All practice questions

Let $m$ and $n$ be positive integers such that $72^2 \cdot m = n^3$. Which of the following statements MUST be true? Select all that apply.

Read the academic passage below regarding galactic dynamics. Based on the structural contrast signal ('do not... but rather') and contextual continuation clues, identify the most appropriate vocabulary word to fill the blank.

An employee's hourly wage increased from $\$20.00$ to $\$25.00$. What was the percent increase in the employee's hourly wage?

If $m$ is an even integer and $n$ is an odd integer, what is the value of $(-1)^m + (-1)^n$?

Read the passage below and determine which terms best complete each blank to preserve the logical and rhetorical coherence of the text. Which words correctly complete the blanks?

On the real number line, the point $P$ corresponds to the real number $x$. If $|x - 3| = 7$, which of the following is a possible value of $x + 5$?

Although the museum curator initially praised the newly acquired Renaissance portrait for its vibrant brushwork, subsequent laboratory analysis proved the attribution to be __________, revealing that extensive overpainting had disguised a much later origin. Which two of the following answer choices, when inserted into the blank, produce completed sentences that are similar in meaning?

In a community library, $\frac{4}{15}$ of the total book collection consists of fiction books, $\frac{2}{5}$ consists of non-fiction books, and the remaining 240 books are children's books. If $\frac{3}{8}$ of the fiction books are hardcovers and the rest are softcovers, how many softcover fiction books are in the library?

While early marine biologists characterized deep-sea abyssal ecosystems as biological deserts devoid of dynamic interaction, recent oceanographic surveys reveal that these environments are paradoxically ________, harboring dense clusters of specialized organisms that thrive on chemosynthetic energy.

Which of the following words best completes the sentence above?

In evolutionary biology, researchers have noted that phenotypic traits are rarely hardwired by genetic sequences alone; rather, certain physiological features remain remarkably plastic, enabling organisms to modify their structures in response to shifting environmental stressors. In the context of the passage, which of the following words best captures the meaning of 'plastic'?

Two positive integers $a$ and $b$ have prime factorizations of the form $a = 2^x \times 3^y \times 5^z$ and $b = 2^u \times 3^v \times 5^w$, where $x, y, z, u, v, w$ are non-negative integers. The greatest common divisor (GCD) of $a$ and $b$ is $180$, and the least common multiple (LCM) of $a$ and $b$ is $54,000$. If $a$ has exactly $24$ positive divisors, what is the value of $b$?

Passage:
In 1891, Dutch paleoanthropologist Eugène Dubois uncovered a fossilized skullcap along the Solo River at Trinil in East Java, designating the specimen Pithecanthropus erectus. Unlike contemporary evolutionists who searched exclusively for intermediate hominin forms in Europe, Dubois conducted excavations in the Dutch East Indies based on Ernst Haeckel's hypothesis that humans originated in the Asian tropics. Dubois's excavations yielded a femur in 1892 from the same stratigraphic layer, possessing a straight shaft indicating obligate bipedalism. Although Dubois argued that the cranial capacity—approximately 900 cubic centimeters—and the bipedal femur proved Pithecanthropus was an intermediate link between apes and humans, prominent anatomist Rudolf Virchow rejected this synthesis. Virchow contended that the skullcap belonged to an extinct giant gibbon and the femur to a modern human, asserting that the spatial separation of 15 meters between the findspots rendered their association biologically invalid. Subsequent radiometric dating confirmed the Trinil fauna to be approximately 700,000 to one million years old, establishing the remains as the first recovered fossils of Homo erectus.

According to the passage, Rudolf Virchow rejected Eugène Dubois's assertion that the excavated fossils represented a single intermediate organism primarily because

While earlier ethnomusicologists dismissed the coastal chants as mere aesthetic embellishments, recent archival discoveries confirm that the songs served a distinctly ________ purpose, encoding critical navigational routes and seasonal tidal patterns for merchant mariners. Which TWO of the following answer choices, when inserted into the sentence, create sentences that are coherent and equivalent in meaning?

Fill in the blank with the word that best completes the sentence logically based on the structural continuation signal.

An employee's annual salary was increased by $20\%$ at the beginning of 2024. At the end of 2024, the salary was decreased by $20\%$ from its updated value. At the beginning of 2025, the salary was increased by $10\%$ from its end-of-2024 value. If the initial salary before any of these changes was $S$, which of the following statements must be true? Select all such statements.

Let $N = 2^a \cdot 3^b \cdot 5^c$, where $a$, $b$, and $c$ are positive integers. The integer $N$ is divisible by $24$, has exactly $36$ positive integer divisors, and $\frac{N}{5}$ is not divisible by $25$. What is the least possible value of $a + b + c$?

On the real number line, $x$ is a real number such that $|x + 2| \le 5$. Which of the following could be the value of $x$? Select all such values.

For decades, oceanographers assumed that deep-sea benthic ecosystems were structurally (i)________, maintained only by the slow, continuous descent of organic detritus from surface waters. However, recent autonomous submersibles revealed that episodic, high-magnitude pulse events—such as whale falls and turbidity currents—exert a far more (ii)________ influence on benthic biodiversity than previously acknowledged. Consequently, rather than exhibiting a static equilibrium, these abyssal communities undergo dynamic cycles of disruption and recovery, rendering traditional steady-state ecological models fundamentally (iii)________.

Which set of terms, when inserted into the blanks, best preserves the cross-sentence structural and contextual coherence of the passage?

While the astronomer's early lab journals were praised for their meticulous empirical detail, her later theoretical monographs were criticized for being exceptionally __________; they relied heavily on unverified premises rather than concrete observational proof. Which two of the following answer choices, when inserted into the sentence, produce completed sentences that are similar in meaning?

Let $a$ and $b$ be positive integers such that $15a = 28b$. Which of the following statements MUST be true? Select all that apply.