greater than $0.40\text{ GWh per MWh}$.
III. Among the zones with a Peak Efficiency of at least $92.0\%$, exactly four zones recorded fewer than $40$ unplanned maintenance hours.

Based on the table provided, is the evaluation that Statement I is False, Statement II is True, and Statement III is True correct?

The table below presents operational metrics for municipal EV charging infrastructure across six urban transit sectors in 2025.

Evaluate the following statement as True or False based on the information provided:

Among all transit sectors where fast-charging stations constitute at least $40\%$ of the total EV stations, the overall proportion of total energy delivered that was consumed by commercial fleets is greater than $50\%$.

Passage:
Recent genomic sequencing of Asgard archaea inhabiting deep-sea hydrothermal vent sediments has provided crucial empirical evidence regarding the origins of eukaryotic cellular complexity. Unlike all previously characterized prokaryotes, Asgard archaea possess functional genes encoding proteins structurally analogous to eukaryotic actin filaments and endosomal sorting complexes. Evolutionary biologists initially hypothesized that eukaryotic progenitor cells acquired these complex structural proteins exclusively after the primary endosymbiotic engulfment of an alpha-proteobacterium—the event that gave rise to mitochondria.

However, the presence of these 'eukaryotic signature proteins' (ESPs) in uncultivated Asgard lineages demonstrates that the structural machinery required for membrane remodeling and cellular engulfment evolved prior to mitochondrial acquisition. Crucially, phylogenetic analyses indicate that while Asgard lineages possess ESPs, they lack the specific lipid synthesis pathways necessary to construct the ester-linked phospholipid membranes characteristic of eukaryotes, retaining instead the ether-linked isoprenoid membranes typical of archaea. Consequently, researchers infer that the transition from ether-linked to ester-linked membrane chemistry occurred after the primitive host cell established stable endosymbiosis with the mitochondrial ancestor, rather than during the initial structural diversification of pre-eukaryotic archaea.

Based on the premises in the passage, evaluate whether the following statement is True or False:
"The evolutionary development of membrane remodeling machinery in the ancestral host lineage preceded the chemical transition from ether-linked to ester-linked membrane lipids."

In 2025, an architectural design firm divided its working hours among commercial, residential, and municipal projects. Commercial projects accounted for $0.40$ of the total hours. Of the remaining hours, $\frac{5}{12}$ were spent on residential projects, and the rest were spent on municipal projects.

In 2026, the firm's total working hours increased by $25\%$. Commercial project hours decreased by $15\%$, while residential project hours increased by $40\%$. By what percent did the number of hours spent on municipal projects increase from 2025 to 2026?

At the start of a fiscal year, a sovereign wealth fund allocated its capital into three asset classes: Stocks, Bonds, and Commodities. Exactly $0.40$ of the total capital was allocated to Stocks. Of the remaining capital, $\frac{1}{3}$ was allocated to Bonds and the rest was allocated to Commodities. Over the course of the fiscal year, the value of Stocks increased by $15\%$ and the value of Bonds decreased by $10\%$. If the total value of the fund increased by $5\%$ by the end of the fiscal year, by what percent did the value of Commodities change?