Tüm alıştırma soruları

In circle $O$, a sector with a central angle of $60^\circ$ has an area of $6\pi$. In circle $P$, a sector with a central angle of $120^\circ$ has an arc length equal to the arc length of the sector in circle $O$. What is the area of the sector in circle $P$?

Match each advanced GRE vocabulary word on the left with its most precise functional near-synonym on the right.

When the positive integer $n$ is divided by $9$, the remainder is $5$. What is the remainder when $n^2 + 4n + 7$ is divided by $9$?

If $|3x - 6| \le 12$, which of the following inequality ranges represents all possible values of $x$?

Historians of technology have traditionally posited that the widespread adoption of mechanical fulling mills in fourteenth-century European cloth production was driven primarily by severe labor shortages following demographic declines. However, a recent analysis of Flemish guild archives reveals that investments in water-powered mills surged during the 1320s—a decade characterized by population growth and depressed real wages. The archival records indicate that cloth merchants financed mill construction primarily to establish centralized administrative oversight and uniform fabric density, features unachievable through decentralized manual fulling. Consequently, researchers concluded that labor scarcity was not a necessary condition for early industrial mechanization in the textile sector.

Which of the following, if true, most seriously undermines the conclusion drawn by the researchers regarding early industrial mechanization?

In studying Holocene marine climate shifts, oceanographers have historically relied on shallow-water reef corals as proxies for sea-surface temperature variations. However, recent analyses of deep-sea scleractinian corals—specifically *Lophelia pertusa* harvested from bathyal depths along the North Atlantic margin—have challenged the assumption that deep-ocean thermal regimes remained stagnant throughout these epochal shifts. Unlike surface-dwelling corals, whose skeletal strontium-to-calcium ($Sr/Ca$) ratios correlate directly with ambient surface temperatures, *Lophelia pertusa* incorporates barium ($Ba/Ca$) into its aragonite skeleton in proportion to localized nutrient upwelling and sub-thermocline oceanic mixing rather than ambient temperature alone. Notably, during the 8.2-kiloyear cold event, while North Atlantic sea-surface temperatures registered marked cooling, deep-coral $Ba/Ca$ ratios exhibited a sharp transient reduction, whereas skeletal $Sr/Ca$ ratios in the same deep-sea specimens remained invariant. Researchers attribute this localized $Ba/Ca$ decline not to temperature fluctuations, but to the suppression of deep-water convective overturn caused by meltwater pulses flooding the subpolar gyre. Consequently, deep-sea coral skeletal geochemistry provides a precise record of vertical hydrographic reorganization independent of surface thermodynamic trends.

According to the passage, the temporary reduction in barium-to-calcium ($Ba/Ca$) ratios observed in *Lophelia pertusa* during the 8.2-kiloyear event was directly caused by which of the following?

Conservators at a national museum recently analyzed a Renaissance portrait attributed to Raphael, who died in 1520. Using X-ray spectroscopy, they examined the portrait's lead-white pigment and detected elemental impurities characteristic exclusively of lead-manufacturing processes introduced after 1650. Based on this finding, the conservators concluded that the portrait is a later forgery rather than an authentic work by Raphael.

Which of the following is an assumption on which the conservators' conclusion depends?

Complete the passage below by filling in each blank with the word that best preserves the logical cause-and-effect relationships established by the context clues.

A regional logistics firm upgraded its ground delivery fleet management software to an automated, predictive routing system. During the six months following the upgrade, the firm recorded a 15 percent decrease in total fuel consumption across all ground routes. The chief operating officer concluded that the new software directly caused the improved fuel efficiency, and subsequently recommended implementing the exact same system across the company's container shipping vessel fleet to achieve an identical 15 percent fuel reduction. Which of the following statements describe logical vulnerabilities in the chief operating officer's reasoning? Select all that apply.

Complete the passage below by providing the appropriate word for each blank that best preserves the logical support and cause-effect relationships established in the sentence.

In the early nineteenth century, astronomers observed subtle irregularities in the orbit of Uranus that could not be accounted for by the gravitational influence of known celestial bodies. While some theorists suggested that Isaac Newton's law of universal gravitation might break down at immense interplanetary distances, Urbain Le Verrier hypothesized the existence of an undiscovered outer planet exerting a gravitational perturbation. By calculating the expected position of this hypothetical body solely through mathematical modeling, Le Verrier directed the Berlin Observatory to the precise coordinates where Neptune was subsequently discovered in 1846. This triumph not only confirmed the existence of a new planet but also dramatically reinforced the universal applicability of Newtonian mechanics across vast cosmic scales.

