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Question 1621Question →

The following passage is about the history of Tyrian purple.

The Golden Dye of Tyre

In the ancient Mediterranean world, color was a potent symbol of status, power, and wealth. No hue carried more prestige than Tyrian purple, a rich, deep violet dye that became synonymous with royalty and imperial authority. The source of this coveted pigment was the humble murex snail, a carnivorous marine mollusk abundant along the rocky coasts of Phoenicia. Extracting the dye, however, was a labor-intensive and notoriously foul-smelling process. Workers gathered the mollusks by lowering traps baited with cockles into the shallow waters. The tiny glands of the snails were then meticulously removed and salted before the heating process began; thousands of snails had to be harvested from the sea and boiled in large lead vats for days to yield just a single gram of the precious secretion.

[Paragraph Break]

[2] While common vegetable-based dyes quickly faded under the Mediterranean sun or washed out during routine laundering, Tyrian purple grew richer and more intense with exposure to sunlight and wear. Consequently, the Phoenician city of Tyre grew incredibly wealthy from this specialized trade, establishing monopoly networks that stretched across the sea. Roman emperors eventually restricted the dye's use by sumptuary laws, decreeing that only the imperial family could wear garments colored with the premium pigment. This legal exclusivity cemented the color's status as the ultimate marker of political authority for centuries.

Which choice provides the most effective transition from the preceding paragraph and introduces the main topic of the second paragraph?

Show answer & explanation

Answer: Despite the unpleasant nature of its production, the resulting dye possessed remarkable durability.

Answer

The sentence stating 'Despite the unpleasant nature of its production, the resulting dye possessed remarkable durability.'
The correct answer provides a transition that connects the foul-smelling production process mentioned at the end of the first paragraph with the durability of the dye described in the second paragraph. It is grammatically correct and logically coherent.

Step-by-Step Solution

1
Analyze the concluding information of the first paragraph and the details of the second paragraph.
The first paragraph describes the foul-smelling, difficult extraction process of Tyrian purple. The second paragraph describes the dye's unique durability and high value.
An effective transitional opener must logically bridge these two distinct ideas.
2
Evaluate the options to identify which choice establishes this logical connection.
The option highlighting the contrast between the unpleasant production and the resulting dye's durability creates a smooth bridge.
This selection connects the ending of the first paragraph with the beginning of the second paragraph.
3
Verify that the selected option is grammatically correct and free of errors.
The correct option is grammatically sound, while other options introduce punctuation errors, redundancy, or irrelevant details.
ACT English questions require both logical cohesion and grammatical correctness.

Key Concept

Opening and Concluding Sentences
Estimated Time:1m 15s
Question 1622Question →

In 1967, astrophysicist Jocelyn Bell Burnell was analyzing radio telescope data when she noticed a series of rapid radio pulses. These pulses, which occurred with a highly precise regularity and kept repeating at constant intervals, initially baffled astronomers, who jokingly named the source 'LGM-1' for 'Little Green Men.'

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

Show answer & explanation

Answer: These highly regular pulses

Answer

These highly regular pulses
The correct answer, 'These highly regular pulses', is the most concise and direct phrasing. It removes the redundant references to the pulses' regularity without introducing any grammatical errors.

Step-by-Step Solution

1
Analyze the underlined portion for redundancy.
The original phrasing 'which occurred with a highly precise regularity and kept repeating at constant intervals' repeats the same concept of regular timing in two different ways, making it wordy and redundant.
ACT English rewards conciseness; redundant synonyms should be eliminated.
2
Evaluate the remaining choices for conciseness and grammatical correctness.
The option 'These highly regular pulses' is concise and grammatically correct. The option 'These pulses, that occurred regularly,' incorrectly uses commas to set off a restrictive clause. The option 'These pulses occurred with high regularity, they' creates a comma splice by joining two independent clauses with only a comma.
The correct choice must be both concise and grammatically sound.

Key Concept

Eliminating Wordiness
Question 1623Question →

What is the integer value of the expression −42+∣−15÷3×2∣−(−3)3-4^2 + | -15 \div 3 \times 2 | - (-3)^3?

Show answer & explanation

Answer: 21

Answer

The correct answer is 21.
The correct answer is obtained by strictly following the order of operations (PEMDAS): first evaluating exponents (−42=−16-4^2 = -16 and (−3)3=−27(-3)^3 = -27), then performing the operations inside the absolute value from left to right (−15÷3=−5-15 \div 3 = -5 followed by −5×2=−10-5 \times 2 = -10, which simplifies to ∣−10∣=10|-10| = 10), and finally executing addition and subtraction from left to right (−16+10−(−27)=21-16 + 10 - (-27) = 21).

