All practice questions

Question 1241Question →

In GRE Sentence Equivalence, candidates must evaluate candidate option pairs against sentence context to eliminate false synonyms and topically related distractors. Consider the following sentence stem: 'Although the lead archaeologist insisted the newly uncovered artifacts would corroborate existing theories of Bronze Age trade, several independent scholars argued that the findings were ______, directly challenging the established timeline.' Which classification best describes each set of candidate vocabulary words based on their contextual fit and semantic relationship?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The pair 'anomalous / aberrant' represents true contextual synonyms; 'spurious / specious' represents a false synonym trap based on inauthenticity; 'inimical / hostile' represents a false synonym trap based on adversity; and 'archaeological / historical' represents topically related distractors.

Matching 'anomalous / aberrant' to true contextual synonyms is correct because both words precisely denote departure from expected patterns, fitting the contrast against 'corroborate'. Matching 'spurious / specious' and 'inimical / hostile' to their respective false synonym classifications correctly identifies that despite internal dictionary synonymy, their specific meanings (forged/misleading and hostile/adverse) misalign with the sentence logic. Matching 'archaeological / historical' to topical distractors correctly reflects their reliance on thematic association without semantic equivalence.

Step-by-Step Solution

1

Analyze sentence syntax and structural clues

The concessive transition 'Although' sets up a contrast between the expectation ('corroborate existing theories') and the scholars' argument. The blank must describe findings that deviate from established expectations, reinforced by 'directly challenging the established timeline'.

Identifying sentence valence and logical direction dictates the precise semantic target.

2

Evaluate candidate pair 'anomalous / aberrant'

Both words signify a departure from normal or expected standards. Substituting either yields identical, logically coherent sentences.

This establishes them as true contextual synonyms.

3

Evaluate false synonym traps ('spurious / specious' and 'inimical / hostile')

'Spurious' and 'specious' form a synonym pair meaning fake or deceptively plausible, but the passage does not suggest the artifacts are forged. 'Inimical' and 'hostile' form a synonym pair meaning adverse or antagonistic, which improperly attributes intent to inanimate findings.

Distinguish dictionary synonymy from precise contextual appropriateness.

4

Evaluate topically related pair 'archaeological / historical'

Although relevant to Bronze Age excavations, these words are neither synonymous with each other nor capable of expressing contrast.

Eliminate options that rely solely on surface thematic associations.

Key Concept

Eliminating False Synonyms and Topically Related Distractors

Question 1242Question →

Although the fossil records of early hominins in Eastern Africa were long considered remarkably ________, exhibiting minimal variation across distinct geographical zones, recent biomechanical re-evaluations of limb bone density suggest that local micro-environments actually fostered significant morphological divergence.

Which of the following words best completes the blank in the sentence?

homogeneous

heterogeneous

fragmented

rudimentary

anomalous

Show answer & explanation

Answer: homogeneous

Answer

The word 'homogeneous' correctly completes the sentence by establishing a contrast between uniform early hominin remains and recent findings of morphological divergence.

The sentence begins with the concessionary pivot 'Although', signaling a contrast between the historical view of hominin fossils and recent re-evaluations. The second clause reveals that recent findings show 'significant morphological divergence'. Therefore, the initial view must have been that the fossils were uniform. The option 'homogeneous' (meaning uniform or composed of similar parts) fits both the contrast with 'divergence' and the descriptive clue 'exhibiting minimal variation'.

Step-by-Step Solution

1

Identify the structural transition word in the sentence stem.

The word 'Although' at the beginning of the sentence functions as a contrast pivot.

Contrast signals indicate that the two main clauses will express opposing or contradictory ideas.

2

Analyze the context clues in both clauses to determine target semantic valence.

The second clause notes 'significant morphological divergence', while the first clause includes the restatement clue 'exhibiting minimal variation'.

The blank must describe a state of uniformity/sameness to contrast with 'divergence' across the pivot.

3

Evaluate the answer choices against the required definition of uniform or unvarying.

'Homogeneous' directly means uniform in structure or composition, satisfying both the local clue 'minimal variation' and the macro-contrast with 'divergence'.

Only 'homogeneous' provides the exact semantic reversal demanded by the sentence structure.

Key Concept

Identifying semantic reversal across concessionary and contrast structural signals (e.g., 'Although').

Estimated Time:1m 0s

Question 1243Question →

Let $x$ be a positive integer. If the expression $x^2 + 3x$ is divisible by $6$ , which of the following statements MUST be true?

x

is divisible by

3

x

is divisible by

6

x

is an even integer

x

is an odd integer

x + 1

is a prime number

Show answer & explanation

Answer: $x$ is divisible by $3$

Answer

x

is divisible by

3

Factoring

x^2 + 3x

yields

x(x+3)

. For any integer

x

, one of

x

or

x+3

is even and the other is odd, so their product

x(x+3)

is always divisible by

2

. For the product to also be divisible by

3

, either

x

or

x+3

must be divisible by

3

. Because

x

and

x+3

differ by

3

,

x+3

is a multiple of

3

if and only if

x

is a multiple of

3

. Thus,

x

must be divisible by

3

.

Step-by-Step Solution

1

Factor the given algebraic expression

x^2 + 3x = x(x + 3)

Factoring allows us to analyze the parity and prime factors of each component separately.

