All practice questions

Question 4601Question →

Although the researchers spent months analyzing the ancient, weathered manuscript, they could not decipher the final chapter.

Which choice is the best version of the underlined portion?

ancient, weathered manuscript, they

ancient, weathered, manuscript they

ancient weathered manuscript, they

ancient, weathered manuscript; they

Show answer & explanation

Answer: ancient, weathered manuscript, they

Answer

The correct option is 'ancient, weathered manuscript, they', which properly places a comma between the coordinate adjectives and uses a comma to separate the introductory dependent clause from the main clause.

The correct option properly places a comma between the coordinate adjectives 'ancient' and 'weathered' because they both independently modify the noun 'manuscript.' It also correctly places a comma after the word 'manuscript' to separate the introductory dependent clause from the main independent clause that follows.

Step-by-Step Solution

1

Determine if 'ancient' and 'weathered' are coordinate adjectives.

Since 'ancient and weathered manuscript' and 'weathered, ancient manuscript' are both grammatically correct and convey the same meaning, they are coordinate adjectives and must be separated by a comma. No comma should separate the final adjective 'weathered' from the noun 'manuscript.'

Coordinate adjectives independently modify the same noun and require a comma between them.

2

Identify the clause boundary and structure.

The sentence begins with the subordinating conjunction 'Although,' establishing an introductory dependent clause that ends at 'manuscript.' The main clause 'they could not decipher...' is independent.

Recognizing clause boundaries is necessary to determine the correct punctuation between clauses.

3

Select the punctuation that correctly connects the dependent clause to the independent clause.

A comma must be placed after 'manuscript' to separate the introductory clause. Using a semicolon here is incorrect because a semicolon can only separate two independent clauses, and using one here results in a fragment.

Introductory dependent clauses must be followed by a comma before the independent clause.

Key Concept

Punctuation rules for coordinate adjectives and introductory dependent clauses

Question 4602Question →

On a standard number line, point $A$ is located at $-24$ and point $B$ is located at $6$ . Point $C$ is located between point $A$ and point $B$ such that the distance from $A$ to $C$ is $\frac{2}{3}$ of the distance from $C$ to $B$ . What is the coordinate of point $C$ ?

Show answer & explanation

Answer: -12

Answer

The coordinate of point

C

is

-12

.

Because point

C

with coordinate

c

lies between

-24

and

6

, the distance from

A

to

C

is

c - (-24) = c + 24

, and the distance from

C

to

B

is

6 - c

. Setting the distance from

A

to

C

to

\frac{2}{3}

of the distance from

C

to

B

gives the equation

c + 24 = \frac{2}{3}(6 - c)

. Multiplying both sides by

3

to clear the fraction results in

3c + 72 = 12 - 2c

. Collecting like terms yields

5c = -60

, which simplifies to

c = -12

.

Step-by-Step Solution

1

Express the distances between the points on the number line using their coordinates.

The distance from

A

to

C

is

c + 24

, and the distance from

C

to

B

is

6 - c

.

Since point

C

is positioned between points

A

and

B

, the inequality

-24 < c < 6

holds. This allows the absolute value distance expressions

|c - (-24)|

and

|6 - c|

to simplify directly to positive expressions without absolute value bars.

2

Formulate an equation based on the specified ratio of distances.

c + 24 = \frac{2}{3}(6 - c)

The problem states that the distance from

A

to

C

is

\frac{2}{3}

of the distance from

C

to

B

.

3

Solve the linear equation for the coordinate

c

.

c = -12

Multiplying both sides by

3

gives

3(c + 24) = 2(6 - c)

, which expands to

3c + 72 = 12 - 2c

. Rearranging the terms by adding

2c

to both sides and subtracting

72

from both sides results in

5c = -60

. Dividing by

5

gives

c = -12

.

Key Concept

Using absolute value properties to express distances on a number line and solving partitioning coordinate problems.

Estimated Time:1m 15s

Question 4603Question →

The following passage is adapted from a historical account of marine biology. Read the passage and write a single, precise word in the blank that best fits the formal, academic tone of the context.

Fill in the blanks below

In 1938, museum curator Marjorie Courtenay-Latimer noticed an unusual blue fish in a local fisherman's catch off the coast of South Africa. Scientists were astonished to discover that the creature was a coelacanth, a prehistoric fish long believed to have gone extinct millions of years ago. This monumental discovery our understanding of vertebrate evolution, proving that these 'living fossils' had survived virtually unchanged.

Show answer & explanation

Answer

reshaped (or a similar precise verb such as redefined, transformed, or revolutionized)

The correct words (such as 'reshaped', 'redefined', 'transformed', or 'revolutionized') precisely describe the significant, profound impact of the coelacanth's discovery on scientific theories of vertebrate evolution, while maintaining the formal and academic register of the passage.

Step-by-Step Solution

1

Analyze the context of the sentence containing the blank to determine the required meaning and tone.

