All practice questions

Question 5421Question →

A box contains $30$ raffle tickets numbered $1$ through $30$ . If one ticket is selected at random from the box, what is the probability that the number on the selected ticket is a multiple of $4$ or a multiple of $6$ ?

\frac{1}{15}

\frac{1}{5}

\frac{1}{3}

\frac{2}{5}

\frac{1}{2}

Show answer & explanation

Answer: $\frac{1}{3}$

Answer

The probability that the number on the selected ticket is a multiple of

4

or a multiple of

6

is

\frac{1}{3}

.

The correct answer is determined by applying the addition rule for non-mutually exclusive events:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

. Out of

30

tickets,

7

are multiples of

4

and

5

are multiples of

6

. The numbers

12

and

24

are multiples of both

4

and

6

, meaning they belong to the intersection. Calculating the total number of unique favorable tickets gives

7 + 5 - 2 = 10

. Dividing

10

favorable outcomes by the

30

total tickets yields a probability of

\frac{10}{30} = \frac{1}{3}

.

Step-by-Step Solution

1

Identify the total number of possible outcomes.

There are

30

total tickets in the box, so the sample space size is

30

.

Each ticket numbered 1 through 30 is equally likely to be selected.

2

Count the outcomes for each individual event.

Multiples of

4

:

\{4, 8, 12, 16, 20, 24, 28\} \rightarrow 7

outcomes.
Multiples of

6

:

\{6, 12, 18, 24, 30\} \rightarrow 5

outcomes.

Listing or dividing

30

by

4

and

6

determines how many tickets satisfy each separate condition.

3

Identify and count the overlapping outcomes (multiples of both

4

and

6

).

Multiples of both

4

and

6

are multiples of

\text{LCM}(4, 6) = 12

, which are

\{12, 24\} \rightarrow 2

outcomes.

These numbers are contained in both individual lists and will be double-counted if not accounted for.

4

Apply the Principle of Inclusion-Exclusion to find the total number of favorable outcomes.

\text{Favorable outcomes} = 7 + 5 - 2 = 10.

Subtracting the intersection prevents double-counting the tickets that satisfy both conditions.

5

Calculate the probability.

P(\text{multiple of } 4 \text{ or } 6) = \frac{10}{30} = \frac{1}{3}.

Probability is the ratio of favorable outcomes to total possible outcomes.

Key Concept

Probability of Non-Mutually Exclusive Events (Inclusion-Exclusion Principle)

Estimated Time:1m 0s

Question 5422Question →

A student is creating a flag design consisting of 3 vertical stripes in a row. The student can choose from 5 different colors: Red, Blue, Green, Yellow, and White. To ensure visual contrast, any 2 adjacent stripes must be different colors. How many different flag designs can be created under these rules?

Show answer & explanation

Answer: 80

Answer

80

To find the total number of flag designs, apply the Fundamental Counting Principle across the three sequential stripe choices. The first stripe can be any of the 5 colors. The second stripe cannot match the first stripe's color, leaving 4 options. The third stripe cannot match the second stripe's color, which also leaves 4 options (since it can re-use the first stripe's color). Multiplying these choices together gives

5 \times 4 \times 4 = 80

unique flag designs.

Step-by-Step Solution

1

Determine choices for the first stripe

5 choices

Any of the 5 available colors can be selected for the first stripe.

2

Determine choices for the second stripe

4 choices

The second stripe must differ in color from the first stripe.

3

Determine choices for the third stripe

4 choices

The third stripe must differ in color from the second stripe (it may be the same color as the first stripe).

4

Apply the Fundamental Counting Principle

5 \times 4 \times 4 = 80

Multiply the options available at each stage to calculate the total number of distinct flag designs.

Key Concept

Fundamental Counting Principle with adjacent restrictions

Estimated Time:1m 15s

Question 5423Question →

If $u = -3$ and $v = -\frac{1}{2}$ , what is the value of the algebraic expression below? Enter your numerical answer in the blank.

Fill in the blanks below

The value of the expression

\frac{4uv^2 - u^2}{2v - u}

is .

Show answer & explanation

Answer

The value of the expression when evaluated at

u = -3

and

v = -\frac{1}{2}

is

-6

.

Substituting

u = -3

and

v = -\frac{1}{2}

into the numerator gives

4(-3)(-\frac{1}{2})^2 - (-3)^2 = -3 - 9 = -12

. Substituting into the denominator gives

2(-\frac{1}{2}) - (-3) = -1 + 3 = 2

. Dividing

-12

by

2

results in

-6

.

Step-by-Step Solution

1

Evaluate the terms containing exponents in the numerator.

v^2 = \left(-\frac{1}{2}\right)^2 = \frac{1}{4}

and

u^2 = (-3)^2 = 9

.

