All practice questions

An agricultural enterprise harvests wheat across three distinct parcels of land: Parcel X, Parcel Y, and Parcel Z. Parcel X covers $120$ acres and yields an average of $45$ bushels per acre. Parcel Y covers $80$ acres and yields an average of $60$ bushels per acre. Parcel Z covers $50$ acres and yields an average of $70$ bushels per acre. What is the overall average yield, in bushels per acre, for the entire enterprise across all three parcels?

An event design company offers three distinct decorative bundles—Bundle X, Bundle Y, and Bundle Z—for corporate gala setups.

• Bundle X contains 3 floral arrangements, 2 LED uplights, and 1 table runner.
• Bundle Y contains 1 floral arrangement, 3 LED uplights, and 2 table runners.
• Bundle Z contains 2 floral arrangements, 1 LED uplight, and 3 table runners.

To decorate a venue, a coordinator orders a combination of these bundles containing a total of 26 floral arrangements, 23 LED uplights, and 23 table runners. If every bundle ordered is used in its entirety, what is the total number of bundles ordered by the coordinator?

A corporate committee needs to form a 5-member project team selected from a department consisting of 4 data analysts, 5 software developers, and 4 cybersecurity experts. The team must include exactly 1 cybersecurity expert, at least 1 data analyst, and at least 1 software developer. How many different 5-member teams can be formed under these conditions?

A motorboat travels $60$ miles downstream in a river with a constant current and then returns upstream along the same route to its starting point. If the motorboat's speed in still water is $20$ miles per hour and the total round-trip journey takes $8$ hours, what is the speed of the river current, in miles per hour?

Data Set $A$ consists of $n$ numbers with mean $\mu$ and standard deviation $\sigma$, where $\sigma > 0$. Data Set $B$ is created by transforming each element $x$ in Data Set $A$ into $y = 5 - 2x$. If the variance of Data Set $B$ is equal to $k$, which of the following expressions represents the standard deviation of Data Set $A$ in terms of $k$?

Set $S$ consists of $n$ consecutive integers listed in increasing order. The product of the least integer and the greatest integer in Set $S$ is equal to $0$. If the sum of all the integers in Set $S$ is $21$, how many integers are in Set $S$?

Let $N = 2^4 \times 3^2 \times 5$. How many distinct prime factors does the integer $N + 9$ have?

An electric utility provider generates energy from three distinct sources: Solar, Wind, and Natural Gas. Solar power accounts for $20\%$ of total production at a generation cost of $\$40$ per megawatt-hour (MWh). Wind power accounts for $40\%$ of total production at a generation cost of $\$30$ per MWh. Natural Gas accounts for the remaining production at a generation cost of $\$80$ per MWh. What is the weighted average cost, in dollars per MWh, of the electricity generated by the utility provider?

For decades, evolutionary biologists faced a conceptual paradox regarding the persistence of sexual reproduction despite its substantial genetic costs. Under classical models, an asexual female passes all of her genes to offspring, whereas a sexual female passes only half, theoretically giving asexual lineages a two-fold reproductive advantage that should lead to the rapid competitive exclusion of sexual populations.

To resolve this discrepancy, early theorists posited that sexual reproduction evolved primarily to facilitate the purge of deleterious mutations. However, this mutation-clearing hypothesis failed to explain why sexual populations persist in dynamic ecological environments where mutation rates are exceptionally low.

More recent empirical research on Potamopyrgus antipodarum, a freshwater snail species featuring coexisting sexual and asexual populations, offers a more robust explanation rooted in host-parasite coevolution. Investigators observed that in habitats characterized by high parasite density, sexual individuals significantly outnumber asexual clones. Because parasites rapidly adapt to infect the most common local genotypes, clonal populations suffer severe frequency-dependent mortality over successive generations. Conversely, the novel genetic combinations generated by sexual recombination present a continually moving target for parasitic infection. In parasite-free shallow waters, however, asexual clones quickly dominate the population, confirming the inherent numerical advantage of asexual reproduction when coevolutionary pressures are absent.

Ultimately, these findings demonstrate that ecological interactions can continuously offset the substantial costs of sex. Rather than viewing sexual reproduction as a universal evolutionary ideal or a mere mechanism for mutation repair, evolutionary biologists must recognize that its maintenance depends heavily on localized biotic selection pressures, such as parasite-driven coevolutionary arms races.

Which of the following best describes the primary purpose of the passage?