Step-by-Step Solution

1
Evaluate the exponent −42-4^2
−16-16
According to the order of operations, the exponent is applied to the base 4 first, and then the negation is applied, yielding −(42)=−16-(4^2) = -16.
2
Evaluate the absolute value expression ∣−15÷3×2∣|-15 \div 3 \times 2|
1010
Multiplication and division have the same precedence and must be performed from left to right: first −15÷3=−5-15 \div 3 = -5, then −5×2=−10-5 \times 2 = -10. Taking the absolute value of −10-10 yields 1010.
3
Evaluate the exponent (−3)3(-3)^3
−27-27
Since the negative sign is inside the parentheses, the base is −3-3, so (−3)3=(−3)×(−3)×(−3)=−27(-3)^3 = (-3) \times (-3) \times (-3) = -27.
4
Combine the values and simplify
2121
Substitute the evaluated parts into the original expression: −16+10−(−27)-16 + 10 - (-27). Simplify by performing addition and subtraction from left to right: −16+10=−6-16 + 10 = -6, and −6−(−27)=−6+27=21-6 - (-27) = -6 + 27 = 21.

Key Concept

Order of operations (PEMDAS) and absolute value properties
Question 1624Question →

A writer is editing a passage about the history of American baking. Read the following paragraph:

In 1938, Ruth Wakefield, co-owner of the Toll House Inn in Massachusetts, made a culinary breakthrough that would redefine American desserts. While preparing a batch of chocolate cookies, she ran out of baker's chocolate and instead chopped up a block of semi-sweet chocolate, expecting it to melt and disperse throughout the dough. [1] Instead, the chocolate pieces held their shape, creating the very first chocolate chip cookies. The recipe, which she called the 'Toll House Chocolate Crunch Cookie,' quickly became a national sensation.

The writer is considering adding the following sentence at point [1]:

'The Toll House Inn, originally built as a toll booth in 1709, had been a popular spot for travelers to change horses and rest.'

Should the writer make this addition?

Show answer & explanation

Answer: No, because it interrupts the sequence of events detailing the accidental creation of the cookie with irrelevant details about the inn's history.

Answer

No, because it interrupts the sequence of events detailing the accidental creation of the cookie with irrelevant details about the inn's history.
The correct option is the one stating that the sentence should not be added because it interrupts the sequence of events detailing the accidental creation of the cookie with irrelevant details about the inn's history. The paragraph's sole focus is the process and result of Wakefield's baking experiment in 1938. The history of the building itself from 1709 is tangential and disrupts the chronological narrative.

Step-by-Step Solution

1
Analyze the main focus of the paragraph.
The paragraph describes the narrative sequence of how Ruth Wakefield accidentally invented the chocolate chip cookie in 1938.
Understanding the paragraph's specific focus is necessary to evaluate if the new sentence adds relevant information or creates a distraction.
2
Analyze the proposed sentence for relevance to that focus.
The proposed sentence provides historical details about the Toll House Inn being built in 1709 for travelers. This information does not contribute to the narrative of how the cookie was formulated or prepared.
Evaluating the proposed sentence determines whether it aligns with the paragraph's development or shifts the focus.
3
Determine the correct decision and logical justification.
The sentence should not be added because it is irrelevant and interrupts the chronological flow of the invention. This matches the option stating that the addition should not be made because it interrupts the sequence of events with irrelevant details.
Comparing the logical conclusion against the choices identifies the correct answer.

Key Concept

Evaluating Relevance for Adding or Deleting Content
Question 1625Question →

Mycorrhizal fungi establish symbiotic networks with plant roots, facilitating the exchange of nutrients and water. These subterranean pathways connect individual plants, allowing them to share resources and transmit chemical warning signals. Scientists have observed that when a host plant is attacked by herbivores, it sends warnings through this network, which helps neighboring plants prepare their defenses. So basically, this awesome web‾\underline{\text{So basically, this awesome web}} functions as an ecological communications infrastructure.

Which choice best maintains the established tone of the passage?

Show answer & explanation

Answer: Consequently, the fungal network

Answer

The choice that provides 'Consequently, the fungal network' best maintains the objective, scientific tone of the passage.
The option 'Consequently, the fungal network' maintains the objective, academic tone established throughout the passage. It uses clear, standard transition words and vocabulary appropriate for a scientific discussion.

Step-by-Step Solution

1
Analyze the tone of the surrounding passage.
The passage uses formal, scientific, and academic language (e.g., 'symbiotic networks', 'facilitating', 'subterranean pathways', 'herbivores').
To determine the appropriate register and stylistic constraints for the underlined portion.
2
Evaluate the options for tone consistency.
The original underlined phrase is too casual, the choice with 'mycelial matrix' is overly pretentious, the choice with 'composed with' contains a grammatical error, and the choice with 'Consequently, the fungal network' maintains a standard academic tone.
To eliminate inconsistent or ungrammatical phrasings.