Exponents must be calculated before multiplication according to the order of operations.

2

Evaluate the numerator

4uv^2 - u^2

.

4(-3)\left(\frac{1}{4}\right) - 9 = -3 - 9 = -12

.

Multiply

4 \times (-3) \times \frac{1}{4}

to get

-3

, then subtract

9

.

3

Evaluate the denominator

2v - u

.

2\left(-\frac{1}{2}\right) - (-3) = -1 + 3 = 2

.

Multiplying

2

by

-\frac{1}{2}

gives

-1

, and subtracting negative

3

is equivalent to adding

3

.

4

Divide the numerator by the denominator.

\frac{-12}{2} = -6

.

Dividing

-12

by

2

yields the final result

-6

.

Key Concept

Evaluating algebraic expressions involving negative numbers, fractions, and order of operations.

Estimated Time:1m 30s

Question 5424Question →

If $a = -3$ and $b = -2$ , what is the value of the expression $\frac{2a^2 - b^3}{(a - b)^2 + ab}$ ?

\frac{26}{7}

\frac{10}{7}

-\frac{10}{7}

\frac{26}{19}

\frac{26}{31}

Show answer & explanation

Answer: $\frac{26}{7}$

Answer

\frac{26}{7}

Substituting

a = -3

and

b = -2

directly into the numerator yields

2(-3)^2 - (-2)^3 = 2(9) - (-8) = 26

. Substituting into the denominator gives

((-3) - (-2))^2 + (-3)(-2) = (-1)^2 + 6 = 7

. Combining these results gives

\frac{26}{7}

.

Step-by-Step Solution

1

Substitute

a = -3

and

b = -2

into the numerator

2a^2 - b^3

.

2(-3)^2 - (-2)^3 = 2(9) - (-8) = 18 + 8 = 26

Squaring

-3

gives

9

, and cubing

-2

gives

-8

. Subtracting

-8

is equivalent to adding

8

.

2

Substitute

a = -3

and

b = -2

into the denominator

(a - b)^2 + ab

.

((-3) - (-2))^2 + (-3)(-2) = (-3 + 2)^2 + 6 = (-1)^2 + 6 = 1 + 6 = 7

Subtracting a negative number becomes addition, and squaring

-1

yields

1

.

3

Form the fraction by dividing the numerator by the denominator.

\frac{26}{7}

The evaluated numerator is

26

and the evaluated denominator is

7

.

Key Concept

Order of operations and handling negative signs when evaluating algebraic expressions involving powers and parentheses.

Estimated Time:1m 0s

Question 5425Question →

If $x = -3$ , $y = -\frac{1}{2}$ , and $z = 8$ , what is the value of the algebraic expression $\frac{x^2 y^{-1} + z^{2/3}}{2xy - 1}$ ?

Show answer & explanation

Answer: -7

Answer

The value of the expression is -7.

Substituting the given values into the expression requires careful application of exponent rules and order of operations. First,

(-3)^2 = 9

and

(-\frac{1}{2})^{-1} = -2

, so

x^2 y^{-1} = 9 \times (-2) = -18

. Second,

8^{2/3} = (\sqrt[3]{8})^2 = 2^2 = 4

. This makes the numerator

-18 + 4 = -14

. The denominator evaluates to

2(-3)(-\frac{1}{2}) - 1 = 3 - 1 = 2

. Dividing

-14

by

2

gives the correct answer of

-7

.

Step-by-Step Solution

1

Substitute

x = -3

and

y = -\frac{1}{2}

into

x^2 y^{-1}

(-3)^2 \cdot (-2) = -18

Squaring

-3

yields

9

, and taking the reciprocal of

-\frac{1}{2}

yields

-2

.

2

Substitute

z = 8

into

z^{2/3}

8^{2/3} = 4

Taking the cube root of

8

gives

2

, and squaring

2

gives

4

.

3

Evaluate the numerator

-18 + 4 = -14

Adding the evaluated terms together.

4

Substitute values into the denominator

2xy - 1

2(-3)\left(-\frac{1}{2}\right) - 1 = 3 - 1 = 2

Multiplying

2

,

-3

, and

-\frac{1}{2}

produces

3

, then subtracting

1

yields

2

.

5

Divide the numerator by the denominator

\frac{-14}{2} = -7

Simplifying the rational expression yields the final numeric answer.

Key Concept

Evaluating algebraic expressions with negative bases, rational exponents, and negative exponents

Question 5426Question →

If $x = -2$ , $y = \frac{1}{3}$ , and $z = -3$ , what is the value of the algebraic expression $\frac{3x^2 y - z^2}{x + yz}$ ?