A financial firm has a team of 10 auditors consisting of 6 certified public accountants (CPAs) and 4 audit assistants. A special audit task force of 3 auditors is to be selected at random from the team. If the probability that the task force contains at least one CPA is expressed as a fraction $\frac{a}{b}$ in simplest form, what is the value of $a + b$?

An express delivery drone flies from Station Alpha to Station Beta at a constant speed of $60$ miles per hour against a headwind. On the return flight along the exact same path from Station Beta to Station Alpha, with the wind acting as a tailwind of identical strength, the drone travels at a constant speed of $90$ miles per hour. If the entire round-trip flight took a total of $5$ hours, what is the distance, in miles, between Station Alpha and Station Beta?

An investor deposits $\$5,000$ into Account B, which earns interest at a rate of $20\%$ per year compounded annually for $2$ years. The same investor deposits another $\$5,000$ into Account A, which earns simple annual interest at a rate of $r\%$ per year for $3$ years. If the total interest earned from Account B exceeds the total interest earned from Account A by $\$400$, what is the value of $r$?

In a dataset of $N$ distinct values arranged in ascending order, the $p\text{th}$ percentile is defined as the value at position $\left\lceil \frac{p}{100} \times N \right\rceil$.

Initially, a dataset contains $100$ distinct test scores. The $40\text{th}$ percentile score is $S_1$ and the $70\text{th}$ percentile score is $S_2$. A researcher adds $x$ new scores that are strictly less than $S_1$, and $y$ new scores that are strictly between $S_1$ and $S_2$, where $x$ and $y$ are positive integers.

If the $40\text{th}$ percentile score of the expanded dataset remains $S_1$ and the $70\text{th}$ percentile score of the expanded dataset remains $S_2$, what is the maximum possible value of $x + y$?

Set $S$ consists of consecutive integers. The sum of all positive integers in set $S$ is $300$, and the median of set $S$ is $-4.5$. How many negative integers are in set $S$?

Consider the following passage:

For over half a century, classical philologists analyzed the undeciphered Minoan Linear B script under the foundational premise that its underlying language was non-Indo-European, likely related to Etruscan or ancient Anatolian dialects. This consensus persisted largely because scholars assumed that the Mycenaean civilization, which produced the tablets found at Knossos and Pylos, developed in complete linguistic isolation from mainland Greek-speaking populations. Consequently, early decipherment attempts focused almost exclusively on establishing phonetic parallels with Mediterranean language isolates, yielding meager contextual coherence.

However, in 1952, architect and self-taught linguist Michael Ventris introduced a radical structural methodology. Rather than attempting to match isolated symbols to existing non-Indo-European vocabularies, Ventris constructed a complex syllabic grid based strictly on the internal positional frequencies and contextual distributions of signs across thousands of clay fragments. This purely cryptographic approach revealed systemic inflectional patterns characteristic of noun declensions and verb conjugations. When Ventris populated this abstract structural matrix with hypothetical phonetic values derived from early Greek dialects, the texts unexpectedly rendered intelligible Mycenaean Greek—an archaic form of the Greek language predating Homer by several centuries.

Ventris’s breakthrough not only resolved a long-standing epigraphic enigma but also fundamentally transformed Aegean historiography. By demonstrating that Linear B recorded an early Greek dialect, his work compelled historians to revise established chronologies regarding Mycenaean cultural hegemony and its linguistic continuity with classical Hellas. Thus, Ventris proved that rigorous structural analysis of internal script patterns can overturn deeply entrenched historical paradigms.

Statement: The primary purpose of the passage is to explain how a novel methodological approach to deciphering Linear B overturned a longstanding linguistic assumption and reshaped historical understanding of Aegean civilization.

A market research study examined the streaming service subscriptions of $250$ households. Every surveyed household subscribes to at least one of three streaming services: Service X, Service Y, or Service Z.

- $130$ households subscribe to Service X.
- $110$ households subscribe to Service Y.
- $120$ households subscribe to Service Z.
- $40$ households subscribe to both Service X and Service Y.
- $35$ households subscribe to both Service Y and Service Z.
- $45$ households subscribe to both Service X and Service Z.

How many households subscribe to all three streaming services?

A commuter drives a total distance of $60$ miles from home to work. Due to heavy morning traffic, the commuter travels the first $30$ miles at a constant speed of $30$ miles per hour. At what constant speed, in miles per hour, must the commuter travel the remaining $30$ miles to achieve an average speed of $40$ miles per hour for the entire $60$-mile trip?