2

Analyze parity (divisibility by 2)

If

x

is even,

x+3

is odd

\Rightarrow

product is even. If

x

is odd,

x+3

is even

\Rightarrow

product is even.

The expression

x(x+3)

is guaranteed to be divisible by

2

for all integers

x

.

3

Analyze divisibility by 3

For

x(x+3)

to be divisible by

3

, at least one factor must be divisible by

3

. Since

x+3 \equiv x \pmod 3

,

x+3

is divisible by

3

if and only if

x

is divisible by

3

.

Since divisibility by

2

is always satisfied, divisibility by

6

requires

x(x+3)

to be divisible by

3

, which requires

x

to be a multiple of

3

.

Key Concept

Divisibility properties of factored integer expressions and modular arithmetic

Estimated Time:1m 15s

Question 1244Question →

Let $n$ be a positive integer of the form $n = 2^a \cdot 3^b$ , where $a$ and $b$ are positive integers. If $n$ is divisible by $6$ and $n^2$ has exactly $35$ positive divisors, how many positive divisors does $6n$ have?

12

18

20

24

70

Show answer & explanation

Answer: 20

Answer

The integer

6n

has 20 positive divisors.

The correct answer is 20. Since

n = 2^a \cdot 3^b

, we have

n^2 = 2^{2a} \cdot 3^{2b}

. The number of divisors of

n^2

is

(2a+1)(2b+1) = 35

. Given

n

is divisible by 6,

a, b \ge 1

, which means

2a+1 \ge 3

and

2b+1 \ge 3

. The factorizations of 35 are

5 \times 7

and

7 \times 5

, giving exponent values of 2 and 3. Then

6n = 2^{a+1} \cdot 3^{b+1}

, which has

(a+2)(b+2) = (2+2)(3+2) = 20

positive divisors.

Step-by-Step Solution

1

Express

n^2

in terms of its prime factorization.

n^2 = (2^a \cdot 3^b)^2 = 2^{2a} \cdot 3^{2b}

Squaring an integer doubles the exponents of its prime factors.

2

Set up the equation for the number of positive divisors of

n^2

.

(2a + 1)(2b + 1) = 35

The number of positive divisors of

p_1^{e_1} p_2^{e_2}

is given by

(e_1 + 1)(e_2 + 1)

.

3

Solve for the exponents

a

and

b

given that

n

is divisible by 6.

Since

n

is divisible by 6, both

a \ge 1

and

b \ge 1

. Thus

2a + 1 > 1

and

2b + 1 > 1

. The only factor pairs of 35 into two integers greater than 1 are

5 \times 7

or

7 \times 5

. Therefore,

\{2a+1, 2b+1\} = \{5, 7\}

, which yields

\{a, b\} = \{2, 3\}

.

Divisibility by 6 guarantees both prime factors 2 and 3 are present in

n

.

4

Find the prime factorization of

6n

and calculate its number of positive divisors.

6n = (2^1 \cdot 3^1) \cdot (2^a \cdot 3^b) = 2^{a+1} \cdot 3^{b+1}

. Using

\{a, b\} = \{2, 3\}

, the exponents are

a+1

and

b+1

, which equal 3 and 4 (in either order). The number of divisors is

(3+1)(4+1) = 4 \times 5 = 20

.

Adding 1 to each exponent in

n

gives the exponents for

6n

, leading to

(a+2)(b+2) = (2+2)(3+2) = 20

.

Key Concept

Divisor Count Formula and Prime Factorization Constraints

Estimated Time:2m 0s

Question 1245Question →

In his treatise on institutional governance, Dr. Aris Thorne contends that rigid procedural rules do not inherently stifle constructive deliberation; rather, when thoughtfully designed, such formal constraints serve to check the erratic impulses of political factions, ensuring that proposed policy shifts are subjected to systematic review.

In the context of the passage, the word "check" most nearly means which of the following?

verify

restrain

investigate

dismantle

document

Show answer & explanation

Answer: restrain

Answer

The correct answer is 'restrain', as the author uses the word to mean curbing or holding back erratic political impulses.

In this context, the word functioning as a verb means to curb, hold back, or keep in check. The author states that procedural rules serve to limit the volatile impulses of political factions. Therefore, the choice meaning 'restrain' is the only option that preserves the author's intended logic.

Step-by-Step Solution

1

Analyze the passage context surrounding the target word.

The target word describes what formal procedural constraints do to 'erratic impulses' so that policy shifts are subjected to systematic review rather than abrupt execution.

Contextual clues like 'constraints' and 'stifle' establish a semantic framework involving limitation and control.

2

Evaluate the primary definition of the target word against the passage context.

The primary meaning ('to verify' or 'to inspect') does not logically describe how constraints affect volatile factional impulses.

Primary definitions frequently serve as distractors in GRE vocabulary-in-context questions.

3

Identify the secondary definition that provides a coherent reading.

The secondary definition ('to hold back, curb, or restrain') fits the structural role of institutional rules moderating volatile behavior.

Substituting 'restrain' maintains the logical argument that rules prevent hasty, unchecked actions.

Key Concept

Secondary Word Meanings in Context

Estimated Time:1m 30s

Question 1246Question →

Which of the following statements about the positive integer $180$ are true? Select all that apply.

Select all that apply

The number of distinct prime factors of

180

is

3

.