\frac{5}{3}

-\frac{13}{3}

\frac{13}{3}

-1

5

Show answer & explanation

Answer: $\frac{5}{3}$

Answer

\frac{5}{3}

Substituting the given values into the expression requires evaluating powers of negative numbers and performing multiplication prior to addition/subtraction. In the numerator,

3(-2)^2(\frac{1}{3}) - (-3)^2 = 3(4)(\frac{1}{3}) - 9 = 4 - 9 = -5

. In the denominator,

-2 + (\frac{1}{3})(-3) = -2 - 1 = -3

. Simplifying the fraction

\frac{-5}{-3}

gives

\frac{5}{3}

.

Step-by-Step Solution

1

Evaluate the numerator

3x^2 y - z^2

by substituting

x = -2

,

y = \frac{1}{3}

, and

z = -3

.

3(-2)^2\left(\frac{1}{3}\right) - (-3)^2 = 3(4)\left(\frac{1}{3}\right) - 9 = 4 - 9 = -5

Squaring negative numbers yields positive values:

(-2)^2 = 4

and

(-3)^2 = 9

.

2

Evaluate the denominator

x + yz

using the same variable values.

-2 + \left(\frac{1}{3}\right)(-3) = -2 + (-1) = -3

Perform the multiplication

y \cdot z

before adding to

x

according to the order of operations.

3

Divide the evaluated numerator by the evaluated denominator.

\frac{-5}{-3} = \frac{5}{3}

Dividing two negative numbers produces a positive quotient.

Key Concept

Evaluating Algebraic Expressions with Negative Values and Rational Numbers

Question 5427Question →

If $m = -4$ and $n = -\frac{1}{2}$ , what is the value of the algebraic expression $\frac{m^2 - 4n^3}{(m + 2n)^2}$ ?

\frac{31}{50}

\frac{33}{50}

\frac{33}{34}

-\frac{31}{50}

\frac{24}{25}

Show answer & explanation

Answer: $\frac{33}{50}$

Answer

\frac{33}{50}

Substituting

m = -4

and

n = -\frac{1}{2}

into the numerator gives

(-4)^2 - 4\left(-\frac{1}{2}\right)^3 = 16 - \left(-\frac{1}{2}\right) = \frac{33}{2}

. Substituting into the denominator gives

\left(-4 + 2\left(-\frac{1}{2}\right)\right)^2 = (-5)^2 = 25

. Dividing the numerator by the denominator yields

\frac{33/2}{25} = \frac{33}{50}

.

Step-by-Step Solution

1

Evaluate the terms in the numerator:

m^2

and

4n^3

.

m^2 = (-4)^2 = 16

and

4n^3 = 4\left(-\frac{1}{2}\right)^3 = 4\left(-\frac{1}{8}\right) = -\frac{1}{2}

.

Substitute

m = -4

and

n = -\frac{1}{2}

while applying powers before multiplication according to PEMDAS.

2

Calculate the complete numerator by subtracting the evaluated terms.

m^2 - 4n^3 = 16 - \left(-\frac{1}{2}\right) = 16 + \frac{1}{2} = \frac{33}{2}

.

Subtracting a negative quantity is equivalent to adding its positive counterpart.

3

Evaluate the expression inside the denominator parentheses, then square it.

m + 2n = -4 + 2\left(-\frac{1}{2}\right) = -4 - 1 = -5

, and

(-5)^2 = 25

.

Grouped operations inside parentheses must be evaluated prior to applying outer exponents.

4

Divide the numerator by the denominator to get the final simplified fraction.

\frac{\frac{33}{2}}{25} = \frac{33}{2 \times 25} = \frac{33}{50}

.

Dividing a fraction by an integer combines the denominators.

Key Concept

Evaluating algebraic expressions involving negative bases, fractions, and order of operations

Estimated Time:1m 30s

Question 5428Question →

Evaluate the algebraic expression $3x^2 - 2xy + y^2$ for $x = -3$ and $y = -2$ .

Fill in the blanks below

The value of the expression

3x^2 - 2xy + y^2

when

x = -3

and

y = -2

is .

Show answer & explanation

Answer

19

Substituting

x = -3

and

y = -2

into

3x^2 - 2xy + y^2

yields

3(-3)^2 - 2(-3)(-2) + (-2)^2 = 3(9) - 12 + 4 = 27 - 12 + 4 = 19

.

Step-by-Step Solution

1

Substitute

x = -3

and

y = -2

into the expression

3(-3)^2 - 2(-3)(-2) + (-2)^2

Replace each variable with its assigned value, using parentheses to properly preserve negative signs.

