All practice questions

An investor allocated a total principal of $\$25,000$ between two savings accounts, Account X and Account Y. Account X earns simple interest at an annual rate of $8\%$, while Account Y earns interest at an annual rate of $10\%$, compounded annually. If after $2$ years the total interest earned from Account Y exceeds the total interest earned from Account X by $\$1,550$, what was the amount, in dollars, invested in Account Y?

In a corporate evaluation of $200$ employees, performance scores range from $0$ to $100$. An employee with a score of $84$ scored strictly higher than $150$ employees and strictly lower than $42$ employees, while the remaining employees received a score of exactly $84$. If the percentile rank of a score is defined as the percentage of all scores strictly below it plus half the percentage of all scores equal to it, what is the percentile rank of a score of $84$?

An analyst at an investment firm evaluates a portfolio of $160$ corporate bonds for two potential risk factors: credit rating downgrade risk and liquidity risk. The evaluation reveals that $60$ bonds have credit rating downgrade risk, $72$ bonds have liquidity risk, and $64$ bonds have neither risk factor. If a bond is selected at random from those in the portfolio that have at least one of the two risk factors, what is the probability that it has credit rating downgrade risk? Express your answer as a decimal.

How many integer values of $x$ satisfy the inequality $||2x - 5| - 7| \leq 4$?

In a survey of $120$ corporate executives, $70$ executives read Magazine A, $50$ read Magazine B, and $25$ read both Magazine A and Magazine B. How many of the executives surveyed read neither Magazine A nor Magazine B?

To mitigate urban heat island effects, municipal planners in Oakhaven proposed planting deciduous trees along major commercial corridors. Critics argued that winter leaf drops would significantly increase sidewalk maintenance costs for local business owners. However, a comprehensive study of similar mid-sized cities revealed that commercial corridors with dense tree canopies consistently experience an eight percent boost in winter foot traffic, generating retail sales revenues that far exceed seasonal street sweeping expenses. Therefore, implementing the tree-planting initiative will yield a net financial gain for corridor merchants.

Which of the following best describes the function of the claim that commercial corridors with dense tree canopies consistently experience an eight percent boost in winter foot traffic?

Many urban planners argue that expanding municipal bus networks is the most effective strategy for reducing downtown traffic congestion. However, recent data from several mid-sized cities indicates that bus route expansions primarily attract previous pedestrians rather than drivers. Therefore, municipal governments seeking to reduce downtown traffic should invest in dedicated bicycle infrastructure rather than expanding bus networks.

Which of the following best expresses the main conclusion of the argument above?

Passage:
In the early twentieth century, large manufacturing enterprises faced unprecedented operational friction under the traditional unitary organizational structure (U-form), which centralized functional departments such as sales, production, and purchasing under a single executive hierarchy. As product lines diversified, senior executives became overwhelmed by daily operational logistics, diminishing their capacity for strategic capital allocation. To resolve this bottleneck, corporate architects introduced the multidivisional structure (M-form), partitioning the enterprise into semi-autonomous operating divisions organized by product or region, each governed by its own general manager. Under the M-form, divisional managers retained sole authority over immediate operational tactics and market adaptations, freeing top executives to focus exclusively on long-term strategy and cross-divisional capital distribution. Crucially, centralized executive control was maintained through rigorous financial auditing mechanisms; top management evaluated divisional performance against standard return-on-investment metrics, reallocating capital away from underperforming units toward high-yield divisions. Consequently, while divisional managers enjoyed operational autonomy, their strategic survival depended directly upon meeting centralized financial benchmarks set by executive management.

Based on the passage above, evaluate whether the following statement is True or False: Under the multidivisional structure (M-form), senior executives relinquished direct operational oversight of product divisions while using standardized financial metrics to retain strategic control over corporate capital deployment.

Recent legislation in a certain state mandates that all commercial buildings install automated energy-management systems. Local business owners claim that the upfront installation costs will force small retail stores into bankruptcy. However, state environmental regulators point out that the energy savings generated within the first six months typically exceed the initial setup costs.

In the argument above, the two bolded statements play which of the following roles?

For over three decades, Denise Schmandt-Besserat’s token-enclosure hypothesis dominated scholarship regarding the origins of Near Eastern writing. Her model posited a seamless, evolutionary progression: plain geometric clay tokens representing specific agricultural commodities were progressively enclosed within hollow clay spheres (bullae), impressed onto the outer surfaces of these containers for visual verification, and ultimately flattened into two-dimensional pictographs impressed upon clay tablets. This gradualist paradigm framed proto-cuneiform not as a deliberate intellectual invention, but as the passive administrative outcome of millennia-old agrarian accounting practices.

However, recent epigraphical re-examinations of the Late Uruk administrative archives have cast substantial doubt on this linear continuum. Scholars such as Jean-Jacques Glassner argue that the token-to-tablet hypothesis conflates two fundamentally distinct semiotic systems. While tokens unquestionably functioned as concrete mnemonic counters in localized transactions, proto-cuneiform script exhibits an abstract, syntactically structured sign system created not merely to tally physical assets, but to record complex institutional relationships and labor obligations. Moreover, precise stratigraphical re-evaluations indicate that complex tokens and fully developed numerical tablets coexisted synchronously within Uruk IV strata, directly undermining the assertion of a strict chronological sequence.