The greatest common divisor (GCD) of

180

and

75

is

15

.

The number

1

is the smallest prime factor of

180

.

The least common multiple (LCM) of

180

and

30

is

5400

.

The prime factorization of

180^2

can be written as

(2 + 3 + 5)^4

.

Show answer & explanation

Answer: The number of distinct prime factors of $180$ is $3$ .; The greatest common divisor (GCD) of $180$ and $75$ is $15$ .

Answer

The true statements are that

180

has

3

distinct prime factors and that the greatest common divisor of

180

and

75

is

15

.

The prime factorization of

180

is

2^2 \times 3^2 \times 5^1

, showing exactly

3

distinct prime factors (

2, 3, 5

). Additionally, comparing this with

75 = 3^1 \times 5^2

confirms that their greatest common divisor is

3^1 \times 5^1 = 15

.

Step-by-Step Solution

1

Find the prime factorization of

180

.

180 = 2^2 \times 3^2 \times 5^1

.

Decomposing

180

into prime factors provides the foundation to evaluate statements regarding prime factors, GCD, and LCM.

2

Count the distinct prime factors of

180

.

The distinct prime bases are

2

,

3

, and

5

, giving

3

distinct prime factors.

Exponents represent multiplicity, so counting distinct bases yields the number of distinct prime factors.

3

Calculate the GCD of

180

and

75

.

Since

75 = 3^1 \times 5^2

,

\text{GCD}(180, 75) = 3^{\min(2,1)} \times 5^{\min(1,2)} = 3^1 \times 5^1 = 15

.

The GCD is found by taking the minimum exponent for each shared prime factor.

4

Verify definition of prime numbers and divisibility rules for remaining choices.

1

is not prime (smallest prime factor is

2

), and

\text{LCM}(180, 30) = 180

because

30

is a factor of

180

.

Eliminate false statements based on arithmetic definitions and divisibility properties.

Key Concept

Prime Factorization, Greatest Common Divisor (GCD), and Least Common Multiple (LCM)

Question 1247Question →

Complete the passage below by filling in the blank with the word that best maintains the contextual tone and connotative valence of the text.

Fill in the blanks below

While the museum curator claimed her catalog essay offered a neutral survey of the movement, her persistent characterization of the artists' techniques as derivative and superficial revealed a distinctly stance.

Show answer & explanation

Answer

pejorative (or synonymous negative tonal terms such as disparaging or derogatory)

The contrast transition 'While' signals a shift between the curator's professed neutrality and the true nature of her stance. Because she characterizes the techniques as 'derivative' and 'superficial'—words with a distinctly negative connotative valence—the correct word must express a critical or uncomplimentary tone, such as 'pejorative' or 'disparaging'.

Step-by-Step Solution

1

Identify structural clues and contrast signals

The sentence begins with the concession signal 'While', establishing a contrast between what the curator 'claimed' (a 'neutral survey') and what her actual characterization revealed.

Contrast signals indicate that the missing word must oppose neutrality and match the tone of her actual descriptions.

2

Analyze the connotative valence of contextual keywords

The keywords 'derivative' and 'superficial' carry strongly negative, uncomplimentary connotations.

The target word must match the negative polarity established by these explicit descriptors.

3

Select a word matching both definition and negative tone polarity

Words such as 'pejorative' or 'disparaging' accurately capture an uncomplimentary, critical attitude that belies claimed objectivity.

Choosing a term with a negative connotation satisfies the structural contrast and maintains tone consistency.

Key Concept

Tone and Connotation Matching

Question 1248Question →

Although the preliminary architecture of the quantum computing framework was touted as impervious to thermal noise, subsequent experimental trials revealed that the system was surprisingly __________, suffering significant coherence loss under even minor temperature fluctuations.

Select the two answer choices that, when used to complete the sentence, fit the meaning of the sentence as a whole and produce completed sentences that are alike in meaning.

Select all that apply

susceptible

vulnerable

volatile

erratic

resilient

immutable

Show answer & explanation

Answer: susceptible; vulnerable

Answer

The correct answer choices are 'susceptible' and 'vulnerable'.

The transition word 'Although' signals a contrast between the initial expectation ('impervious') and the actual trial results. The subsequent clause elaborates that the system suffers significant coherence loss from minor temperature shifts. The words 'susceptible' and 'vulnerable' both precisely describe a state of being easily affected or harmed by external forces, completing the sentence with equivalent overall meaning.

Step-by-Step Solution

1

Analyze structural pivot signals and sentence polarity.

The sentence begins with the concession word 'Although' and contrasts 'touted as impervious' with the empirical finding in the main clause ('revealed that the system was surprisingly __________').

The contrast signal indicates that the missing word must mean the opposite of 'impervious' (unaffected/immune).

2

Determine the required contextual meaning of the blank.

The target word must mean open to damage, sensitive, or easily affected by thermal noise, as elaborated by 'suffering significant coherence loss'.

The elaboration clause directly defines the nature of the system's weakness.

3

Identify matching synonym pairs among choices.

'susceptible' and 'vulnerable' form a precise contextual synonym pair meaning exposed to harm or easily influenced.

Both words complete the sentence to produce identical, coherent meanings.

Key Concept

Sentence Equivalence: Contextual Synonym Pair Selection

Estimated Time:1m 15s

Question 1249Question →

Complete the passage below by filling in each blank with the word that correctly reflects the contrast established by the sentence structure.