2

Evaluate the exponent terms

3(9) - 2(-3)(-2) + 4

Follow the order of operations (PEMDAS) by evaluating powers first:

(-3)^2 = 9

and

(-2)^2 = 4

.

3

Perform the multiplications

27 - 12 + 4

Multiply the numerical factors:

3 \times 9 = 27

and

-2 \times (-3) \times (-2) = -12

.

4

Perform addition and subtraction from left to right

19

Subtract

12

from

27

to get

15

, then add

4

to arrive at

19

.

Key Concept

Evaluating Algebraic Expressions with Negative Values

Question 5429Question →

If $x = -3$ , $y = -\frac{1}{2}$ , and $z = 4$ , what is the numerical value of the algebraic expression $\frac{x^2 - 4y^2}{x + yz}$ ?

Show answer & explanation

Answer: -1.6

Answer

The numerical value of the expression is

-1.6

.

Substituting

x = -3

,

y = -\frac{1}{2}

, and

z = 4

into

\frac{x^2 - 4y^2}{x + yz}

gives a numerator of

(-3)^2 - 4\left(-\frac{1}{2}\right)^2 = 9 - 4\left(\frac{1}{4}\right) = 8

and a denominator of

-3 + \left(-\frac{1}{2}\right)(4) = -3 - 2 = -5

. Evaluating

\frac{8}{-5}

yields

-1.6

.

Step-by-Step Solution

1

Evaluate the numerator

x^2 - 4y^2

8

Squaring

-3

gives

9

, and squaring

-\frac{1}{2}

gives

\frac{1}{4}

. Thus,

9 - 4\left(\frac{1}{4}\right) = 9 - 1 = 8

.

2

Evaluate the denominator

x + yz

-5

Multiplying

-\frac{1}{2}

by

4

gives

-2

. Adding

-3 + (-2)

yields

-5

.

3

Compute the final fraction quotient

-1.6

Dividing the numerator

8

by the denominator

-5

yields

-1.6

.

Key Concept

Evaluating algebraic expressions using order of operations with negative bases and fractional values.

Estimated Time:1m 30s

Question 5430Question →

If $a = -2$ , $b = -\frac{1}{2}$ , and $c = 3$ , what is the value of the algebraic expression $\frac{a^3 b - 2c^2}{a - b^{-2}}$ ?

\frac{7}{3}

\frac{11}{3}

-7

\frac{16}{3}

-\frac{7}{3}

$

Show answer & explanation

Answer: $\frac{7}{3}$

Answer

The correct answer is

\frac{7}{3}

.

Substituting

a = -2

,

b = -\frac{1}{2}

, and

c = 3

gives a numerator of

(-2)^3 \left(-\frac{1}{2}\right) - 2(3)^2 = (-8)\left(-\frac{1}{2}\right) - 18 = 4 - 18 = -14

, and a denominator of

-2 - \left(-\frac{1}{2}\right)^{-2} = -2 - 4 = -6

. Dividing

-14

by

-6

simplifies to

\frac{7}{3}

.

Step-by-Step Solution

1

Substitute

a = -2

,

b = -\frac{1}{2}

, and

c = 3

into the numerator

a^3 b - 2c^2

.

Numerator

= (-2)^3 \cdot \left(-\frac{1}{2}\right) - 2(3)^2 = (-8) \cdot \left(-\frac{1}{2}\right) - 2(9) = 4 - 18 = -14

.

Apply exponents first, then multiplication, and finally subtraction.

2

Substitute

a = -2

and

b = -\frac{1}{2}

into the denominator

a - b^{-2}

.

Denominator

= -2 - \left(-\frac{1}{2}\right)^{-2} = -2 - (-2)^2 = -2 - 4 = -6

.

A negative exponent indicates the reciprocal of the base, so

\left(-\frac{1}{2}\right)^{-2} = (-2)^2 = 4

.

3

Divide the numerator by the denominator and simplify the fraction.

\frac{-14}{-6} = \frac{14}{6} = \frac{7}{3}.

Dividing two negative numbers yields a positive quotient, which simplifies by dividing the numerator and denominator by 2.

Key Concept

Evaluating algebraic expressions with negative bases and negative integer exponents

Estimated Time:1m 30s

Question 5431Question →

The following sentence is missing a pronoun. To ensure grammatically correct pronoun-antecedent agreement, what word should be placed in the blank?

Fill in the blanks below

Although the research team expected the cluster of stars to drift together, each of the stellar bodies in the outer ring has maintained independent trajectory.