To resolve these empirical discrepancies, contemporary paleographers propose a dual-track framework. They assert that while token usage established a cultural precedent for symbolic external memory, true writing emerged through a deliberate conceptual rupture—a centralized, state-sponsored structural innovation engineered to standardize record-keeping across expanding urban polities. Far from representing a mere transcript of physical token counting, early proto-cuneiform constituted an autonomous cognitive technology capable of generating novel semantic categories. Although this revised synthesis acknowledges the preliminary role of token administrative tools, it ultimately reframes the emergence of literacy not as an organic byproduct of accounting, but as a conscious structural leap in social governance and information architecture.

Which of the following best describes the rhetorical organization of the passage as a whole?

What is the sum of all integer values of $x$ that satisfy the inequality $|x^2 - 6x + 5| < 2x - 2$?

Passage:
In late nineteenth-century municipal public health governance, European cities increasingly shifted water supply systems from private concessionaires to municipal ownership. Historical analysis often attributes this transition exclusively to growing epidemiological awareness regarding waterborne pathogens, such as cholera and typhoid. However, fiscal records indicate that private water providers frequently faced insurmountable capital constraints when required to extend filtration infrastructure into low-density urban peripheries, where prospective consumer revenues could not offset fixed distribution costs. Concurrently, municipal authorities gained access to low-interest municipal bond markets that were legally inaccessible to private entities. Consequently, local governments were able to finance capital-intensive filtration facilities while maintaining uniform user tariffs across diverse residential districts. Nevertheless, in municipalities where private operators had secured long-term contracts with guaranteed rate returns, municipalization was routinely delayed by decades, regardless of the local incidence of waterborne diseases. Thus, while public health concerns provided the ideological justification for municipal takeover, the timing and execution of this administrative shift were primarily determined by municipal debt access and existing contractual guarantees.

Statement: Based on the passage, a European municipality experiencing a high incidence of waterborne disease and possessing access to low-interest municipal bond markets would still experience significant delays in transitioning to municipal water ownership if private concessionaires held long-term contracts with guaranteed rate returns.

To alleviate chronic water scarcity in arid agricultural regions, several regional authorities have introduced market-based water rights trading. Proponents contend that allowing farmers to sell unused allocations incentivizes water conservation and directs resources to high-value industrial uses. However, critics argue that unrestricted trading leads to 'water farming,' where investors purchase land purely to extract and export groundwater, permanently depleting local aquifers and undermining rural economies. Nonetheless, proponents maintain that proper regulatory caps on transfer volumes can prevent over-extraction while preserving economic efficiency.

In the argument above, the statement that unrestricted trading leads to 'water farming' functions in which of the following ways?

For all real numbers $x$ and $y$ such that $xy \neq 0$ and $|x| \neq |y|$, the Data Sufficiency Yes/No target question "Is $\frac{x^2 y - x y^2}{x^3 y - x y^3} > 0$?" is algebraically equivalent to asking "Is $x + y > 0$?".

A metropolitan transit authority recently installed automated, contactless payment turnstiles across its subway network, allowing commuters to tap credit cards directly rather than purchasing paper farecards. Following the installation, queue times at station entrances decreased significantly, and recorded incidents of gate-jumping fare evasion dropped by 40 percent. However, during the six months after the rollout, total fare revenue collected by the transit authority decreased by 12 percent compared to the same period in the previous year, despite total ridership remaining constant and base ticket prices remaining unchanged. Which of the following, if true, most helps to resolve the apparent discrepancy described above?

A recent study observed that city residents who regularly visit public parks report lower average stress levels than residents who rarely visit parks. Based on this observation, the city council concluded that spending time in public parks directly causes a reduction in stress levels for city residents. The reasoning in the city council's argument is most vulnerable to criticism on which of the following grounds?

Read the following passage:

In economic history, the long-held institutionalist perspective posits that formal legal frameworks are the sole driver of post-industrial market liquidity. However, recent empirical analyses of nineteenth-century maritime credit markets suggest a more complex dynamic. While formal statutes provided baseline enforcement, informal reputation networks among merchant syndicates routinely mitigated transaction costs far more effectively than statutory courts, which suffered from severe administrative delays. Rather than replacing formal legal structures, these informal networks operated synergistically with them, relying on statutory arbitration only as a secondary recourse when reputation-based sanctions failed. Thus, characterizing early market liquidity purely as a product of legal codification oversimplifies the dual mechanism that actually sustained commercial expansion.

True or False: The primary purpose of the passage is to challenge a single-factor explanation of historical market liquidity by illustrating how informal networks operated alongside formal legal structures.

A manufacturing shop produces two models of custom bicycle frames: Standard and Deluxe. Producing each Standard frame requires $2$ hours of welding and $1$ hour of painting. Producing each Deluxe frame requires $3$ hours of welding and $2$ hours of painting. During a single week, the shop logged a total of $130$ hours of welding and $75$ hours of painting for these two models. How many Deluxe bicycle frames were produced during that week?

A company recorded the number of daily sales over a 7-day week. The numbers of daily sales, when arranged in ascending order, are $12, 15, 18, x, 22, y, 30$. If the median of the 7 daily sales figures is $20$ and the arithmetic mean is $21$, what is the value of $y$?

Consider the following excerpt from an economic history of nineteenth-century Ottoman municipal finance:

"While nineteenth-century Ottoman fiscal reformers routinely blamed the persistent deficits of provincial treasuries on the administrative costs of tax farming (iltizam), Reşid Pasha’s 1845 financial audit revealed that provincial revenue shortfalls occurred primarily because local merchants systematically underreported agricultural yields prior to tax assessment, regardless of whether tax collection was managed directly by state bureaucrats or auctioned to private tax farmers."

Statement: Based on the excerpt, replacing private tax farmers with direct state administration would not, on its own, eliminate the primary factor driving provincial treasury deficits.