All practice questions

### Models of Venusian Resurfacing

The surface of Venus has remarkably few impact craters, and they are randomly distributed across the planet. This indicates that the surface is geologically young, with an estimated age of $300$ to $600\text{ million years}$. Two models have been proposed to explain how the Venusian surface was renewed.

Model 1 (Catastrophic Resurfacing)
Venus has a single, thick, rigid lithospheric plate. Because Venus lacks plate tectonics, internal radiogenic heat cannot be continuously released. Instead, heat accumulates in the mantle, causing it to warm and soften. Eventually, the hot mantle weakens the overlying lithosphere, causing the entire lithosphere to founder and sink into the mantle in a catastrophic, planet-wide event. This is accompanied by massive global volcanism that completely covers the planet in lava, destroying all pre-existing craters within a short span of $10$ to $50\text{ million years}$. Following this event, the lithosphere cools and solidifies again, remaining geologically inactive for hundreds of millions of years until the next cycle.

Model 2 (Gradual Resurfacing)
Venus does not experience planet-wide catastrophes. Instead, it undergoes steady, ongoing tectonic and volcanic activity that is localized. Plumes of hot mantle material rise continuously, causing localized volcanic eruptions and rifting that renew small portions of the surface at any given time. Over hundreds of millions of years, these smaller, scattered volcanic events resurface the entire planet incrementally. While this process is slow and continuous, it produces a spatially random distribution of craters because new craters are constantly forming while older craters are randomly covered by localized lava flows.

Based on the models described, match each scientific assertion on the left with the model(s) that support it on the right.

On a certain map, a distance of $3$ inches represents an actual distance of $45$ miles. If the distance between two cities on this map is $8$ inches, what is the actual distance, in miles, between the two cities?

A highway has exits at mile markers $-7$ and $9$. A new rest stop is to be built at mile marker $c$ such that its distance from the exit at mile marker $-7$ is exactly $3$ times its distance from the exit at mile marker $9$. Which of the following is a possible value of $c$?

A scientist is writing a report on acoustic levitation. Review the short excerpt below, and determine which of the words—'hold', 'clutch', 'suspend', or 'snatch'—most precisely and clearly fits the blank to maintain the formal register of the writing?

The software developer successfully wrote the code for the new mobile application, but the testing team discovered several critical bugs during the trial run.

Which choice is the best version of the underlined portion?

In a school auditorium, $\frac{3}{8}$ of the total seats are in the balcony, and the remaining seats are on the main floor. For the spring play, $80\%$ of the balcony seats were occupied, and $60\%$ of the main floor seats were occupied. If there were exactly 117 empty seats in the auditorium, what was the total number of seats in the auditorium?

Sourdough bread relies on a wild yeast starter, which is a symbiotic culture of yeast and bacteria. Because this starter must be fed water and flour on a regular basis at scheduled intervals, bakers often treat it like a household pet.

Which of the following choices best replaces the underlined portion of the sentence?

Discovered in 1799 by French soldiers in Egypt, the Rosetta Stone provided the key to deciphering Egyptian hieroglyphs. The stone features a decree written in three different scripts: hieroglyphic, Demotic, and Ancient Greek. Because Greek was widely understood at the time, scholars could use it to translate the other two scripts. For decades, researchers went all out and did everything they could to unlock the mysterious symbols carved into the dark granodiorite. Finally, in 1822, French scholar Jean-François Champollion announced the complete translation, opening a window into ancient Egyptian history.

Which of the following choices to replace the underlined portion best maintains the formal, academic tone of the passage?

### Origin of Titan's Atmospheric Nitrogen

Titan, Saturn’s largest moon, has a dense, nitrogen-rich atmosphere. Scientists debate the origin of this atmospheric molecular nitrogen ($N_2$).