Show answer & explanation

Answer

its

The correct answer is the singular possessive pronoun 'its.' In the sentence, the pronoun must refer back to its antecedent. The subject of the clause is the singular indefinite pronoun 'each.' Although the intervening prepositional phrase 'of the stellar bodies in the outer ring' contains the plural noun 'bodies,' the pronoun must agree in number with the actual subject 'each.' Since 'each' is singular and refers to an inanimate object, the singular neuter possessive pronoun 'its' is grammatically correct.

Step-by-Step Solution

1

Identify the antecedent of the missing pronoun.

The subject and antecedent of the clause containing the blank is the singular indefinite pronoun 'each.'

The prepositional phrase 'of the stellar bodies in the outer ring' contains plural nouns but functions only as a modifier, not as the grammatical subject of the clause.

2

Determine the grammatical number of the antecedent.

The pronoun 'each' is singular, which is also confirmed by the singular verb 'has maintained.'

Indefinite pronouns such as 'each' are always singular in standard formal English.

3

Select the correct pronoun that matches the antecedent in number and gender.

The singular possessive pronoun 'its' is selected.

Because 'each' is singular and refers to inanimate stellar bodies, the singular neuter possessive pronoun 'its' must be used to agree with it.

Key Concept

Pronoun-Antecedent Agreement with Indefinite Pronouns

Estimated Time:1m 0s

Question 5432Question →

In the late nineteenth century, many pioneering female journalists found that they could establish their careers by writing under pseudonyms, reporting from overseas conflict zones, and they investigated municipal corruption in major cities.

Which choice best replaces the underlined portion to maintain a parallel structure in the sentence?

they investigated

investigating

to investigate

investigations of

Show answer & explanation

Answer: investigating

Answer

investigating

The correct answer is 'investigating' because it is a gerund phrase ('investigating municipal corruption in major cities') that matches the grammatical format of the other two elements in the series ('writing under pseudonyms' and 'reporting from overseas conflict zones'), which are also gerund phrases.

Step-by-Step Solution

1

Identify the items in the list and their grammatical structures.

The preposition 'by' introduces a list of three actions: 'writing under pseudonyms' (gerund phrase) and 'reporting from overseas conflict zones' (gerund phrase).

To maintain parallel structure, all items in a list governed by the same preposition must share the same grammatical form.

2

Analyze the underlined portion to see if it matches the established pattern.

The underlined portion 'they investigated' is a clause (subject + verb), which does not match the gerund structure of the first two list items.

Identifying the grammatical mismatch highlights the structural error that needs correction.

3

Select the choice that uses the gerund form to make the third item parallel.

The choice 'investigating' is a gerund, which matches 'writing' and 'reporting' perfectly.

Using the gerund form completes the list with a consistent, parallel grammatical structure.

Key Concept

Parallel structure in lists requires all items in a series to share the same grammatical form (e.g., all gerunds, all infinitives, or all clauses).

Question 5433Question →

In 1967, astrophysicist Jocelyn Bell Burnell detected a series of highly regular radio pulses in her telescopic data. Her advisor initially dismissed the signals as man-made interference, but Bell Burnell persisted in analyzing the anomaly, eventually proving the existence of pulsars.

Which choice is the most grammatically correct and logical version of the underlined portion of the sentence?

advisor initially dismissed the signals as man-made interference, but Bell Burnell

advisor initially dismissed the signals as man-made interference, Bell Burnell

advisor initially dismissing the signals as man-made interference; Bell Burnell

advisor initially dismissed the signals as man-made interference. While Bell Burnell

Show answer & explanation

Answer: advisor initially dismissed the signals as man-made interference, but Bell Burnell

Answer

The correct choice is the original phrasing, which uses the coordinating conjunction 'but' along with a comma to join two independent clauses.

The correct option preserves the grammatical integrity of the sentence by correctly linking two independent clauses using the coordinating conjunction 'but' preceded by a comma.

Step-by-Step Solution

1

Identify the clauses in the passage.

The text contains two primary assertions: 'Her advisor initially dismissed the signals as man-made interference' and 'Bell Burnell persisted in analyzing the anomaly.'

Understanding the boundary between clauses is essential to determine whether we are connecting independent or dependent ideas.

2

Analyze the grammatical status of each clause.

Both assertions can stand alone as complete sentences, meaning they are both independent clauses.

Identifying the clauses as independent dictates that we must use a proper coordinating conjunction with a comma, a semicolon, or separate them into two sentences.

3

Evaluate the choices based on coordination and subordination rules.

The original phrasing correctly links these two independent clauses with a comma and the coordinating conjunction 'but', establishing a logical contrast between the advisor's dismissal and Bell Burnell's persistence.

This ensures the sentence is grammatically correct and expresses the intended relationship between the ideas.

Key Concept

Using coordinating conjunctions to join independent clauses and avoiding run-ons, comma splices, or sentence fragments.