The sentence discusses a major scientific discovery (the coelacanth) and its impact on 'our understanding of vertebrate evolution'. The tone of the passage is formal, academic, and historical.

Identifying the register and semantic requirements of the sentence ensures that the chosen word fits both grammatically and stylistically.

2

Evaluate potential verbs that mean to change or influence in a profound way.

Words like 'reshaped', 'redefined', 'transformed', or 'revolutionized' convey a significant, academic-level change in understanding.

Selecting a word that precisely indicates a significant change in scientific understanding maintains the passage's formal tone.

Key Concept

Selecting the most precise and contextually appropriate word to maintain tone and clarity.

Question 4604Question →

Three cyclists start riding laps around a closed circular track at the same time from the same starting line. Cyclist A completes a lap in $\frac{2}{3}$ of a minute, Cyclist B completes a lap in $\frac{3}{4}$ of a minute, and Cyclist C completes a lap in $\frac{5}{6}$ of a minute. If they maintain these constant rates, after how many minutes will all three cyclists cross the starting line together again?

12

30

\frac{5}{2}

\frac{1}{12}

\frac{10}{13}

Show answer & explanation

Answer: $30$

Answer

30 minutes

To find when the three cyclists meet at the starting line again, we calculate the least common multiple (LCM) of their lap times:

\frac{2}{3}

,

\frac{3}{4}

, and

\frac{5}{6}

minutes. Using the formula

\text{LCM}(\text{fractions}) = \frac{\text{LCM of numerators}}{\text{GCD of denominators}}

, the LCM of

2

,

3

, and

5

is

30

, and the GCD of

3

,

4

, and

6

is

1

. The LCM is

\frac{30}{1} = 30

minutes. At this time, each cyclist will have completed an integer number of laps (

45

,

40

, and

36

laps, respectively).

Step-by-Step Solution

1

Identify the required mathematical concept.

We need to find the least common multiple (LCM) of the three lap times:

\frac{2}{3}

,

\frac{3}{4}

, and

\frac{5}{6}

minutes.

The next time all three cyclists cross the starting line together is the smallest positive time that is an integer multiple of each individual lap time.

2

Apply the formula for the LCM of a set of fractions.

\text{LCM}\left(\frac{a}{b}, \frac{c}{d}, \frac{e}{f}\right) = \frac{\text{LCM}(a, c, e)}{\text{GCD}(b, d, f)}

The LCM of fractions is determined by dividing the LCM of the numerators by the greatest common divisor (GCD) of the denominators.

3

Calculate the LCM of the numerators and the GCD of the denominators.

The LCM of

2

,

3

, and

5

is

30

. The GCD of

3

,

4

, and

6

is

1

.

For the numerators, since

2

,

3

, and

5

are prime numbers, their LCM is

2 \times 3 \times 5 = 30

. For the denominators, the only positive integer that divides

3

,

4

, and

6

is

1

.

4

Compute the final LCM value.

\frac{30}{1} = 30\text{ minutes}

Dividing the numerator LCM by the denominator GCD gives the least common multiple of the fractions.

Key Concept

Calculating the least common multiple (LCM) of a set of fractions to solve a periodic scheduling word problem.

Question 4605Question →

A video streaming service has three subscription tiers: Basic, Standard, and Premium. Originally, $\frac{2}{5}$ of the subscribers are on the Basic tier and $45\%$ are on the Standard tier. During a promotional campaign, $\frac{1}{4}$ of the Basic subscribers upgrade to the Standard tier, and $20\%$ of the original Standard subscribers upgrade to the Premium tier. If no other subscription changes occur, what percent of the total subscribers are now on the Premium tier?

24\%

26\%

35\%

65\%

9\%

Show answer & explanation

Answer: $24\%$

Answer

The correct answer is

24\%

of the total subscribers.

To find the new Premium subscriber percentage, we first convert the basic tier fraction to a percent:

\frac{2}{5} = 40\%

. Since the Standard tier is

45\%

, the original Premium tier must contain the remaining subscribers, which is

100\% - 40\% - 45\% = 15\%

of the total. The upgrade represents

20\%

of the original

45\%

Standard subscribers, which is

0.20 \times 45\% = 9\%

of the total subscribers. Adding this

9\%

upgrade to the original

15\%

Premium percentage results in a final percentage of

24\%

.

Step-by-Step Solution

1

Determine the original subscriber percentages for all three tiers.

Basic:

\frac{2}{5} = 40\%

. Standard:

45\%

. Premium:

100\% - (40\% + 45\%) = 15\%

.

Establishing the starting percentages allows us to track changes relative to the total subscriber population.

2

Calculate the percentage of total subscribers upgrading from Standard to Premium.

20\%

of the original

45\%

Standard subscribers =

0.20 \times 45\% = 9\%

of the total subscribers.

Since the upgrade rate is relative to the Standard tier, we multiply the rate by the Standard tier's share of the total population.

3

Calculate the final Premium percentage by adding the upgrade percentage to the original Premium percentage.