Key Concept

Tone Consistency
Estimated Time:1m 0s
Question 1626Question →

[1] In 1965, chemist Stephanie Kwolek was analyzing a liquid crystal polymer solution to find a lightweight fiber for tires. [2] The resulting mixture was unusually runny and cloudy, prompting other researchers to suggest discarding it. [3] Kwolek, however, believed that the solution had potential and insisted on testing the fluid in a spinneret machine. [4] The machine spun the liquid into a remarkably durable fiber. [5] Today, this material, known as Kevlar, is widely used in bulletproof vests and aerospace engineering.

The writer wants to add the following sentence to the paragraph:

"To her surprise, the spun fiber proved to be five times stronger than steel."

Where should this sentence be placed to make the paragraph most logical?

Show answer & explanation

Answer: after Sentence 4

Answer

after Sentence 4
Placing the sentence after Sentence 4 is correct because it links the action of spinning the fiber in Sentence 4 to the properties of the resulting 'spun fiber' mentioned in the target sentence. This also creates a smooth transition to Sentence 5, which discusses the modern applications of the material.

Step-by-Step Solution

1
Analyze the target sentence for logical and grammatical clues.
The target sentence contains the noun phrase 'the spun fiber,' which indicates it must follow a sentence that introduces the concept of the fiber being spun.
Identifying these clues helps determine the chronological order of the narrative.
2
Scan the paragraph to locate where the spinning process and the fiber are first described.
Sentence 4 states that the machine 'spun the liquid into a remarkably durable fiber.'
This establishes the necessary antecedent context for the target sentence's reference to 'the spun fiber.'
3
Evaluate the placement of the target sentence after Sentence 4.
Inserting the target sentence after Sentence 4 naturally flows into Sentence 5, which discusses the modern uses of 'this material' (Kevlar).
This creates a logical transition from the creation of the fiber (Sentence 4), to its surprising strength (the target sentence), and finally to its modern applications (Sentence 5).

Key Concept

Sentence placement relies on locating specific nouns, pronouns, or transition words that connect ideas logically and chronologically.
Estimated Time:1m 0s
Question 1627Question →

An expression is given as 26⋅34\sqrt{2^6 \cdot 3^4}. What is the value of this expression?

Show answer & explanation

Answer: 72

Answer

72
The correct answer of 7272 is obtained by applying the rules of exponents under a radical. Evaluating 26⋅34\sqrt{2^6 \cdot 3^4} simplifies to 23⋅322^3 \cdot 3^2, which equals 8⋅9=728 \cdot 9 = 72.

Step-by-Step Solution

1
Express the square root as a fractional exponent of 1/2.
(26⋅34)12(2^6 \cdot 3^4)^{\frac{1}{2}}
The square root of any non-negative number xx can be written as x12x^{\frac{1}{2}}.
2
Apply the power of a product rule (ab)n=anbn(ab)^n = a^n b^n and power of a power rule (am)n=amn(a^m)^n = a^{mn} to simplify the exponents.
26⋅12⋅34⋅12=23⋅322^{6 \cdot \frac{1}{2}} \cdot 3^{4 \cdot \frac{1}{2}} = 2^3 \cdot 3^2
Exponents are multiplied when raising a power to a power.
3
Evaluate the simplified exponential expressions and multiply the results.
8⋅9=728 \cdot 9 = 72
Evaluating 23=82^3 = 8 and 32=93^2 = 9 and calculating their product gives the final simplified value.

Key Concept

Simplifying expressions containing exponents and square roots
Question 1628Question →

The following passage is adapted from an essay about medieval architecture.

Gothic cathedrals are renowned for their soaring heights and intricate designs, which were made possible by key structural innovations. The pointed arch, for instance, distributed weight more efficiently than the rounded Romanesque arch, allowing walls to be built taller and thinner. To prevent these high walls from collapsing outward, medieval masons developed flying buttresses, which towed the lateral thrust of the roof to external supports. This arrangement not only stabilized the massive stone structures but also freed up wall space for expansive stained-glass windows.

Which choice most precisely and clearly expresses the idea in the underlined portion of the sentence?

Show answer & explanation

Answer: channeled

Answer

channeled
The word 'channeled' is the most precise and contextually appropriate verb because it accurately describes the physical redirection of lateral force or thrust from the cathedral's walls to its external supports. In physics and structural engineering, forces are guided or directed along paths, which is best represented by the word 'channeled'.