Estimated Time:1m 0s

Question 5434Question →

During the mid-nineteenth century, naturalists frequently traveled alongside surveyors to document the flora of the American West. While the surveyors mapped the rugged terrain, the naturalists collected specimens of rare wildflowers. Because they were often preoccupied with the physical demands of the journey, many specimens remained undocumented for decades.

Which of the following choices most effectively clarifies the underlined pronoun in the passage?

NO CHANGE

the naturalists

it

they themselves

Show answer & explanation

Answer: the naturalists

Answer

The correct answer is the option that replaces the pronoun with 'the naturalists' to resolve the ambiguity.

The correct choice replaces the ambiguous pronoun 'they' with the specific noun 'the naturalists.' In the original sentence, 'they' could refer to either 'the surveyors' or 'the naturalists,' both of which are plural nouns in the preceding sentence. Specifying 'the naturalists' clarifies who was preoccupied with the demands of the journey.

Step-by-Step Solution

1

Identify the underlined pronoun and its potential antecedents in the preceding context.

The pronoun 'they' is plural and has multiple potential plural antecedents: 'naturalists,' 'surveyors,' and 'wildflowers.'

To evaluate pronoun clarity, you must trace the pronoun back to its logical antecedent in the sentence.

2

Determine if the pronoun reference is clear or ambiguous.

The reference is ambiguous because both 'naturalists' and 'surveyors' could logically be preoccupied with the physical demands of the journey.

Pronouns must refer clearly and unambiguously to a single noun antecedent.

3

Evaluate the choices to find the one that replaces the pronoun with a clear, specific noun.

Replacing 'they' with 'the naturalists' directly resolves the ambiguity without introducing redundancy or grammatical errors.

ACT English questions require choosing the most clear, precise, and grammatically correct phrasing.

Key Concept

Pronoun Clarity and Reference

Question 5435Question →

The restoration of the medieval cathedral's stained glass windows required a painstaking process of chemical stabilization, because the glass was susceptible to "glass disease," a progressive decay caused by moisture. Artists had to apply a protective silica coating to the exterior surfaces, however, this intervention, which successfully halted the decay, slightly altered the refraction of light through the glass. Consequently, the team had to calibrate the coating's thickness to preserve the windows' original luminosity.

Which of the following options is the most grammatically correct replacement for the underlined portion?

NO CHANGE

surfaces; however, this intervention, which

surfaces; however, because this intervention, which

surfaces; however, this intervention, that

Show answer & explanation

Answer: surfaces; however, this intervention, which

Answer

The correct answer is the option that replaces the underlined text with a semicolon followed by 'however,' a comma, and the relative pronoun 'which'.

The correct answer correctly uses a semicolon to separate the two independent clauses before the conjunctive adverb 'however.' It also properly punctuates the non-restrictive relative clause ('which successfully halted the decay') with commas.

Step-by-Step Solution

1

Analyze the clause structure of the passage surrounding the transition word 'however'.

The clauses before and after 'however' are both independent clauses capable of standing alone as complete sentences.

This determines that a strong punctuation mark (like a semicolon or period) or a coordinating conjunction is required to connect them.

2

Evaluate the grammar of the original sentence (Option A).

The original sentence joins the independent clauses with only a comma before 'however,' which is a conjunctive adverb, resulting in a comma splice.

This rules out the option containing the original punctuation.

3

Examine the remaining options for sentence structure and punctuation errors.

Adding 'because' after 'however' (Option C) creates a dependent clause and a fragment. Using 'that' within commas (Option D) creates a restrictive comma error since 'that' clauses cannot be set off by commas. Only Option B correctly uses a semicolon to join the clauses and maintains the proper non-restrictive pronoun 'which'.

This confirms the correct choice by process of elimination of standard grammatical errors.

Key Concept

Run-on Sentences and Comma Splices

Estimated Time:1m 0s

Question 5436Question →

Restoring vintage arcade cabinets is a rewarding hobby that requires both woodworking and electronic skills. Enthusiasts often spend months sourcing original parts, they must also carefully repair the cathode-ray tube monitors. Once the cabinet is fully restored, it serves as a functional piece of gaming history.

Which of the following is the best replacement for the underlined portion?

parts, they

parts; they

parts; because they

parts. Because they

Show answer & explanation

Answer: parts; they

Answer

parts; they

The option 'parts; they' is correct because a semicolon is a standard and grammatically sound punctuation mark used to separate two closely related independent clauses.

Step-by-Step Solution

1

Identify the two clauses in the sentence.

The clauses are 'Enthusiasts often spend months sourcing original parts' and 'they must also carefully repair the cathode-ray tube monitors'. Both can stand alone as independent sentences.