15\% + 9\% = 24\%

.

The final Premium percentage is the sum of the original Premium percentage and the percentage of subscribers who upgraded from Standard.

Key Concept

Calculating percentages of subpopulations and translating them to percentages of the entire population.

Question 4606Question →

In 1746, a group of London booksellers commissioned Samuel Johnson to write an authoritative dictionary of the English language. Johnson spent nearly nine years compiling the work, defining over 40,000 words. Unlike modern lexicographers who work in large teams, Johnson completed the monumental task almost entirely on his own. Throughout the process, he carefully selected illustrative quotations from famous authors, which helped demonstrate how words were used in context. Upon its publication in 1755, the dictionary was widely praised for its comprehensive scope and became the standard reference for over a century, reaping massive props from contemporary scholars who thought it was totally awesome.

Which choice best maintains the established tone and style of the passage?

NO CHANGE

eliciting enthusiastic encomiums from contemporaneous academicians who deemed it exceptionally laudable

earning high praise from contemporary scholars

receiving favorable commendations and praise from scholars of the time who liked it and approved of it

Show answer & explanation

Answer: earning high praise from contemporary scholars

Answer

earning high praise from contemporary scholars

The correct option maintains the informative, objective historical tone of the passage. It avoids informal slang, is not overly pretentious, and expresses the idea clearly and concisely.

Step-by-Step Solution

1

Analyze the context and established tone of the passage.

The passage uses a neutral, informative, and historical tone to detail Samuel Johnson's creation of his dictionary.

Stylistic appropriateness requires selecting an option that matches the stylistic register of the surrounding text.

2

Identify any tone or style errors in the underlined portion.

The original phrasing in the passage uses informal modern slang, which creates an abrupt tone clash with the objective historical style.

Recognizing that the original text has a tone error eliminates the 'NO CHANGE' option.

3

Evaluate the remaining choices for tone, precision, and conciseness.

The option containing overly complex vocabulary is too pretentious, and the long option is highly redundant. The simple, standard phrase maintains the correct tone and is direct.

Selecting the option that is both stylistically consistent and concise ensures the writing remains effective and professional.

Key Concept

Stylistic Appropriateness

Question 4607Question →

An astronomical unit (AU) is a unit of length equal to the average distance from the Earth to the Sun, approximately $1.5 \times 10^8$ kilometers. A scientific probe travels through space at a constant speed of $2.5 \times 10^4$ meters per second. How many hours would it take the probe to travel a distance of $3.6 \times 10^2$ AU?

6.0 \times 10^2

6.0 \times 10^5

6.0 \times 10^{11}

3.6 \times 10^7

3.75 \times 10^{14}

Show answer & explanation

Answer: $6.0 \times 10^5$

Answer

6.0 \times 10^5

hours

To find the travel time, we first determine the total distance in meters. Since

1\text{ AU} = 1.5 \times 10^8\text{ km}

and

1\text{ km} = 10^3\text{ m}

,

1\text{ AU} = 1.5 \times 10^{11}\text{ m}

. Thus, a distance of

3.6 \times 10^2\text{ AU}

equals

(3.6 \times 10^2) \times (1.5 \times 10^{11}) = 5.4 \times 10^{13}\text{ m}

. Dividing this distance by the speed of

2.5 \times 10^4\text{ m/s}

yields the travel time in seconds:

\frac{5.4 \times 10^{13}}{2.5 \times 10^4} = 2.16 \times 10^9\text{ s}

. Finally, converting seconds to hours by dividing by

3.6 \times 10^3\text{ s/h}

gives

\frac{2.16 \times 10^9}{3.6 \times 10^3} = 0.6 \times 10^6 = 6.0 \times 10^5\text{ hours}

.

Step-by-Step Solution

1

Convert the total distance from astronomical units (AU) to kilometers, and then to meters.

Distance =

3.6 \times 10^2 \text{ AU} \times 1.5 \times 10^8 \text{ km/AU} = 5.4 \times 10^{10} \text{ km} = 5.4 \times 10^{13} \text{ m}

.

Since the speed is given in meters per second, the total distance must be in meters to keep units consistent.

2

Calculate the travel time in seconds by dividing the distance in meters by the speed in meters per second.

Time in seconds =

\frac{5.4 \times 10^{13} \text{ m}}{2.5 \times 10^4 \text{ m/s}} = 2.16 \times 10^9 \text{ s}

.

Time is equal to distance divided by speed (

t = \frac{d}{s}

).

3

Convert the travel time from seconds to hours by dividing by

3.6 \times 10^3

(the number of seconds in one hour).

Time in hours =

\frac{2.16 \times 10^9}{3.6 \times 10^3} = 6.0 \times 10^5 \text{ hours}

.

Dividing the total seconds by

3,600

yields the time in hours.

Key Concept

Operations with scientific notation and dimensional analysis involving distance, rate, and time.

Alternative Method

Convert the speed to astronomical units per hour first, then divide the distance in astronomical units by this speed.