Step-by-Step Solution

1
Read the sentence containing the underlined word to understand its role and meaning in context.
The sentence describes how flying buttresses prevent high walls from collapsing by directing the 'lateral thrust of the roof' to 'external supports'.
Analyzing the context helps identify the precise action being performed by the architectural structure.
2
Evaluate the original word and the choices based on their definitions and connotations.
'Towed,' 'hauled,' and 'lugged' all imply active pulling, dragging, or physical carrying of cargo, often by a person or vehicle. 'Channeled' means to direct or guide along a specific path.
Comparing definitions allows you to eliminate words that are imprecise or contextually inaccurate.
3
Determine which word fits the formal, academic tone of the passage.
'Lugged' is too informal. 'Towed' and 'hauled' are imprecise for static forces. 'Channeled' is both precise and formal.
ACT English requires both semantic precision and stylistic consistency.

Key Concept

Word Precision and Clarity
Question 1629Question →

A security guard has two patrol routes. Route A takes 18 minutes to complete, and Route B takes 24 minutes to complete. The guard starts both routes at the same time at 6:00 PM. Assuming the guard works continuously without any breaks, how many times will both routes be completed at the same time between 6:01 PM and 11:59 PM on the same evening?

Show answer & explanation

Answer: 4

Answer

4
The correct answer is 4. The least common multiple (LCM) of 18 and 24 is 72, which means both routes are completed at the same time every 72 minutes (1 hour and 12 minutes). Starting from 6:00 PM, the simultaneous completions occur at 7:12 PM, 8:24 PM, 9:36 PM, 10:48 PM, and 12:00 AM. Only the four times between 7:12 PM and 10:48 PM fall strictly between 6:01 PM and 11:59 PM.

Step-by-Step Solution

1
Find the Least Common Multiple (LCM) of the two cycle times, 18 minutes and 24 minutes.
LCM(18, 24) = 72 minutes
Both routes are completed at the same time at intervals that are common multiples of their individual durations. The first time they align after the start is the LCM.
2
List the times when both routes are completed simultaneously, starting after 6:00 PM.
7:12 PM, 8:24 PM, 9:36 PM, 10:48 PM, and 12:00 AM
Add multiples of 72 minutes (1 hour 12 minutes) to the starting time of 6:00 PM.
3
Determine which of the calculated times fall strictly within the window from 6:01 PM to 11:59 PM.
4 times (7:12 PM, 8:24 PM, 9:36 PM, and 10:48 PM)
The times 7:12 PM, 8:24 PM, 9:36 PM, and 10:48 PM are within the specified window. The completion at 12:00 AM is outside the window.

Key Concept

Least Common Multiple (LCM) in scheduling word problems
Question 1630Question →

Passage

Polynesian wayfinders navigated thousands of miles of open ocean without any modern instruments, relying instead on natural cues like stars, ocean swells, and bird migration patterns to guide their canoes. [1] Consequently, a sudden overcast sky or an unexpected shift in wind could disorient even a skilled navigator, stalling the journey for days.

Which choice best replaces the underlined word [1] to establish a logical transition between the two sentences?

Show answer & explanation

Answer: However

Answer

However
The transition 'However' is correct because it signals a contrast or limitation: although wayfinders successfully used natural cues, those same cues were vulnerable to weather changes, which could disorient them.

Step-by-Step Solution

1
Analyze the relationship between the first sentence describing navigation methods and the second sentence describing weather disruptions.
The first sentence explains the reliance on natural cues, while the second sentence describes how easily these cues can be disrupted by the weather.
This establishes that the second sentence presents a limitation or challenge to the methods mentioned in the first sentence.
2
Identify the logical transition category required.
A contrast transition is needed to connect the two thoughts logically.
Contrast transitions highlight a contradiction, exception, or shift in tone between sentences.
3
Evaluate the choices to find the correct contrast transition.
'However' is the only choice that signals contrast. 'Consequently' shows cause-effect, 'For example' shows illustration, and 'Moreover' shows addition.
Matching the correct category of transition ensures sentence-level coherence.

Key Concept

Sentence-Level Transitions
Question 1631Question →

What is the value of the expression 53−645^3 - \sqrt{64}?

Show answer & explanation

Answer: 117

Answer

The correct answer is 117117.
Evaluating 535^3 gives 125125 since 5×5×5=1255 \times 5 \times 5 = 125. The square root of 6464 is 88 because 82=648^2 = 64. Subtracting 88 from 125125 yields the correct result of 117117.

Step-by-Step Solution

1
Evaluate the exponential term 535^3
125125
An exponent indicates how many times a base is multiplied by itself. Here, 53=5×5×5=1255^3 = 5 \times 5 \times 5 = 125.
2
Evaluate the radical term 64\sqrt{64}
88
The square root of a number is the non-negative value that, when multiplied by itself, equals the original number. Since 8×8=648 \times 8 = 64, 64=8\sqrt{64} = 8.
3
Subtract the evaluated terms
117117
Subtract the value of the radical from the value of the exponent to simplify the expression: 125−8=117125 - 8 = 117.