Fill in the blanks below

While earlier economic historians characterized the medieval guild system as fundamentally , bound by outdated conventions and resistant to innovation, recent archival findings demonstrate that guild masters were surprisingly when responding to shifting market demands.

Show answer & explanation

Answer

Blank 1 requires a word denoting stagnation or rigidity, such as 'sclerotic' or 'stagnant'. Blank 2 requires a word denoting flexibility or responsiveness to change, such as 'adaptable' or 'nimble'.

The contrast transition word 'While' sets up an explicit opposition between earlier historical assumptions and recent findings. The descriptive phrase 'bound by outdated conventions and resistant to innovation' indicates that Blank 1 must mean inflexible or stagnant (such as 'sclerotic'). The word 'surprisingly' acts as a reversal clue, signaling that recent evidence reveals the opposite quality for Blank 2—namely, being capable of adjustment and change (such as 'adaptable').

Step-by-Step Solution

1

Identify the contrast structural signal 'While' at the beginning of the sentence and the descriptive elaboration 'bound by outdated conventions and resistant to innovation'.

Determine that Blank 1 must convey an idea synonymous with rigid, unyielding, or stagnant.

The introductory clause establishes a traditional view of guilds as inflexible institutions.

2

Analyze the pivot word 'surprisingly' along with the clue 'responding to shifting market demands' in the main clause.

Determine that Blank 2 must reverse the initial assertion of rigidity by expressing flexibility or responsiveness.

The word 'surprisingly' signals that recent findings contradict the traditional view, requiring a concept opposing rigidity.

Key Concept

Contrast and Reversal Clues

Estimated Time:1m 0s

Question 1250Question →

Far from being a mere passive spectator during cabinet debates, the minister of finance exercised a __________ influence over fiscal legislation, quietly redrafting statutory provisions behind closed doors. Which TWO of the following options, when inserted into the sentence, produce completed sentences that are equivalent in meaning?

Select all that apply

covert

flamboyant

surreptitious

ostentatious

dominant

judicious

Show answer & explanation

Answer: covert; surreptitious

Answer

The two words that complete the sentence with equivalent meaning are 'covert' and 'surreptitious'. Both words express secret or stealthy action, which perfectly matches the context of redrafting provisions 'quietly' and 'behind closed doors'.

The correct choices are the words meaning secret, stealthy, or hidden ('covert' and 'surreptitious'). The sentence contrast specifies that the minister was not passive, and the descriptive clause indicates that the work was done 'quietly' and 'behind closed doors'. Both selected words fit this context precisely and yield identical sentence meanings.

Step-by-Step Solution

1

Analyze structural signals and context clues in the stem.

The phrase 'Far from being a mere passive spectator' sets up a contrast, while 'quietly redrafting statutory provisions behind closed doors' provides a clear direction for the target tone: stealthy, hidden, or secret influence.

Identifying the target word valence and definition prevents selecting words that match the topic but violate the contextual tone.

2

Evaluate potential synonym pairs among the six choices.

Two distinct synonym pairs exist in the options: ('covert', 'surreptitious') meaning secret or clandestine, and ('flamboyant', 'ostentatious') meaning showy or notice-seeking. 'Dominant' and 'judicious' have no matching synonym pairs in the list.

Sentence Equivalence requires selecting two choices that create sentences with identical meanings.

3

Select the pair that fits the contextual clues.

The pair consisting of 'covert' and 'surreptitious' fits the requirement of operating secretly behind closed doors. The pair consisting of 'flamboyant' and 'ostentatious' presents the exact opposite meaning.

Only one synonym pair aligns with the specific contextual requirement established by the sentence.

Key Concept

Sentence Equivalence: Contextual Synonym Pair Selection

Question 1251Question →

Read the following passage from an art history essay:

"In her reevaluation of Renaissance iconography, Dr. Thorne argues that religious symbolism does not merely decorate the canvas; rather, theological doctrine informs every choice of color and spatial arrangement, giving structural coherence to the composition."

In the context of the passage, which of the following words most nearly means "informs"?

animates

instructs

discloses

dictates

validates

Show answer & explanation

Answer: animates

Answer

The word 'informs' in this context means 'animates' or imbues with character and structure.

In formal academic writing, the verb 'inform' frequently carries the secondary definition of 'to imbue, permeate, or give essential form/character to.' In the passage, the author asserts that theological doctrine does not just sit on the surface as decoration, but rather animates and shapes every choice of color and spatial arrangement. Therefore, 'animates' is the correct contextual synonym.

Step-by-Step Solution

1

Analyze the sentence structure and contextual clues surrounding the target word.

The text contrasts 'merely decorate' with 'informs every choice of color... giving structural coherence'.

The structural contrast ('not merely...; rather...') indicates that 'informs' describes an active, underlying influence that shapes and gives life to the artwork.

2

Evaluate the primary versus secondary meanings of the verb 'inform'.

While the primary definition is 'to impart knowledge or notify,' its secondary academic definition is 'to imbue, inspire, or give form and essential quality to.'

Grammatically, the subject is 'theological doctrine' influencing 'every choice of color,' demanding the secondary meaning of pervading or animating.

3

Select the option that matches this secondary meaning.

'Animates' conveys the sense of giving life, character, and underlying direction to the artistic composition.