Estimated Time:2m 0s

Question 4608Question →

Arrange the following four mathematical expressions in order from least to greatest value:

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from least to greatest is

S

,

P

,

R

, and

Q

, which correspond to the decimal values

0.16 < 0.25 < 0.28 < 0.3

.

Evaluating each term yields decimal values:

S = 0.16

,

P = 0.25

,

R = 0.28

, and

Q = 0.3

. Ordering these from least to greatest gives

0.16 < 0.25 < 0.28 < 0.3

, which corresponds to the sequence

S, P, R, Q

.

Step-by-Step Solution

1

Convert the fractional squared expression

S

to a decimal.

S = \left(\frac{2}{5}\right)^2 = \frac{4}{25} = 0.16

Squaring a fraction involves squaring both the numerator and denominator, then converting the resulting fraction to decimal form.

2

Convert the negative exponent expression

P

to a decimal.

P = 4^{-1} = \frac{1}{4} = 0.25

A negative exponent represents the reciprocal of the base raised to the positive power.

3

Convert the scientific notation expression

R

to a decimal.

R = 2.8 \times 10^{-1} = 0.28

Multiplying by

10^{-1}

shifts the decimal point one position to the left.

4

Convert the square root expression

Q

to a decimal.

Q = \sqrt{0.09} = 0.3

Finding the square root of a decimal less than

1

results in a value larger than the original decimal, since

0.3 \times 0.3 = 0.09

.

5

Compare the resulting decimal values to order them from least to greatest.

0.16 < 0.25 < 0.28 < 0.3

, so the order is

S < P < R < Q

.

Ordering the converted decimal values yields the correct final arrangement.

Key Concept

Converting exponential, radical, and scientific notation expressions to decimals to compare and order their values.

Question 4609Question →

### Venusian Resurfacing

The surface of Venus has remarkably few impact craters, suggesting a relatively young surface age of 300 to 600 million years. Scientists agree that volcanism is responsible for erasing older craters, but they debate the timeline and nature of this resurfacing.

*Hypothesis 1*
Venus experiences episodic, global volcanic events. Because Venus lacks Earth-like plate tectonics, internal heat cannot escape steadily. Instead, heat builds up in the mantle over hundreds of millions of years, eventually causing the lithosphere to weaken and overturn. This leads to rapid, planet-wide volcanic resurfacing within a span of less than 100 million years, followed by a long period of geological inactivity during which heat accumulates again.

*Hypothesis 2*
Venus undergoes gradual, localized resurfacing. The planet is geologically active, with continuous but small-scale volcanic eruptions and tectonic deformation occurring in various regions at different times. Over hundreds of millions of years, these scattered, ongoing events gradually bury and erase older craters, maintaining a young average surface age without requiring a single, catastrophic global event.

Which of the following statements best summarizes the core claim of Hypothesis 2 regarding the resurfacing of Venus?

The surface is renewed through steady, ongoing volcanic and tectonic processes occurring in localized areas.

The surface is renewed through sudden, global volcanic events triggered by mantle heat buildup.

The surface is renewed through the continuous subduction and movement of global tectonic plates.

The surface is renewed by intense solar radiation melting the crust in a uniform, planet-wide pattern.

Show answer & explanation

Answer: The surface is renewed through steady, ongoing volcanic and tectonic processes occurring in localized areas.

Answer

The surface is renewed through steady, ongoing volcanic and tectonic processes occurring in localized areas.

The correct answer states that the surface is renewed through steady, ongoing volcanic and tectonic processes occurring in localized areas. This matches Hypothesis 2, which argues that resurfacing on Venus happens gradually via continuous, localized, small-scale volcanic and tectonic activity rather than a single global catastrophe.

Step-by-Step Solution

1

Identify the target viewpoint in the question.

The question asks for the core claim of Hypothesis 2.

Focusing on the correct hypothesis prevents misattributing claims from Hypothesis 1.

2

Locate the description of Hypothesis 2 in the passage and summarize its main mechanism.

Hypothesis 2 describes 'gradual, localized resurfacing' driven by 'continuous but small-scale volcanic eruptions and tectonic deformation occurring in various regions.'

This establishes the factual basis for identifying the correct summary.

3

Compare the summary of Hypothesis 2 with the given options.

The option stating that resurfacing occurs through steady, localized processes directly matches the description of Hypothesis 2, while other options describe Hypothesis 1, introduce plate tectonics, or mention unrelated processes like solar radiation.

This determines the correct option by elimination and direct matching.

Key Concept

Identifying Core Claims and Hypotheses

Estimated Time:1m 0s

Question 4610Question →

Forgotten in a dusty attic, the archivist was finally able to restore the vintage film print to its original clarity.

Which choice best corrects the underlined portion of the sentence?