Hypothesis 1
Titan formed in a warm region of the Saturnian subnebula where molecular nitrogen gas could not condense. Instead, Titan accreted nitrogen primarily in the form of ammonia ($NH_3$) ice. Over time, internal heating caused the ammonia to outgas into the early atmosphere. Solar ultraviolet (UV) radiation then photolyzed the atmospheric ammonia, splitting it into nitrogen gas ($N_2$) and hydrogen gas ($H_2$). The lighter hydrogen escaped into space, leaving behind a thick layer of $N_2$. Thus, Titan’s atmospheric nitrogen is a secondary product of chemical reactions.

Hypothesis 2
Titan accreted in a much colder region of the Saturnian subnebula, allowing molecular nitrogen ($N_2$) gas to be directly trapped as clathrate hydrates (icy cages) within Titan's silicate and water-ice core during formation. As Titan heated up internally due to radioactive decay, this primordial $N_2$ gas was released directly from the interior into the atmosphere through cryovolcanism. Under this hypothesis, Titan’s atmospheric nitrogen is primordial, having undergone no major chemical conversion from ammonia.

According to Hypothesis 1, which of the following processes was directly responsible for producing the molecular nitrogen ($N_2$) now found in Titan's atmosphere?

While studying the ruins of Pompeii, archaeologists discovered murals preserved in remarkable detail. The reason why the murals survived is because the volcanic ash sealed them from oxygen.

Which of the following options best replaces the underlined portion of the sentence?

Bioluminescent fungi grow on decaying wood in damp forests, emitting a soft green glow that attracts nocturnal insects. Found primarily in tropical climates, mycologists have identified over one hundred species of these glowing mushrooms. The light is produced by a chemical reaction involving a compound called luciferin.

Which of the following is the most grammatically correct and effective version of the underlined portion?

Complete the sentence by typing the correct subject from the choices ('the pianist' or 'the concerto') to avoid a dangling modifier.

Three machines—$X$, $Y$, and $Z$—produce widgets at constant rates. The ratio of the production rate of Machine $X$ to Machine $Y$ to Machine $Z$ is $3:4:6$, respectively. Working together at their constant rates, the three machines can complete a standard production order in exactly $8$ hours. A new order of the same size is started with all three machines working together. After $3$ hours, Machine $Z$ breaks down and stops working, and the production rate of Machine $Y$ decreases by $25\%$. If Machine $X$ and the slowed Machine $Y$ continue working to complete the order, what is the total number of hours required to complete this entire second order?

In 1766, Jeanne Baret embarked on a global voyage of discovery disguised as a male assistant to the expedition’s botanist. Over the next several years, she gathered thousands of plant specimens from diverse ecosystems. Her contributions were crucial to the expedition's success, yet her true identity was eventually uncovered during the journey. Despite the challenges she faced, her botanical discoveries helped broaden our understanding of global biodiversity.

Which choice most precisely and clearly fits the context of the sentence?

Which of the following is equal to the sum of $4 \times 10^4$ and $3 \times 10^3$, written in scientific notation?

The archaeologist discovered a hidden chamber inside the ancient temple, she carefully photographed the artifacts.

Which choice is the best version of the underlined portion?

A company allocates its annual marketing budget among digital, print, and television advertisements in the ratio $4:3:5$, respectively. Due to a strategy change, the company increases its digital advertising budget by $25\%$, decreases its print advertising budget by $40\%$, and increases its television advertising budget by $15\%$. If the company's total marketing budget after these changes is $\$376,500$, what was the company's original print advertising budget?

If $x$ and $y$ are integers such that $|x + 3| = 4$ and $|y - 2| = 6$, what is the maximum possible value of $|x - y|$?

Historical preservationists face a unique set of challenges when restoring nineteenth-century structures. To maintain historical integrity, they must source authentic materials, however, this process often requires searching salvage yards across the country. Additionally, modern building codes must be met without compromising the aesthetic value of the original design.

Which of the following is the best replacement for the underlined portion of the passage?

The variable $p$ represents the value $8 \times 10^5$, and the variable $q$ represents the value $2 \times 10^{-3}$. When the expression $\sqrt{\frac{p}{q}}$ is simplified and written in scientific notation, which of the following is the resulting value?