Determining clause type is necessary to apply correct punctuation rules.

2

Check the punctuation connecting the independent clauses.

The original text uses only a comma, which creates a comma splice.

Two independent clauses cannot be joined by a comma alone without a coordinating conjunction.

3

Evaluate the choices to find a grammatically correct way to separate the clauses.

Using a semicolon without a subordinating conjunction correctly separates the two clauses.

A semicolon is designed to connect independent clauses without creating a fragment or comma splice.

Key Concept

Run-on Sentences and Comma Splices

Question 5437Question →

The following passage describes a challenge in modern astronomy. What is the correct present-tense form of the verb 'to explain' that completes the passage to maintain proper subject-verb agreement?

Fill in the blanks below

In the field of astronomy, researchers constantly analyze anomalies in the night sky. Neither of the proposed mathematical models the strange orbital decay observed in the outer rings of Saturn. Consequently, astrophysicists must continue to refine their hypotheses to account for this data.

Show answer & explanation

Answer

The correct answer is 'explains'.

The verb must agree in number with its subject, which is the singular indefinite pronoun 'Neither'. The correct present-tense form for a singular subject is 'explains'. The intervening prepositional phrase 'of the proposed mathematical models' contains the plural noun 'models', but nouns within modifying prepositional phrases do not affect subject-verb agreement.

Step-by-Step Solution

1

Identify the subject of the verb in the sentence containing the blank.

The subject is the indefinite pronoun 'Neither'.

The prepositional phrase 'of the proposed mathematical models' modifies the subject but does not change it; the head of the subject phrase is the pronoun 'Neither'.

2

Determine the number of the subject to establish agreement.

The subject 'Neither' is singular.

Indefinite pronouns such as 'each', 'either', and 'neither' are singular and require singular verbs.

3

Form the correct present-tense verb that agrees with the singular subject.

The correct present-tense form is 'explains'.

For a singular subject in the third person, the verb must end in '-s' (explains) to agree with the subject 'Neither'.

Key Concept

Subject-Verb Agreement with Indefinite Pronouns

Estimated Time:1m 0s

Question 5438Question →

The new library features large glass windows; it receives a significant amount of natural light during the day.

Which of the following options is the best replacement for the underlined portion of the sentence?

windows; it

windows, it

windows; which

windows; because it

Show answer & explanation

Answer: windows; it

Answer

The correct option is the one that uses a semicolon to connect the two independent clauses: 'windows; it'.

The correct option uses a semicolon to properly join two related independent clauses. Both parts of the sentence express complete thoughts and can stand alone as sentences, making the semicolon the correct punctuation mark.

Step-by-Step Solution

1

Analyze the grammatical structure of the clauses surrounding the underlined portion.

The clause before the punctuation ('The new library features large glass windows') and the clause after ('it receives a significant amount of natural light during the day') are both independent clauses because they can each stand alone as a complete sentence.

Identifying whether clauses are independent or dependent determines which punctuation mark is appropriate to connect them.

2

Select the correct punctuation mark to join the two independent clauses without a coordinating conjunction.

A semicolon is the correct grammatical choice to link two closely related independent clauses. Therefore, the original sentence structure is correct.

This punctuation prevents errors such as comma splices and sentence fragments.

Key Concept

Using a semicolon to link two closely related independent clauses.

Question 5439Question →

The economic advisors recommended a series of abrupt, radical, policy changes to curb inflation, the treasury department delayed implementation until the next fiscal quarter.

Which of the following options best punctuates the underlined portion of the sentence?

NO CHANGE

abrupt, radical policy changes to curb inflation; the treasury department delayed

abrupt, radical policy changes, to curb inflation; the treasury department delayed

abrupt, radical policy changes to curb inflation; although the treasury department delayed

Show answer & explanation

Answer: abrupt, radical policy changes to curb inflation; the treasury department delayed

Answer

The option that reads 'abrupt, radical policy changes to curb inflation; the treasury department delayed' is correct because it properly punctuates the coordinate adjectives, avoids inserting a comma before a restrictive modifier, and correctly separates the two independent clauses with a semicolon.

The correct option correctly punctuates the coordinate adjectives 'abrupt' and 'radical' with a comma while omitting any punctuation before the noun phrase 'policy changes'. It also correctly avoids commas around the restrictive modifier 'to curb inflation' and properly connects the two independent clauses using a semicolon.

Step-by-Step Solution

1

Analyze the relationship between the adjectives 'abrupt' and 'radical' modifying 'policy changes'.

The adjectives are coordinate because they can be reversed ('radical, abrupt') and joined by 'and' ('abrupt and radical') while retaining the same meaning. Thus, they must be separated by a comma, but no comma should be placed between the final adjective 'radical' and the modified noun phrase 'policy changes'.