NO CHANGE

the vintage film print was finally restored by the archivist

the vintage film print being finally restored by the archivist

the archivist finally restored the vintage film print, she restored it

Show answer & explanation

Answer: the vintage film print was finally restored by the archivist

Answer

The correct choice is the option that replaces the underlined portion with 'the vintage film print was finally restored by the archivist'. This resolves the dangling modifier by placing the noun being modified immediately after the introductory phrase.

The correct choice resolves the dangling modifier by changing the subject of the main clause to 'the vintage film print', which is the noun logically modified by the introductory phrase 'Forgotten in a dusty attic'.

Step-by-Step Solution

1

Identify the introductory modifying phrase in the sentence.

The modifying phrase is 'Forgotten in a dusty attic.'

Understanding which part of the sentence functions as a modifier is the first step in assessing its correctness.

2

Identify the subject that immediately follows the modifying phrase.

The subject immediately following the comma is 'the archivist.'

An introductory modifier must logically describe the subject of the clause that follows it.

3

Evaluate the logical relationship between the modifier and the subject.

The archivist was not forgotten in a dusty attic; the vintage film print was.

This logical mismatch creates a dangling modifier, indicating the sentence needs revision.

4

Select the choice that places the correct logical subject immediately after the modifier.

Replacing the underlined portion with 'the vintage film print was finally restored by the archivist' resolves the error.

This placement aligns the modifier with the noun it describes, restoring logical clarity to the sentence.

Key Concept

Introductory modifiers must be immediately followed by the noun or pronoun they logically describe. When the subject following the modifier is incorrect, it creates a dangling modifier.

Estimated Time:45s

Question 4611Question →

A bookstore has a sale where the price of any paperback book is reduced by $4$ dollars. If the sale price of a paperback book is $12$ dollars, and its original price is $p$ dollars, which of the following equations can be used to find $p$ ?

p - 4 = 12

p + 4 = 12

4 - p = 12

4p = 12

\frac{p}{4} = 12

Show answer & explanation

Answer: $p - 4 = 12$

Answer

The equation

p - 4 = 12

The original price of the book is

p

dollars. Since the price is reduced by

4

dollars, we subtract

4

from

p

, which is written as

p - 4

. Since this resulting sale price is equal to

12

dollars, the correct equation representing the relationship is

p - 4 = 12

.

Step-by-Step Solution

1

Identify the variable and the mathematical values given in the scenario.

The original price is represented by the variable

p

. The price reduction is

4

dollars, and the final sale price is

12

dollars.

This sets up the translation of the word problem into algebraic terms.

2

Translate the phrase 'reduced by

4

dollars' into an algebraic expression.

A reduction of

4

dollars from the original price

p

is written as

p - 4

.

A reduction or discount represents subtraction from the starting amount.

3

Equate the expression representing the sale price to the given sale price value.

The equation is

p - 4 = 12

.

Since the sale price is given as

12

dollars, the expression for the reduced price must equal

12

.

Key Concept

Translating real-world discount scenarios into one-step linear equations.

Estimated Time:45s

Question 4612Question →

In the dry valleys of Antarctica, gravity-driven katabatic winds descend from the high polar plateau. These powerful winds can reach speeds of up to two hundred miles per hour, they dry out the soil and prevent any vegetation from growing. Consequently, scientists use this unique, arid environment to simulate conditions on Mars.

Which of the following choices best replaces the underlined portion of the passage?

NO CHANGE

hour; drying

hour, drying

hour. Because they dry

Show answer & explanation

Answer: hour, drying

Answer

hour, drying

The correct option replaces the comma splice with a comma followed by a participial phrase. This eliminates the second independent clause and turns it into a dependent modifier, resolving the comma splice grammatically.

Step-by-Step Solution

1

Analyze the original sentence structure to identify if there is a grammatical error.

The original sentence contains two independent clauses joined only by a comma, which is an incorrect comma splice.

Identifying the error type helps narrow down the correct punctuation and structure needed.

2

Evaluate the choices to find the one that corrects the comma splice without introducing new fragments or punctuation errors.

The choice using a comma followed by a present participle ('drying') correctly transforms the second clause into a modifying participial phrase, eliminating the comma splice.

Choosing a modifying participial phrase smoothly connects the action to the main subject and maintains sentence flow.

Key Concept

Identifying and correcting comma splices and run-on sentences using participial phrases or proper punctuation.

Question 4613Question →

The following sentence segments, when combined, should form a single, grammatically correct sentence. Arrange the segments in the correct order to construct a sentence that contains no misplaced or dangling modifiers.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order of the sentence segments is: 'Dressed in a sleek tuxedo, the master of ceremonies warmly greeted the patrons who were entering the theater.'

The correct order places the introductory participial phrase 'Dressed in a sleek tuxedo,' directly before the noun it modifies, 'the master of ceremonies.' It then follows with the main verb phrase 'warmly greeted the patrons' and concludes with the relative clause 'who were entering the theater,' which correctly modifies 'the patrons.' This arrangement ensures that all modifiers are adjacent to their targets and the sentence structure is clear and grammatical.