Based on the passage, which of the following can be inferred regarding the theorists who questioned Newton's law of universal gravitation prior to 1846?

Throughout the twentieth century, environmental conservation was largely defined by a philosophy of preservationism, which held that natural ecosystems should be left entirely undisturbed by human activity. Proponents of this view believed that wilderness possessed an intrinsic balance capable of self-regulation. However, contemporary ecological research has increasingly challenged this passive model, demonstrating that historical human disturbances and global trade have irreversibly altered natural habitats. Modern ecologists argue that deliberate human intervention is frequently required to check the proliferation of invasive species that threaten vulnerable native biodiversity. Without targeted management, aggressive non-native flora can rapidly outcompete endemic species for nutrients and light, destabilizing entire food webs. Consequently, contemporary environmental management has evolved from strict non-interference to active stewardship, recognizing that preserving ecological integrity often demands strategic, hands-on intervention rather than mere observation.

In the context of the passage, which of the following words most nearly means 'check'?

Consider the following excerpt from a draft Analytical Writing response discussing public policy and urban planning:

"Proponents of municipal automation contend that replacing human-driven transit fleets with autonomous vehicles will inherently eliminate urban traffic congestion through real-time traffic optimization. [________], preliminary data from initial pilot programs indicate that total vehicle miles traveled actually increased due to empty autonomous shuttles continuously cruising while awaiting dispatch. Therefore, relying exclusively on algorithmic efficiency fails to mitigate the underlying systemic demand for urban mobility."

Which of the following transitional phrases, if inserted into the blank, most effectively establishes a precise logical progression and cohesive shift from the proponents' claim to the counter-evidence?

Read the short passage and identify the structural role of the second sentence. Fill in the blank with a verb that accurately describes its rhetorical function.

While early twentieth-century historians generally attributed the rapid expansion of the textile industry in New England primarily to technological innovations in water-powered looms, recent archival research reveals that capital accumulation strategies played an equally decisive role. Specifically, regional merchant-capitalists redirected profits from maritime trade into industrial infrastructure during the embargo of 1807. Unlike European manufacturers, who relied heavily on skilled artisan guilds, New England factory owners implemented standardized operational protocols that allowed them to employ unskilled labor. Consequently, despite facing higher raw material costs than their foreign competitors, American mills achieved lower per-unit production costs by significantly reducing labor expenses and maximizing machinery throughput.

According to the passage, New England factory owners were able to employ unskilled labor because they did which of the following?

Many urban planners argue that introducing high-speed rail lines between adjacent metropolitan areas always stimulates economic growth in smaller intermediate towns along the route. However, a recent comprehensive study of regional transit networks over the past two decades demonstrates that such rail links predominantly funnel commerce and skilled labor toward the larger terminal cities. Consequently, rather than revitalizing smaller intermediate municipalities, high-speed rail connections often accelerate their economic decline by facilitating outward commuting and business relocation. Therefore, municipal governments in smaller towns should refrain from heavily subsidizing high-speed rail infrastructure under the assumption of guaranteed local growth.

Which of the following express main claims or conclusions advocated by the author in the passage above? (Select all that apply.)

In the figure, line $l_1$ is parallel to line $l_2$. Point $A$ lies on line $l_1$, while points $B$ and $C$ lie on line $l_2$ such that $B$ is to the left of $C$. Line segments $AB$ and $AC$ extend from line $l_1$ to line $l_2$ to form $\triangle ABC$. The measure of interior angle $\angle BAC$ is $(2x + 10)^\circ$, the measure of interior angle $\angle ABC$ is $(3x - 15)^\circ$, and the measure of the exterior angle at vertex $C$ along line $l_2$ is $(6x - 35)^\circ$. What is the degree measure of angle $\angle BAC$?

If $|2x - 4| \le 6$, which of the following values could be a solution for $x$? Select all that apply.

If $x > 1$, which of the following expressions are equivalent to $\frac{\sqrt{x^5 \cdot x^3}}{(x^{-2})^{-1}}$? Select all such expressions.

If $x$ satisfies the inequality $|3 - 2x| > 9$, which of the following could be the value of $x$? Select all that apply.