It captures the pervasive structural role played by the doctrine in shaping the painting.

Key Concept

Secondary Word Meanings in Context (Polysemy)

Question 1252Question →

Let $a$ and $b$ be rational numbers such that $-1 < a < 0 < b < 1$ . Which of the following expressions MUST be strictly greater than $1$ ? Select all such expressions.

Select all that apply

\frac{b - a}{b}

\frac{1 + b}{1 + a}

\frac{a + b}{b}

\frac{b - a}{1 - a}

\frac{1}{b - a}

Show answer & explanation

Answer: $\frac{b - a}{b}$ ; $\frac{1 + b}{1 + a}$

Answer

The expressions

\frac{b - a}{b}

and

\frac{1 + b}{1 + a}

MUST be strictly greater than 1.

The expression representing the difference

(b - a)

divided by

b

simplifies to

1 + \frac{-a}{b}

. Because

-a

and

b

are both positive, this term is strictly greater than 1. Similarly, the expression

\frac{1 + b}{1 + a}

divides a numerator greater than 1 by a positive denominator less than 1, which always yields a value strictly greater than 1.

Step-by-Step Solution

1

Analyze the expression

\frac{b - a}{b}

by splitting the fraction.

\frac{b - a}{b} = \frac{b}{b} - \frac{a}{b} = 1 - \frac{a}{b}

.

Since

a < 0

and

b > 0

, the quotient

\frac{a}{b}

is strictly negative. Subtracting a negative number from 1 is equivalent to adding a positive number, so

1 - \frac{a}{b} > 1

.

2

Analyze the expression

\frac{1 + b}{1 + a}

by establishing bounds for the numerator and denominator.

Since

b > 0

,

1 + b > 1

. Since

-1 < a < 0

, adding 1 yields

0 < 1 + a < 1

.

Dividing any real number greater than 1 by a positive real number less than 1 produces a value strictly greater than 1.

3

Evaluate the remaining options with counterexamples or algebraic bounds to verify they are not guaranteed to be greater than 1.

The expression

\frac{a + b}{b} = 1 + \frac{a}{b} < 1

; the expression

\frac{b - a}{1 - a} < 1

because

b < 1 \implies b - a < 1 - a

; and

\frac{1}{b - a}

can be less than 1 when

b - a > 1

(e.g.,

b = 0.8, a = -0.5 \implies b - a = 1.3

).

Demonstrating that an expression is less than 1 or can be less than 1 eliminates it from being strictly greater than 1 for all valid rational numbers

a

and

b

.

Key Concept

Properties and Inequalities of Rational Numbers

Question 1253Question →

Far from viewing the painter's final canvas as a radical departure from her earlier compositions, modern art historians regard the work's understated tone as thoroughly ______ with her lifelong preference for thematic restraint. Which two of the following options, when inserted into the blank, produce completed sentences that are identical in meaning?

Select all that apply

congruent

minimalist

incongruous

consistent

incompatible

ostentatious

Show answer & explanation

Answer: congruent; consistent

Answer

The options 'congruent' and 'consistent' both logically complete the sentence to indicate that the final artwork aligns with the artist's historical preference for restraint.

The introductory clause 'Far from viewing... as a radical departure' indicates that art historians consider the painting's understated tone to be in complete alignment with the artist's traditional style. Both 'congruent' and 'consistent' express this alignment and yield sentences with identical overall meanings.

Step-by-Step Solution

1

Analyze structural contrast clues in the stem.

The opening phrase 'Far from viewing... as a radical departure' signals that the blank must express harmony, agreement, or alignment between the work's understated tone and the painter's established preference for restraint.

The sentence refutes the claim of a departure, requiring a word that denotes continuity or consistency.

2

Identify synonymous word pairs among the six choices.

Two distinct synonym pairs exist: 'congruent' / 'consistent' (meaning in agreement or harmony) and 'incongruous' / 'incompatible' (meaning conflicting or at odds).

Sentence Equivalence requires picking two choices that create identical sentence meanings.

3

Eliminate false synonym traps and unpaired topical distractors.

'Incongruous' and 'incompatible' form a valid pair but reverse the required positive polarity. 'Minimalist' and 'ostentatious' are topically relevant art criticism terms, but neither has a matching synonym in the option set.

Distractors that lack synonym pairs or reverse the logical context must be eliminated.

Key Concept

Eliminating False Synonyms and Topically Related Distractors

Question 1254Question →

Although the court archivist asserted that the imperial mint had instituted a systematic policy of debasing silver coinage during the late third century, recent metallurgical analysis of recovered coin hoards indicates that such monetary manipulations were in fact __________, occurring only during isolated financial panics rather than as part of a sustained administrative program. Which two of the following answer choices, when inserted into the blank, produce completed sentences that are equivalent in meaning?

Select all that apply

ubiquitous

sporadic

pervasive

insidious

fitful

deliberate

Show answer & explanation

Answer: sporadic; fitful

Answer

The correct selections are the pair of words meaning irregular or occurring in isolated instances ('sporadic' and 'fitful').

The contrast word 'Although' indicates that the actual practice of debasing coinage was opposite to a 'systematic' or 'sustained' policy. The clause following the blank confirms that these manipulations occurred 'only during isolated financial panics'. Therefore, the blank requires words meaning intermittent or irregular. Both 'sporadic' and 'fitful' precisely convey this meaning and produce logically equivalent completed sentences.