Step-by-Step Solution

1

Identify the introductory modifier.

The phrase 'Dressed in a sleek tuxedo,' is identified as an introductory participial phrase.

Participial phrases at the beginning of a sentence must immediately precede the noun they modify to avoid a dangling modifier.

2

Determine the subject of the modifier.

The noun phrase 'the master of ceremonies' is the logical subject who is dressed in the tuxedo.

Placing this noun phrase directly after the introductory phrase ensures the modifier is placed correctly.

3

Connect the verb and object to complete the main clause.

The verb phrase 'warmly greeted the patrons' follows the subject.

This establishes the core action of the sentence in a natural subject-verb-object order.

4

Place the relative clause next to its antecedent.

The relative clause 'who were entering the theater.' modifies 'the patrons'.

Placing this clause immediately after 'the patrons' prevents it from mismodifying other nouns like the master of ceremonies or the tuxedo.

Key Concept

Modifiers must be placed as close as possible to the words they are intended to modify to ensure clarity and grammatical correctness.

Estimated Time:1m 0s

Question 4614Question →

Read the passage about the Voyager 1 space probe. Fill in the blank with the correct form of the verb 'become' to maintain grammatical consistency within the passage.

Fill in the blanks below

Launched by NASA in 1977, the Voyager 1 space probe was designed to study the outer Solar System. As it passed Jupiter and Saturn, it captured detailed images that revealed active volcanoes on Jupiter's moon Io. Over the next few decades, the probe continued its journey, and in 2012, it the first human-made object to enter interstellar space.

Show answer & explanation

Answer

became

The correct answer is 'became'. The passage establishes a consistent past-tense narrative through verbs such as 'was designed', 'passed', and 'continued'. Because the event in the final clause occurred in the past (in 2012), the verb must also be in the simple past tense to maintain consistency. The simple past tense of 'become' is 'became'.

Step-by-Step Solution

1

Identify the verb tense established in the passage.

The verbs 'was designed', 'passed', 'captured', and 'continued' are in the simple past tense, establishing a past narrative timeline.

Verbs in a passage must remain consistent in tense unless there is a clear chronological shift.

2

Determine the temporal context of the blank.

The action occurred 'in 2012', which is a completed event in the past.

The time marker indicates that the event is historical and requires a past tense verb.

3

Conjugate the base verb 'become' to the simple past tense.

The past tense form of 'become' is 'became'.

This maintains the simple past tense consistency of the narrative.

Key Concept

Verb Tense and Consistency

Question 4615Question →

A manufacturing plant operates two types of machines, Type A and Type B. The ratio of the number of Type A machines to Type B machines is $3:5$ . Each Type A machine produces widgets at a constant rate that is $60\%$ faster than the constant rate of a Type B machine. When all machines of both types are operating simultaneously, they produce a total of $98$ widgets per hour. If the plant increases the number of Type A machines by $50\%$ and decreases the number of Type B machines by $20\%$ , what is the total number of widgets the new setup will produce in $3$ hours?

112

246

312

336

382

Show answer & explanation

Answer: 336

Answer

336

The correct answer is 336 because setting up the initial production equation based on the ratios gives a compound constant of

xr = 10

. Applying the percentage adjustments yields a new hourly production rate of 112 widgets. Multiplying this hourly rate by the specified 3 hours gives a total of 336 widgets.

Step-by-Step Solution

1

Represent the machine counts and rates using variables based on the given ratios.

Let the number of Type A machines be

3x

and the number of Type B machines be

5x

. Let the rate of a Type B machine be

r

widgets/hour. The rate of a Type A machine is

1.6r

widgets/hour.

This establishes algebraic expressions for the quantities in terms of common multipliers

x

and

r

.

2

Set up an equation for the initial total hourly production and solve for

xr

.

(3x)(1.6r) + (5x)(r) = 98 \implies 4.8xr + 5xr = 98 \implies 9.8xr = 98 \implies xr = 10

.

This allows us to find the value of the joint constant factor

xr

needed for subsequent calculations.

3

Determine the new machine counts after the percentage changes.

New Type A count:

3x \times 1.50 = 4.5x

. New Type B count:

5x \times 0.80 = 4x

.

This applies the 50% increase to Type A and the 20% decrease to Type B machine counts.

4

Calculate the new total hourly production rate using the value of

xr

.

New hourly rate:

(4.5x)(1.6r) + (4x)(r) = 7.2xr + 4xr = 11.2xr

. Substituting

xr = 10

yields

11.2 \times 10 = 112

widgets/hour.

This finds the rate at which widgets are produced in the new configuration.

5

Multiply the new hourly rate by the specified time of 3 hours.

Total production:

112 \text{ widgets/hour} \times 3 \text{ hours} = 336

widgets.

This yields the final total quantity of widgets produced over the 3-hour duration.