Key Concept

Evaluating basic exponents and square roots
Question 1632Question →

On a standard number line, the distance between two points, AA and BB, is 1212 units. If the coordinate of point AA is −18-18, which of the following is a possible coordinate for point BB?

Show answer & explanation

Answer: −30-30

Answer

−30-30
The correct answer is −30-30 because the distance between two points on a number line is found by taking the absolute value of the difference between their coordinates. Setting up the relation ∣b−(−18)∣=12|b - (-18)| = 12 simplifies to ∣b+18∣=12|b + 18| = 12. Solving this absolute value equation yields two possible locations: b+18=12b + 18 = 12 (which gives b=−6b = -6) and b+18=−12b + 18 = -12 (which gives b=−30b = -30). Among the choices, −30-30 is the only possible coordinate listed.

Step-by-Step Solution

1
Set up the absolute value equation representing the distance between point A and point B on the number line.
Let bb be the coordinate of point BB. The distance between AA and BB is given by ∣−18−b∣=12|-18 - b| = 12.
On a standard number line, the distance between any two coordinates xx and yy is given by the absolute value of their difference, ∣x−y∣|x - y|.
2
Solve the absolute value equation for the two possible cases.
Case 1: −18−b=12⇒−b=30⇒b=−30-18 - b = 12 \Rightarrow -b = 30 \Rightarrow b = -30. Case 2: −18−b=−12⇒−b=6⇒b=−6-18 - b = -12 \Rightarrow -b = 6 \Rightarrow b = -6.
An equation of the form ∣x∣=d|x| = d (where d≥0d \geq 0) splits into two distinct equations: x=dx = d and x=−dx = -d.
3
Compare the possible solutions with the given options.
The value −30-30 is one of the possible coordinates and is listed in the options.
To identify which of the two mathematically correct coordinates (-30 or -6) is provided as an answer choice.

Key Concept

The distance between two points on a number line with coordinates xx and yy is represented by the absolute value of their difference, ∣x−y∣|x - y|.
Estimated Time:45s
Question 1633Question →

A writer is editing a passage about the invention of the windshield wiper and has drafted the following paragraph:

During a freezing trolley ride in New York City in 1902, Mary Anderson observed that the motorman had to keep the front window panes open to wipe away the accumulating sleet. Upon returning home to Alabama, Anderson sketched a design for a hand-operated blade that could clear a windshield from inside the vehicle. [1] In 1903, she was awarded a patent for her window-cleaning device, though many people initially doubted its safety, fearing it would distract drivers. Today, automatic wipers are a standard feature in virtually every automobile.

The writer is considering adding the following sentence at Point [1]:

Alabama is known for its humid subtropical climate and mild winters.

Should the writer make this addition?

Show answer & explanation

Answer: No, because it shifts the paragraph's focus from the development of Anderson's invention to irrelevant geographical details.

Answer

No, because it shifts the paragraph's focus from the development of Anderson's invention to irrelevant geographical details.
The paragraph focuses on the development, patenting, and ultimate standard adoption of Mary Anderson's invention of the windshield wiper. The proposed sentence discusses the climate of Alabama, which is completely irrelevant to the invention's history. Therefore, the sentence should not be added because it introduces an off-topic shift in focus to geographical details.

Step-by-Step Solution

1
Analyze the main focus of the paragraph.
The paragraph describes how Mary Anderson conceived the windshield wiper during a trip to New York, designed it in Alabama, and patented it, transitioning to its modern status.
Understanding the paragraph's theme is necessary to evaluate the relevance of any proposed addition.
2
Evaluate the relevance of the proposed sentence.
The proposed sentence discusses Alabama's climate (humid subtropical, mild winters), which is unrelated to the process of inventing or patenting the windshield wiper.
Adding off-topic sentences disrupts the flow and unity of the paragraph.
3
Determine the correct decision and justification.
The sentence should not be added (No) because it introduces an irrelevant shift in focus to geographical details.
The correct option must state both the correct decision ('No') and the rhetorically sound reason.

Key Concept

Evaluating Relevance for Adding or Deleting Content
Question 1634Question →

The following passage is from an essay about the preservation of historic musical instruments.

Restoring a historic pipe organ requires a delicate balance of art and engineering. Conservators must meticulously clean each pipe and repair the intricate windchest without altering the instrument's original acoustic character. Ultimately, the goal is to preserve the unique voice of the instrument for future generations.

Which choice best maintains the established tone of the passage?

Show answer & explanation

Answer: NO CHANGE

Answer

NO CHANGE
The correct option maintains the professional and academic tone established in the passage. The phrase 'preserve the unique voice of the instrument' is formal, precise, and consistent with terms like 'acoustic character' and 'meticulously clean'.

