All practice questions

An animal shelter has a ratio of cats to dogs of $4:7$. If there are 28 cats currently at the shelter, what is the total number of cats and dogs at the shelter?

What is the value of the expression $\frac{\sqrt{144} \times 2^{-3}}{3^2}$?

A writer is editing a passage about the development of the Braille writing system. Read the following paragraph:

Louis Braille was only fifteen years old in 1824 when he developed his tactile writing system for the visually impaired. Inspired by a military code of "night writing" created by Charles Barbier, Braille reduced Barbier's complex twelve-dot grid to a more manageable six-dot cell. [1] This modification allowed readers to recognize an entire character with a single touch of a fingertip, dramatically increasing reading speed. Braille's system eventually became the global standard, opening up new educational and professional opportunities for millions.

The writer is considering adding the following sentence at point [1]:
"Barbier was a captain in the French Army who also designed several other code systems for military use."

Should the writer make this addition?

Consider the following paragraph from an essay about Wangari Maathai:

[1] In 1977, Kenyan environmentalist Wangari Maathai observed that rural streams were drying up and agricultural soil was eroding. [2] She reasoned that the widespread clearing of forests to make room for commercial agriculture was the root cause of these ecological problems. [3] To address these issues, she encouraged local women to plant seedlings in their communities, providing them with a small stipend for each tree that survived. [4] This grassroots approach eventually grew into the Green Belt Movement, an organization that has helped plant over fifty million trees. [5] Through this work, Maathai became the first African woman to receive the Nobel Peace Prize.

To make the paragraph flow as logically as possible, where should the following sentence be inserted?

'Before achieving this historic honor, however, she faced years of political opposition and harassment from local authorities.'

A machine at a factory seals $15$ boxes every $4$ minutes. At this rate, how many minutes will it take the machine to seal $90$ boxes?

In 1952, computer scientist Grace Hopper developed the first compiler, a pioneering technology that translated English-like instructions into computer code. By streamlining this translation process, the writing of computer programs was made to be a task that was far faster and more efficient than before by her.

Which choice most effectively and concisely completes the underlined portion of the sentence?

Signals Across the Hills

[1]
In the late eighteenth century, communication over long distances was limited by the speed of a galloping horse. During the French Revolution, however, Claude Chappe and his brothers developed the semaphore telegraph, a revolutionary system of visual signaling. The system consisted of a series of towers built on high hills, each equipped with a large wooden apparatus containing two movable arms. Operators adjusted these arms using ropes and pulleys to represent different letters and symbols. These configurations could be seen from the next tower through a telescope, allowing messages to be passed rapidly from one station to the next.

[2]
The impact of this invention was immediate and profound. A message could travel from Paris to Lille—a distance of over one hundred and forty miles—in just ten minutes, a feat that previously took an entire day. By the early nineteenth century, France was crisscrossed by hundreds of semaphore towers, which provided the government with a crucial administrative and military tool. Yet, the system had significant limitations. It was useless at night or in heavy fog, and it required a massive, expensive workforce of operators who had to remain constantly vigilant.

[3]
Despite these drawbacks, the Chappe semaphore telegraph remained the gold standard of long-distance communication for decades. It was only rendered obsolete in the mid-nineteenth century with the advent of the electrical telegraph, which could transmit information instantly regardless of weather or time of day. _______________________

The writer wants to add a concluding sentence at the end of the passage (following the blank in Paragraph 3) that reinforces the historical significance of the semaphore telegraph as a precursor to modern telecommunications. Which of the following sentences best achieves this goal?

Three lighthouse beacons flash at regular intervals. Beacon A flashes every $24$ seconds, Beacon B flashes every $36$ seconds, and Beacon C flashes every $s$ seconds, where $s$ is a positive integer. If all three beacons flash at the same instant, and the next time they all flash at the same instant is exactly $6$ minutes later, what is the number of possible values for $s$?

Termite mounds in the African savannah maintain a remarkably stable internal temperature despite extreme external weather fluctuations , for instance, architects have studied these structures to design self-cooling buildings.