Key Concept

Solving compound ratio and rate problems with percentage changes

Alternative Method

Instead of variables, you can plug in convenient numbers that satisfy the ratios. Suppose there are initially

30

machines of Type A and

50

machines of Type B. Let a Type B machine produce at a rate of

1

widget/hour, so a Type A machine produces

1.6

widgets/hour. The total initial hourly rate is

30(1.6) + 50(1) = 48 + 50 = 98

widgets/hour, which matches the prompt. Increasing Type A by 50% gives

45

machines, and decreasing Type B by 20% gives

40

machines. The new hourly rate is

45(1.6) + 40(1) = 72 + 40 = 112

widgets/hour. For 3 hours, this gives

112 \times 3 = 336

widgets.

Estimated Time:3m 0s

Question 4616Question →

Arrange the following mathematical expressions in order from least to greatest value:

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from least to greatest value is

(2.5 \times 10^1)^2

, followed by

\sqrt[3]{3.43 \times 10^8}

, then

\sqrt{6.4 \times 10^5}

, and finally

\frac{5.4 \times 10^6}{6 \times 10^3}

.

Each expression is simplified to a standard integer representation:

(2.5 \times 10^1)^2 = 625

,

\sqrt[3]{3.43 \times 10^8} = 700

,

\sqrt{6.4 \times 10^5} = 800

, and

\frac{5.4 \times 10^6}{6 \times 10^3} = 900

. Comparing these integers from smallest to largest yields the correct sequence.

Step-by-Step Solution

1

Evaluate the expression

\sqrt{6.4 \times 10^5}

by converting the radicand to a standard square value.

\sqrt{64 \times 10^4} = 8 \times 10^2 = 800

Converting the base to 64 and reducing the exponent of 10 to an even number allows easy extraction of the square root.

2

Evaluate the expression

(2.5 \times 10^1)^2

by simplifying the terms inside the parentheses first.

(25)^2 = 625

Multiplying 2.5 by 10 simplifies the base to 25 before applying the exponent.

3

Evaluate the expression

\frac{5.4 \times 10^6}{6 \times 10^3}

using rules of scientific division.

0.9 \times 10^3 = 900

Dividing the coefficients (

5.4 \div 6 = 0.9

) and subtracting the exponent in the denominator from the numerator (

10^{6-3} = 10^3

) yields the result.

4

Evaluate the expression

\sqrt[3]{3.43 \times 10^8}

by converting the radicand to a standard cube value.

\sqrt[3]{343 \times 10^6} = 7 \times 10^2 = 700

Converting the base to 343 and adjusting the exponent to 6 (a multiple of 3) allows easy extraction of the cube root.

5

Compare the evaluated integers to determine the correct order from least to greatest.

625 < 700 < 800 < 900

Comparing the simplified values reveals that the correct sequence is

(2.5 \times 10^1)^2

,

\sqrt[3]{3.43 \times 10^8}

,

\sqrt{6.4 \times 10^5}

, and

\frac{5.4 \times 10^6}{6 \times 10^3}

.

Key Concept

Simplification of exponential, radical, and scientific notation expressions to comparable decimal values.

Alternative Method

Instead of converting all expressions to standard numbers, convert them all to scientific notation with a base power of

10^2

(i.e.,

6.25 \times 10^2

,

7.0 \times 10^2

,

8.0 \times 10^2

, and

9.0 \times 10^2

) to compare their coefficients directly.

Estimated Time:2m 0s

Question 4617Question →

Four different brands of a sports drink contain different proportions of electrolytes by weight. The proportions for each brand are listed below:

* Brand P: $\frac{5}{12}$ of its weight is electrolytes
* Brand Q: $41.8\%$ of its weight is electrolytes
* Brand R: $0.416$ of its weight is electrolytes
* Brand S: $\frac{13}{30}$ of its weight is electrolytes

Arrange the brands in order from the least proportion of electrolytes to the greatest proportion of electrolytes.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from least to greatest proportion of electrolytes is Brand R, Brand P, Brand Q, and Brand S.

To compare the values, converting each to a decimal is the most reliable strategy. Brand R is already a decimal (

0.416

). Converting Brand P yields

\frac{5}{12} \approx 0.4167

. Converting Brand Q yields

41.8\% = 0.418

. Converting Brand S yields

\frac{13}{30} \approx 0.4333

. Comparing these decimals reveals that

0.416 < 0.4167 < 0.418 < 0.4333

, corresponding to the sequence: Brand R, Brand P, Brand Q, Brand S.

Step-by-Step Solution

1

Identify and list all values given for each brand.

Brand P:

\frac{5}{12}

, Brand Q:

41.8\%

, Brand R:

0.416

, Brand S:

\frac{13}{30}

.

This establishes the raw numbers that need comparison.

2

Convert each value into a decimal format to allow direct comparison, rounding to four decimal places where necessary.

Brand R:

0.4160

; Brand P:

5 \div 12 \approx 0.4167

; Brand Q:

41.8\% = 0.4180

; Brand S:

13 \div 30 \approx 0.4333

.