Step-by-Step Solution

1

Analyze structural contrast and contextual clues

The concession signal 'Although' contrasts the archivist's claim of a 'systematic policy' and 'sustained administrative program' with the physical evidence.

Identifying sentence pivots establishes the required semantic valence of the blank.

2

Determine the required meaning of the blank

The blank must describe coinage debasement as irregular, occasional, or restricted to rare moments ('occurring only during isolated financial panics').

The sentence requires a word conveying non-systematic, intermittent occurrence.

3

Evaluate option pairs for semantic equivalence and contextual fit

'Sporadic' and 'fitful' both mean occurring irregularly or intermittently, completing two sentences with equivalent meaning.

Both words satisfy the contextual fit requirement and form a functional near-synonym pair.

Key Concept

Identifying contextual contrast signals and selecting functional near-synonym pairs in GRE Sentence Equivalence

Question 1255Question →

A jacket originally priced at $\$80$ is on sale for $20\%$ off the original price. What is the sale price of the jacket?

\$64

\$16

\$96

\$60

\$72

Show answer & explanation

Answer: $\$64$

Answer

\$64

To find the sale price after a

20\%

discount, calculate

20\%

of the original price (

0.20 \times 80 = 16

) and subtract it from the original price (

80 - 16 = 64

). Alternatively, multiply the original price by

(1 - 0.20) = 0.80

, giving

80 \times 0.80 = 64

.

Step-by-Step Solution

1

Calculate the dollar value of the discount

\text{Discount} = 0.20 \times \$80 = \$16

A

20\%

discount means reducing the original price by

20

hundredths of its total value.

2

Subtract the discount from the original price

\text{Sale Price} = \$80 - \$16 = \$64

The final sale price equals the original price minus the discount amount.

Key Concept

Percentage Discount and Net Price

Estimated Time:45s

Question 1256Question →

Given $x = 3.6 \times 10^{-3}$ and $y = 1.2 \times 10^{-4}$ , which of the following statements are true? Select all that apply.

Select all that apply

x

is greater than

y

.

The ratio

\frac{x}{y}

is equal to

30

.

The sum

x + y

is equal to

4.8 \times 10^{-7}

.

The product

x \times y

is equal to

4.32 \times 10^{12}

.

The value of

y

expressed as a standard decimal is

0.0012

.

Show answer & explanation

Answer: $x$ is greater than $y$ .; The ratio $\frac{x}{y}$ is equal to $30$ .

Answer

The statement that

x

is greater than

y

and the statement that the ratio

\frac{x}{y}

is equal to

30

are both correct.

The statement asserting that

x

is greater than

y

is true because

3.6 \times 10^{-3} = 0.0036

is larger than

1.2 \times 10^{-4} = 0.00012

. The statement regarding the ratio

\frac{x}{y}

is true because dividing coefficients

\frac{3.6}{1.2} = 3

and subtracting exponents

-3 - (-4) = 1

yields

3 \times 10^1 = 30

.

Step-by-Step Solution

1

Convert both numbers to standard decimal notation to compare them.

x = 0.0036

and

y = 0.00012

.

Converting to standard form makes place value comparison direct.

2

Compare

x

and

y

.

0.0036 > 0.00012

, so

x > y

.

The thousandths digit of

x

(

3

) is greater than the thousandths digit of

y

(

0

).

3

Calculate the ratio

\frac{x}{y}

using properties of exponents.

\frac{3.6 \times 10^{-3}}{1.2 \times 10^{-4}} = \left(\frac{3.6}{1.2}\right) \times 10^{-3 - (-4)} = 3 \times 10^1 = 30

.

Divide the coefficients and subtract the exponents for scientific notation division.

Key Concept

Decimals and Scientific Notation Operations

Question 1257Question →

An investment fund allocates its total portfolio assets among three asset classes: stocks, bonds, and real estate. Initially, $\frac{5}{12}$ of the total portfolio is invested in stocks and $\frac{1}{3}$ of the total portfolio is invested in bonds, with the remaining fraction invested in real estate. If $\frac{2}{5}$ of the stock portfolio and $\frac{1}{4}$ of the bond portfolio are subsequently liquidated, what fraction of the fund's remaining total portfolio is invested in real estate?

\frac{1}{4}

\frac{3}{10}

\frac{1}{3}

\frac{4}{9}

\frac{5}{12}

Show answer & explanation

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

Answer

The fraction of the fund's remaining total portfolio invested in real estate is

\frac{1}{3}

.

Let the original total portfolio be

T

. Initially, stocks are

\frac{5}{12}T

, bonds are

\frac{4}{12}T

, and real estate is

1 - \frac{9}{12}T = \frac{3}{12}T

. After liquidating

\frac{2}{5}

of stocks and

\frac{1}{4}

of bonds, the remaining stock value is

\frac{3}{5} \times \frac{5}{12}T = \frac{3}{12}T

and the remaining bond value is

\frac{3}{4} \times \frac{4}{12}T = \frac{3}{12}T

. Real estate remains

\frac{3}{12}T

. The new total portfolio is

\frac{3}{12}T + \frac{3}{12}T + \frac{3}{12}T = \frac{9}{12}T = \frac{3}{4}T

. Therefore, real estate represents

\frac{3/12 T}{9/12 T} = \frac{3}{9} = \frac{1}{3}

of the remaining total portfolio.