Which choice provides the most logical transition between the two clauses?

Simplify each of the following expressions and arrange them in order of their value from least to greatest.

A chef uses $\frac{1}{3}$ cup of milk and $\frac{1}{4}$ cup of water for a recipe. What fraction of a cup is the total liquid used in the recipe?

A school supply drive has $72$ notebooks, $96$ pens, and $120$ pencils. Volunteers want to pack these supplies into identical boxes so that each box contains the same number of notebooks, the same number of pens, and the same number of pencils, with no supplies left over. If they pack the maximum possible number of boxes, how many pens will be in each box?

The rates at which three pipes, $A$, $B$, and $C$, can fill a pool are in the ratio $3:4:6$, respectively. To fill an empty pool, pipes $A$ and $B$ are turned on. After $2\text{ hours}$, pipe $A$ is turned off and pipe $C$ is turned on. It takes another $3\text{ hours}$ for pipes $B$ and $C$ to finish filling the pool. What fraction of the pool's total volume was filled by pipe $B$?

For decades, bioluminescent dinoflagellates have fascinated marine biologists studying the dynamics of coastal ecosystems. During nocturnal blooms, these microscopic organisms emit a striking blue glow when agitated by wave action. This luminous display, which transforms dark waves into shimmering ribbons of light, is a super cool sight to see.

Which choice best maintains the tone established in the passage?

[1] Leafcutter ants are renowned for their highly structured colonies and complex agricultural practices. [2] They do not actually eat the leaves they harvest; instead, they use them to cultivate a specialized fungus that serves as the colony’s primary food source. [3] This fungal garden requires constant maintenance and protection from foreign contaminants. [4] To safeguard their crop, the ants secrete potent antibiotics from glands on their bodies to suppress the growth of unwanted weed molds. [5] Consequently, the health of the entire colony depends on this delicate, symbiotic relationship.

The writer wants to add the following sentence to the paragraph:
"Without these protective secretions, the invasive molds would quickly overrun and destroy their food supply."

To make the paragraph most logical, where should this sentence be placed?

In 1856, eighteen-year-old chemist William Henry Perkin set out to synthesize quinine, a treatment for malaria. Instead, he accidentally created a dark purple mixture by chance, this unexpected substance became mauveine, the world’s first synthetic aniline dye.

Which choice best maintains the sentence's meaning while eliminating redundancy and ensuring grammatical correctness?

The following sentences are from a paragraph about the invention of the windshield wiper. Arrange the sentences in the most logical order to create a cohesive paragraph that begins with the most effective introduction and ends with the most effective conclusion.

Read the following passage and consider the underlined portion:

During the cold, wet summer of 1816, Mary Shelley and her companions stayed near Lake Geneva, where they challenged one another to write ghost stories. Shelley was inspired by talks about the nature of life, and she then proceeded to write her masterpiece, which was a novel. The book, *Frankenstein*, became a landmark of science fiction.

Which choice best eliminates wordiness and redundant phrasing while maintaining the grammatical correctness and meaning of the sentence?

An event coordinator is preparing identical welcome packets for a conference. She has $72$ promotional pens, $108$ notebooks, and $130$ keychains. She plans to distribute all of the pens and notebooks into the maximum number of identical packets such that no pens or notebooks are left over. She also wants to distribute the keychains equally among these packets. Finally, the coordinator requires that the total number of items (pens, notebooks, and keychains combined) in each packet is a multiple of $6$. To meet these conditions, she must purchase additional keychains. What is the minimum number of additional keychains she needs to buy?

A chemist has three different acid solutions: Solution $X$, Solution $Y$, and Solution $Z$. In Solution $X$, the ratio of acid to water is $1:3$ by volume. In Solution $Y$, the ratio of acid to water is $3:2$ by volume. In Solution $Z$, the ratio of acid to water is $5:1$ by volume. If the chemist mixes Solution $X$, Solution $Y$, and Solution $Z$ in a volume ratio of $4:5:3$, respectively, what is the ratio of acid to water in the final mixture?