Step-by-Step Solution

1
Analyze the established tone of the surrounding sentences in the passage.
The passage uses formal, precise, and objective language, establishing a scholarly tone.
Understanding the established tone is necessary to determine which option maintains consistency.
2
Evaluate the choices to see which one matches this scholarly tone while remaining grammatically correct.
The original phrasing 'preserve the unique voice of the instrument' fits perfectly. The alternative options are either too informal, overly pretentious, or grammatically incorrect due to an unidiomatic preposition.
This identifies the correct choice that preserves both stylistic tone and grammatical correctness.

Key Concept

Tone Consistency
Question 1635Question →

To complete a project, Alice works in shifts that last 34\frac{3}{4} of an hour, and Bob works in shifts that last 56\frac{5}{6} of an hour. If they both begin their first shift at the exact same time, after how many hours will they next begin a shift at the same time?

Show answer & explanation

Answer: 152\frac{15}{2}

Answer

The two workers will next begin a shift at the same time after 152\frac{15}{2} hours.
To find when both Alice and Bob will next start their shifts at the same time, we need to find the Least Common Multiple (LCM) of their shift durations, 34\frac{3}{4} and 56\frac{5}{6} hours. One way to do this is to convert the durations into minutes: 34×60=45\frac{3}{4} \times 60 = 45 minutes, and 56×60=50\frac{5}{6} \times 60 = 50 minutes. The prime factorizations are 45=32×545 = 3^2 \times 5 and 50=2×5250 = 2 \times 5^2. The LCM of 4545 and 5050 is 2×32×52=4502 \times 3^2 \times 5^2 = 450 minutes. Converting this back to hours gives 45060=152\frac{450}{60} = \frac{15}{2} hours. Alternatively, using the formula for the LCM of fractions: LCM(ab,cd)=LCM(a,c)GCD(b,d)\text{LCM}\left(\frac{a}{b}, \frac{c}{d}\right) = \frac{\text{LCM}(a, c)}{\text{GCD}(b, d)}, we get LCM(3,5)GCD(4,6)=152\frac{\text{LCM}(3, 5)}{\text{GCD}(4, 6)} = \frac{15}{2} hours.

Step-by-Step Solution

1
Identify the mathematical concept needed to solve the simultaneous starting times.
The next simultaneous starting time is the Least Common Multiple (LCM) of the two shift durations, 34\frac{3}{4} and 56\frac{5}{6} hours.
Because both shifts start at multiples of their respective durations, the first time they start together again must be a common multiple of both intervals.
2
Calculate the LCM of the fractions 34\frac{3}{4} and 56\frac{5}{6}.
Using the fraction LCM formula, LCM(ab,cd)=LCM(a,c)GCD(b,d)\text{LCM}(\frac{a}{b}, \frac{c}{d}) = \frac{\text{LCM}(a, c)}{\text{GCD}(b, d)}, we find LCM(3,5)=15\text{LCM}(3, 5) = 15 and GCD(4,6)=2\text{GCD}(4, 6) = 2, yielding 152\frac{15}{2} hours.
This formula correctly scales the numerator multiples while accounting for the common division in the denominators.

Key Concept

Finding the Least Common Multiple (LCM) of fractional values or using unit conversion to find the LCM of integers.

Alternative Method

Convert the fractional hours into minutes first. Alice's shifts are 34\frac{3}{4} of an hour, which is 4545 minutes. Bob's shifts are 56\frac{5}{6} of an hour, which is 5050 minutes. Find the LCM of 4545 and 5050 by listing their multiples or using their prime factorizations: 45=32×545 = 3^2 \times 5 and 50=2×5250 = 2 \times 5^2, so their LCM is 2×32×52=4502 \times 3^2 \times 5^2 = 450 minutes. Finally, convert 450450 minutes back to hours by dividing by 6060, which simplifies to 45060=152\frac{450}{60} = \frac{15}{2} hours.
Estimated Time:2m 0s
Question 1636Question →

The following sentences are from a paragraph about the use of falconry at airports. Arrange the sentences in the most logical order to create a cohesive paragraph that begins with a clear introduction of the problem and ends with a strong concluding thought.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence begins with the introduction of the bird strike threat, followed by the introduction of falconry as a solution, then the details of how the raptors deter flocking birds, and ends with the concluding summary sentence.
The correct order establishes a logical progression: first, the paragraph defines the problem of bird strikes; second, it introduces falconry as the solution; third, it describes how the raptors operate; and finally, it concludes by reflecting on the effectiveness of this ancient art for a modern problem.