Converting to decimals standardizes the formats and makes close comparisons straightforward.

3

Compare the standardized decimal values from smallest to largest.

0.4160 < 0.4167 < 0.4180 < 0.4333

, which corresponds to the order: Brand R, Brand P, Brand Q, Brand S.

Ordering the values correctly identifies the brands from the least proportion of electrolytes to the greatest.

Key Concept

Comparing and ordering rational numbers by converting fractions, decimals, and percents into a single consistent format.

Alternative Method

Instead of converting to decimals, all values can be converted to percentages: Brand R is

41.6\%

, Brand P is

\frac{5}{12} \times 100\% \approx 41.67\%

, Brand Q is

41.8\%

, and Brand S is

\frac{13}{30} \times 100\% \approx 43.33\%

. Comparing these values gives

41.6\% < 41.67\% < 41.8\% < 43.33\%

.

Estimated Time:1m 30s

Question 4618Question →

A set of cards is numbered consecutively from $1$ to $N$ . If exactly $12$ of these cards have a number that is a multiple of both $6$ and $8$ , what is the greatest possible value of $N$ ?

Show answer & explanation

Answer: 311

Answer

The greatest possible value of

N

is

311

.

The correct value is 311. Since the numbers must be multiples of both 6 and 8, they must be multiples of their least common multiple, which is 24. The twelfth multiple of 24 is 288, and the thirteenth multiple is 312. To have exactly 12 such multiples, the maximum number N must be at least 288 but strictly less than 312, meaning the largest integer value is 311.

Step-by-Step Solution

1

Find the least common multiple (LCM) of 6 and 8.

The LCM of 6 and 8 is 24.

Any number that is a multiple of both 6 and 8 must be a multiple of their least common multiple.

2

Calculate the 12th and 13th multiples of 24.

The 12th multiple is

12 \times 24 = 288

and the 13th multiple is

13 \times 24 = 312

.

To have exactly 12 multiples in the set, the set must include the 12th multiple but exclude the 13th multiple.

3

Determine the maximum value of

N

such that 312 is not included.

N = 311

.

The largest integer less than 312 is 311. If

N

were 312 or greater, the set would contain 13 or more multiples.

Key Concept

Least Common Multiple and Divisibility Properties

Question 4619Question →

While the volunteers cleaned the park, the children planted flowers near the entrance.

Which choice is the best version of the underlined portion?

NO CHANGE

park; the children

park, and the children

park. The children

Show answer & explanation

Answer: NO CHANGE

Answer

The correct version is 'park, the children' (represented by the option to make no changes) because it properly uses a comma to separate the introductory dependent clause from the main independent clause.

The correct version properly uses a comma to separate the introductory dependent clause from the main independent clause.

Step-by-Step Solution

1

Identify the boundary between the introductory clause and the main clause.

The clause 'While the volunteers cleaned the park' is a dependent clause, and 'the children planted flowers near the entrance' is the main independent clause.

The word 'While' is a subordinating conjunction, making the first clause dependent.

2

Determine the correct punctuation to join an introductory dependent clause to an independent clause.

A comma must be used at the end of the introductory dependent clause.

Standard English conventions require a comma after introductory clauses to prevent confusion.

3

Evaluate the choices based on this punctuation rule.

The option containing the comma and no extra conjunctions or incorrect end marks is correct.

Other options introduce errors such as fragmenting the dependent clause with a semicolon or period, or rendering the sentence incomplete with a coordinating conjunction.

Key Concept

Using commas to separate introductory dependent clauses from main clauses

Estimated Time:45s

Question 4620Question →

The following passage is adapted from an essay about astrophysics.

In 1967, astrophysicist Jocelyn Bell Burnell noticed a series of anomalous, highly regular radio pulses while analyzing data from a radio telescope. While some colleagues initially dismissed the signals as man-made interference, Burnell painstakingly ruled out terrestrial sources. Her meticulous observations eventually led to the discovery of pulsars, which are rotating neutron stars that dump beams of electromagnetic radiation into space.

Which of the following options most precisely and clearly replaces the underlined word 'dump' to maintain the formal, academic tone of the passage?

NO CHANGE

emit

spill

distribute

Show answer & explanation

Answer: emit

Answer

emit

The word 'emit' is the most precise and appropriate choice in this scientific context. It formally describes the process of releasing or sending out radiation, aligning perfectly with the academic tone established in the passage.

Step-by-Step Solution

1

Analyze the context of the underlined word to determine the appropriate tone and precision required.

The passage describes a scientific discovery in a formal, academic tone.

Word choice must match the established formal register of the scientific description.

2

Evaluate each option against the context of celestial bodies radiating energy.

The word 'emit' is the precise scientific term for discharging or sending forth radiation, whereas 'dump' and 'spill' are too informal, and 'distribute' is conceptually inaccurate.

Selecting the most precise and stylistically appropriate word ensures clarity and maintains register.

Key Concept

Word Precision and Clarity

Estimated Time:1m 0s

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