Coordinate adjectives require separating punctuation, but the final adjective must not be separated from the noun it modifies.

2

Determine if the phrase 'to curb inflation' is essential (restrictive) or nonessential (nonrestrictive) to the meaning of the noun 'policy changes'.

The infinitive phrase 'to curb inflation' is restrictive because it specifies the exact purpose of the recommended policy changes. Therefore, no comma should separate it from the noun it modifies.

Restrictive modifiers must not be set off by commas.

3

Analyze the clause structures surrounding the boundary between 'inflation' and the second part of the sentence.

The clause before the boundary ('The economic advisors recommended a series of abrupt, radical policy changes to curb inflation') and the clause after ('the treasury department delayed implementation until the next fiscal quarter') are both independent. To join them without a coordinating conjunction, a semicolon must be used.

Joining two independent clauses with only a comma creates a comma splice, while placing a subordinating conjunction after a semicolon creates a dependent clause fragment.

Key Concept

Coordinate adjectives, restrictive modifiers, and independent clause punctuation rules

Estimated Time:1m 30s

Question 5440Question →

Safeguarding the Future: The Svalbard Global Seed Vault

[1]
Deep inside a sandstone mountain on the Norwegian island of Spitsbergen, halfway between mainland Norway and the North Pole, lies the Svalbard Global Seed Vault. Often referred to as the "Doomsday Vault," this facility is designed to withstand both natural and man-made disasters. It serves as a safety net for the world's agricultural heritage, protecting millions of seed samples from around the globe against accidental loss in traditional genebanks.

[2]
The vault's location was chosen with meticulous care. Svalbard is geologically stable, reducing the risk of earthquakes. Furthermore, its extreme northern latitude offers natural permafrost, which helps keep the seeds frozen even if the facility's mechanical cooling systems fail. The seeds are stored at a constant temperature of minus eighteen degrees Celsius. Wrapped in moisture-resistant foil packages and placed in sealed boxes, the seeds are shielded from moisture and oxygen, ensuring their viability for decades or even centuries.

[3]
While local genebanks exist in almost every country, they are vulnerable to war, political instability, and natural disasters. For example, during the Syrian Civil War, researchers at the International Center for Agricultural Research in the Dry Areas (ICARDA) in Aleppo were forced to abandon their facility. Fortunately, because they had previously deposited duplicates of their seed collection in the Svalbard vault, they were able to retrieve the seeds and re-establish their operations in Lebanon and Morocco. This real-world test demonstrated the indispensable role of the vault in global food security.

Suppose the writer's goal had been to write an essay that describes the construction challenges and architectural engineering details of building the Svalbard Global Seed Vault. Would this essay successfully accomplish this goal?

Yes, because the essay describes the geological stability of the mountain and the temperature requirements for storing the seeds.

Yes, because the essay explains how the ICARDA researchers re-established their operations in Lebanon and Morocco using duplicate seeds.

No, because the essay focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than the specific construction methods and engineering plans used to build it.

No, because the essay argues that the vault was poorly positioned and vulnerable to failure, which contradicts the goal of describing a successful engineering project.

Show answer & explanation

Answer: No, because the essay focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than the specific construction methods and engineering plans used to build it.

Answer

No, because the essay focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than the specific construction methods and engineering plans used to build it.

The correct answer is the option stating that the essay would not accomplish the goal because it focuses on the purpose, environmental suitability of the location, and real-world utility of the vault rather than specific construction methods and engineering plans. The passage provides a general overview of why the vault exists and where it is located, but it does not detail the technical blueprints, machinery used, or architectural engineering challenges involved in its physical creation.

Step-by-Step Solution

1

Analyze the proposed writing goal.

The goal is to describe the construction challenges and architectural engineering details of building the Svalbard Global Seed Vault.

Understanding the target goal allows for comparison with the actual content of the passage.

2

Evaluate the passage content against the proposed goal.

The passage discusses the vault's geographic location, its preservation mechanism (permafrost, foil packaging), and its real-world utility (ICARDA case study). It does not discuss blueprints, excavation techniques, construction materials, structural engineering, or specific construction challenges.

Determining what the passage actually covers helps identify whether it meets the proposed goal.

3

Select the correct option that matches the evaluation.

The correct option must state that the goal was not met ('No') and provide the reason that the essay focuses on the purpose and utility rather than the construction and engineering details.

This aligns the logical analysis of the passage with the correct answer choice.

Key Concept

Evaluating whole-essay goals requires analyzing the primary focus and scope of the entire passage to determine if it aligns with a newly proposed writing purpose.

Estimated Time:1m 30s

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