Step-by-Step Solution

1
Identify the introductory sentence.
The sentence about bird strikes posing a threat to aircraft at busy airports is identified as the opener because it introduces the primary topic without relying on external pronouns or transitional hooks.
An effective introduction must establish the subject and context independently.
2
Determine the logical next sentence by looking for transitional links.
The sentence introducing falconry is placed second because it starts with 'To combat this hazard,' which directly refers back to the threat of bird strikes.
Cohesion is maintained by connecting the solution directly to the defined hazard.
3
Find the detail sentence that follows the solution introduction.
The sentence detailing how the raptors deter flocking birds is placed third because it uses the pointer 'These raptors' to refer back to the 'trained birds of prey'.
Pronoun antecedents must be established in preceding sentences to avoid ambiguity.
4
Identify the concluding sentence.
The sentence starting with 'Ultimately' is placed last because it summarizes the overall paragraph and provides a cohesive conclusion.
Concluding sentences resolve the discussion by connecting the specific solution back to the broader challenge.

Key Concept

Opening and Concluding Sentences
Estimated Time:1m 30s
Question 1637Question →

For all non-zero real numbers xx and yy, which of the following is equivalent to the expression below?

x−y[x−(y−x)]−y2 x - y[x - (y - x)] - y^2
Show answer & explanation

Answer: x−2xyx - 2xy

Answer

The correct answer is x−2xyx - 2xy.
The correct answer is x−2xyx - 2xy. We begin by simplifying the innermost grouping symbols first. The expression inside the parentheses is x−(y−x)=x−y+x=2x−yx - (y - x) = x - y + x = 2x - y. Substituting this back into the expression gives x−y[2x−y]−y2x - y[2x - y] - y^2. Next, we distribute the factor of −y-y to the terms inside the brackets, yielding −y(2x)−y(−y)=−2xy+y2-y(2x) - y(-y) = -2xy + y^2. The expression then becomes x−2xy+y2−y2x - 2xy + y^2 - y^2. Finally, combining the like terms +y2+y^2 and −y2-y^2 cancels them out, resulting in the simplified expression x−2xyx - 2xy.

Step-by-Step Solution

1
Simplify the expression inside the innermost parentheses: x−(y−x)x - (y - x).
2x−y2x - y
Distribute the negative sign to the terms inside the parentheses: −(y−x)=−y+x-(y - x) = -y + x. Combining like terms gives x+x−y=2x−yx + x - y = 2x - y.
2
Substitute the simplified expression back into the main expression: x−y[2x−y]−y2x - y[2x - y] - y^2.
x−y[2x−y]−y2x - y[2x - y] - y^2
This updates the expression to show the next level of grouping symbols to resolve.
3
Distribute the −y-y to the terms inside the brackets: −y[2x−y]-y[2x - y].
−2xy+y2-2xy + y^2
Apply the distributive property: −y×2x=−2xy-y \times 2x = -2xy, and −y×(−y)=y2-y \times (-y) = y^2.
4
Combine the distributed terms back into the expression and simplify: x−2xy+y2−y2x - 2xy + y^2 - y^2.
x−2xyx - 2xy
The +y2+y^2 and −y2-y^2 terms cancel each other out, leaving the simplified expression x−2xyx - 2xy.

Key Concept

Applying the order of operations (PEMDAS) to evaluate expressions with nested grouping symbols, and correctly distributing positive and negative signs.
Estimated Time:1m 30s
Question 1638Question →

Passage

The *Welwitschia* plant survives in the hyper-arid Namib Desert by absorbing moisture from early morning fog. Nonetheless, it has developed an extensive, shallow root system to capture any sporadic rainfall that touches the desert floor.

Which choice best replaces the underlined word to establish the most logical relationship between the two sentences?

Show answer & explanation

Answer: Furthermore,

Answer

Furthermore,
The correct option is 'Furthermore,'. The first sentence explains one way the plant gathers water (fog absorption), and the second sentence details another way (shallow roots). Because the second sentence adds another supporting point to the first, an additive transition like 'Furthermore' is the most logical choice.

Step-by-Step Solution

1
Analyze the relationship between the two sentences connected by the transition.
The first sentence describes how the plant absorbs moisture from early morning fog. The second sentence describes how the plant uses a shallow root system to capture rainfall. Both sentences describe different, complementary adaptations for gathering water.
Understanding the logical connection between the ideas is essential to selecting the correct transition word.
2
Evaluate the transition category needed.
Since both sentences describe supporting details of the plant's survival strategy, an additive transition (like 'Furthermore' or 'In addition') is required.
The transition must accurately signal that the second point is an additional piece of information supporting the same overall theme.
3
Evaluate the choices against the required category.
'NO CHANGE' (Nonetheless) and 'Alternatively' show contrast or choice, and 'Consequently' shows cause-and-effect. Only 'Furthermore' correctly functions as an additive transition.
Eliminating options with incorrect logical relationships leaves the correct choice.