Step-by-Step Solution

1

Determine the initial fraction invested in real estate.

Real estate accounts for

1 - \left(\frac{5}{12} + \frac{1}{3}\right) = 1 - \frac{9}{12} = \frac{3}{12} = \frac{1}{4}

of the original total portfolio.

The sum of all three asset fractions must equal 1.

2

Calculate the remaining fractions for stocks and bonds after liquidation.

Remaining stocks =

\left(1 - \frac{2}{5}\right) \times \frac{5}{12} = \frac{3}{5} \times \frac{5}{12} = \frac{3}{12}

. Remaining bonds =

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

.

Multiplying the unliquidated fraction by each asset's initial fraction gives its remaining fraction relative to the original total.

3

Calculate the total remaining portfolio fraction.

Total remaining portfolio =

\frac{3}{12} \text{ (stocks)} + \frac{3}{12} \text{ (bonds)} + \frac{3}{12} \text{ (real estate)} = \frac{9}{12} = \frac{3}{4}

of the original total portfolio.

Sum the remaining portions of all three asset categories.

4

Compute the ratio of real estate to the remaining total portfolio.

\frac{\text{Real Estate}}{\text{Remaining Total}} = \frac{\frac{1}{4}}{\frac{3}{4}} = \frac{1}{3}.

The question asks for the fraction relative to the new reduced total portfolio.

Key Concept

Sequential Fraction Allocation and Reduced Base Ratios

Estimated Time:1m 30s

Question 1258Question →

Complete the following excerpt by identifying the words that maintain logical and structural coherence across the sentences.

Fill in the blanks below

For decades, paleobiologists regarded the abrupt appearance of complex fauna in the early Cambrian fossil record as an evolutionary , assuming that soft-bodied ancestral lineages must have diverged long before without leaving trace fossils. However, recent taphonomical analyses indicate that geochemical conditions prior to the boundary were actively to organic preservation, rendering the missing fossil record an artifact of sampling rather than evidence of a sudden biological leap. Consequently, the longstanding hypothesis that Cambrian body plans emerged via an unprecedented, hyper-accelerated burst of speciation has become increasingly , as empirical proxies now support a far more protracted evolutionary trajectory.

Show answer & explanation

Answer

Blank (i): anomaly; Blank (ii): inimical; Blank (iii): precarious.

The correct completions establish seamless logical flow across all three sentences. In sentence 1, 'anomaly' captures the perception of the Cambrian event as an unexpected deviation. In sentence 2, 'inimical' explains that harsh conditions prevented fossil preservation, framing the missing record as a geological artifact. In sentence 3, 'precarious' logically follows 'Consequently' to describe how new evidence of gradual evolution destabilizes the sudden-burst hypothesis.

Step-by-Step Solution

1

Analyze Blank (i) using the contextual clues in the first sentence.

The word 'abrupt' paired with the assumption that lineages diverged 'long before without leaving trace fossils' indicates that researchers viewed this sudden appearance as a departure from the expected gradual process, pointing to 'anomaly' (an aberration or deviation from the norm).

Terms like 'culmination' or 'precedent' contradict the notion of an unexpected, isolated appearance.

2

Analyze Blank (ii) by tracing the pivot marked by 'However' and the conclusion 'rendering the missing fossil record an artifact of sampling'.

If the absence of fossils is an artifact of sampling rather than lack of organisms, the geochemical environment must have prevented fossilization. Thus, conditions were 'inimical' (hostile or detrimental) to preservation.

Words suggesting favorable conditions (such as 'conducive' or 'propitious') would fail to explain why pre-Cambrian fossils were not preserved.

3

Analyze Blank (iii) by evaluating the causal marker 'Consequently' and the shift to a 'far more protracted evolutionary trajectory'.

If empirical evidence now supports a gradual ('protracted') timeline, the old view of a hyper-accelerated burst is weakened, making it 'precarious' (unstable, questionable, or dubious).

Words implying strength or widespread acceptance (such as 'unassailable' or 'canonical') contradict the evidence supporting a protracted timeline.

Key Concept

Cross-Sentence Contextual Coherence and Discourse Clues

Question 1259Question →

Read the passage below and determine the vocabulary word that best completes the blank based on the structural clues and transition signals.

Fill in the blanks below

For decades, economic historians interpreted the sudden cessation of official guild registries in late-seventeenth-century Lyon as definitive proof of commercial decay. Far from signaling institutional , however, this administrative hiatus actually reflected a calculated pivot toward informal, network-based merchant credit. Indeed, rather than denoting systemic paralysis, the deliberate abandonment of codified record-keeping allowed local traders to circumvent onerous municipal tariffs while maintaining robust transaction volume through private contractual agreements. Consequently, what earlier scholars dismissed as structural atrophy was in fact an adaptive mechanism engineered to preserve market liquidity.

Show answer & explanation

Answer

A word denoting failure, breakdown, or institutional neglect (such as 'dereliction', 'dissolution', or 'atrophy') correctly completes the blank.

The contrast transition 'Far from signaling... however... actually reflected' establishes a direct opposition between the target blank and 'calculated pivot'. Furthermore, structural continuation clues such as 'systemic paralysis' and 'structural atrophy' confirm that the blank requires a word signifying breakdown, neglect, or institutional decay (e.g., 'dereliction', 'dissolution', or 'atrophy').

Step-by-Step Solution

1

Analyze the macro-structure and contrast signal

The phrase 'Far from signaling institutional {{blank_1}}, however, this administrative hiatus actually reflected a calculated pivot...' uses a contrast signal ('Far from... however... actually') to set up an opposition between the blank and 'calculated pivot'.

The contrast structure requires the word in the blank to be antonymous to an intentional, positive realignment ('calculated pivot').

2

Examine continuation and parallel structural clues

The subsequent sentence uses 'Indeed, rather than denoting systemic paralysis...' and concludes with 'what earlier scholars dismissed as structural atrophy...'

The continuation signal 'Indeed' and parallel clause structure indicate that the target blank reinforces the traditional interpretation of 'commercial decay', 'systemic paralysis', and 'structural atrophy'.

3

Synthesize the semantic requirement for the blank

The correct word must mean institutional failure, breakdown, or neglect.

Words like 'dereliction', 'dissolution', or 'atrophy' align precisely with both the contrast marker and the parallel textual evidence.

Key Concept

Deciphering Meaning via Structural Clues and Contrast/Continuation Signals

Estimated Time:2m 0s

Question 1260Question →

Let

a

,

b

, and

c

be positive integers, and define three rational numbers

x

,

y

, and

z

as follows:

x = \frac{a}{a+b}, \quad y = \frac{b}{b+c}, \quad \text{and} \quad z = \frac{c}{c+a}

Which of the following statements MUST be true for all such positive integers

a

,

b

, and

c

? Select all that apply.

Select all that apply

The sum

x + y + z

satisfies the inequality

1 < x + y + z < 2

.

The product

(1 - x)(1 - y)(1 - z)

is identically equal to

xyz

.

The product

xyz

cannot exceed

\frac{1}{8}

.

The sum

x + y + z

can be equal to an integer.

If

x + y + z = \frac{3}{2}

, then it must be that

x = y = z = \frac{1}{2}

.

Show answer & explanation

Answer: The sum $x + y + z$ satisfies the inequality $1 < x + y + z < 2$ .; The product $(1 - x)(1 - y)(1 - z)$ is identically equal to $xyz$ .; The product $xyz$ cannot exceed $\frac{1}{8}$ .

Answer

The statements asserting that

1 < x + y + z < 2

, that

(1 - x)(1 - y)(1 - z) = xyz

, and that

xyz \le \frac{1}{8}

are all true.

The statement bounding the sum between 1 and 2 is correct because adjusting denominators to a common sum

a+b+c

reveals that the sum is strictly greater than 1 and strictly less than 2. The identity statement is correct because subtracting each fraction from 1 shifts the numerators cyclically without changing the overall product. The statement placing an upper bound of

\frac{1}{8}

on the product is correct by applying the AM-GM inequality to each denominator term.

Step-by-Step Solution

1

Establish strict bounds on the sum

x + y + z

.

Since

a, b, c > 0

, we have

\frac{a}{a+b} > \frac{a}{a+b+c}

. Summing all three terms gives

x + y + z > \frac{a+b+c}{a+b+c} = 1

. To find the upper bound, rewrite

\frac{a}{a+b} < \frac{a+c}{a+b+c}

. Summing all three terms gives

x + y + z < \frac{(a+c)+(a+b)+(b+c)}{a+b+c} = 2

. Thus,

1 < x + y + z < 2

.

This proves that the sum of the three fractions must always lie strictly between 1 and 2.

2

Compute the product

(1-x)(1-y)(1-z)

algebraically.

1 - x = 1 - \frac{a}{a+b} = \frac{b}{a+b}

,

1 - y = \frac{c}{b+c}

, and

1 - z = \frac{a}{c+a}

. The product is

\frac{b \cdot c \cdot a}{(a+b)(b+c)(c+a)} = \frac{abc}{(a+b)(b+c)(c+a)} = xyz

.

This proves the structural algebraic identity between

(1-x)(1-y)(1-z)

and

xyz

.

3

Apply the AM-GM inequality to find the upper bound of

xyz

.

Since

a+b \ge 2\sqrt{ab}

,

b+c \ge 2\sqrt{bc}

, and

c+a \ge 2\sqrt{ca}

, their product satisfies

(a+b)(b+c)(c+a) \ge 8\sqrt{a^2b^2c^2} = 8abc

. Taking the reciprocal gives

xyz = \frac{abc}{(a+b)(b+c)(c+a)} \le \frac{abc}{8abc} = \frac{1}{8}

.

This confirms that

xyz

has a maximum possible value of

\frac{1}{8}

(achieved when

a=b=c

).

4

Test counterexamples for the remaining statements.

Since

1 < x + y + z < 2

, no integer value is possible, ruling out integer sums. Additionally, substituting

a=1, b=2, c=1

gives

x=\frac{1}{3}, y=\frac{2}{3}, z=\frac{1}{2}

, whose sum is

\frac{3}{2}

despite

x, y, z

not being equal to

\frac{1}{2}

.

This disproves the statements claiming the sum can be an integer or that a sum of

\frac{3}{2}

requires all three fractions to be equal.

Key Concept

Bounding and algebraic properties of cyclic rational fractions

Estimated Time:3m 0s

Answer

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