Key Concept

Selecting the transition word that accurately reflects the logical relationship (contrast, cause-effect, addition, or illustration) between sentences.
Estimated Time:1m 0s
Question 1639Question →

The following paragraph contains numbered sentences:

[1] In 1885, a young farmer named Wilson Bentley attached a bellows camera to a microscope in his drafty shed in Jericho, Vermont. [2] The process was painstakingly slow, requiring him to capture the ice crystals on black velvet before they melted. [3] Over his lifetime, Bentley photographed more than 5,000 snowflakes, discovering that no two were exactly alike. [4] Through these delicate images, he became the first person to document the intricate, hexagonal structures of individual snow crystals. [5] Indeed, he spent years refining this technique of photomicrography, adapting his equipment to withstand the freezing temperatures.

For the sake of the logic and cohesion of this paragraph, Sentence 5 should be placed:

Show answer & explanation

Answer: after Sentence 1.

Answer

after Sentence 1.
Placing the sentence after Sentence 1 is correct because the phrase 'this technique of photomicrography' refers back to the action of attaching a camera to a microscope described in Sentence 1. This sequence establishes a clear relationship between the invention of the technique and the years spent refining it, before describing the slow process of capturing the images in Sentence 2.

Step-by-Step Solution

1
Analyze the target sentence (Sentence 5) for logical and transitional clues.
The target sentence contains the phrase 'this technique of photomicrography,' which indicates a specific photographic technique must be introduced prior to this sentence.
Identifying demonstrative adjectives like 'this' helps locate the antecedent or description of the technique in the paragraph.
2
Scan the paragraph to find where the photographic technique is first described.
Sentence 1 describes Bentley attaching a bellows camera to a microscope. This is the definition and demonstration of the 'technique of photomicrography.'
Establishing this connection shows that Sentence 5 must follow Sentence 1 to maintain logical continuity.
3
Evaluate the flow of the entire paragraph with the new placement.
Placing Sentence 5 after Sentence 1 groups the technical description of the equipment and its refinement together. Sentence 2 then describes the slow process of using this refined technique, followed by Sentence 3 and 4, which transition to Bentley's lifetime results and legacy.
Checking the flow ensures the paragraph progresses chronologically and conceptually.

Key Concept

Sentence Reordering and Placement
Estimated Time:1m 15s
Question 1640Question →

A writer is editing a passage about the decipherment of the Rosetta Stone.

[1] In 1822, French scholar Jean-François Champollion made a breakthrough in deciphering the Rosetta Stone, an ancient slab of black granodiorite. [2] The stone, discovered in 1799, featured a single decree written in three scripts: hieroglyphic, Demotic, and Ancient Greek. [3] By comparing the Greek text, which scholars could already read, with the mysterious Egyptian hieroglyphs, Champollion began to map out the phonetic sounds of the ancient characters. [4] He worked diligently in a small Paris study, often ignoring his failing health to translate long passages late into the night. [5] Eventually, this comparative analysis allowed him to reconstruct the alphabet used by the scribes, unlocking centuries of Egyptian history.

The writer is considering adding the following sentence to the paragraph (placed after Sentence 3):

Ancient Greek was widely spoken and used for administrative purposes throughout the eastern Mediterranean during the Hellenistic period.

Should the writer make this addition?

Show answer & explanation

Answer: No, because it interrupts the paragraph's focus on Champollion's decipherment process with irrelevant historical background about the Greek language.

Answer

The correct answer states that the sentence should not be added because it interrupts the paragraph's focus on Champollion's decipherment process with irrelevant historical background about the Greek language.
The correct option correctly identifies that the proposed sentence should not be added. The paragraph centers on Jean-François Champollion's scientific process of using comparative analysis to decipher ancient Egyptian hieroglyphs. Introducing details about the administrative use of Ancient Greek in the Hellenistic period shifts the focus away from Champollion's bilingual methodology and personal diligence.

Step-by-Step Solution

1
Analyze the main focus of the paragraph.
The paragraph focuses on Jean-François Champollion's methodology and process for deciphering the Rosetta Stone using comparative analysis.
To evaluate relevance, we must first establish the central theme of the existing text.
2
Evaluate the function of the proposed sentence.
The proposed sentence provides historical details about the widespread administrative use of Ancient Greek during the Hellenistic period.
This helps determine whether the new sentence supports the main focus or introduces a digression.
3
Compare the proposed sentence to the paragraph's theme and choose the correct decision.
The proposed sentence is irrelevant to Champollion's translation efforts and should not be added because it shifts the focus to Hellenistic history.
Since the sentence is irrelevant, the correct decision is 'No' because the sentence interrupts the flow of the passage with unnecessary background details.

Key Concept

Evaluating Relevance for Adding or Deleting Content
Estimated Time:1m 0s
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