All practice questions

Question 1341Question →

If $x$ is a positive integer such that $120$ is a factor of $x^2$ , what is the least possible value of $x$ ?

60

30

120

15

360

Show answer & explanation

Answer: 60

Answer

60

The prime factorization of 120 is

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

. For

x^2

to be divisible by 120,

x^2

must contain at least three 2s, one 3, and one 5. Because

x^2

is a perfect square, all exponents in its prime factorization must be even numbers. Thus, the minimum prime factorization for

x^2

is

2^4 \times 3^2 \times 5^2

, which means

x

must be at least

2^2 \times 3^1 \times 5^1 = 60

.

Step-by-Step Solution

1

Find the prime factorization of 120.

120 = 2^3 \times 3^1 \times 5^1

Decomposing 120 into prime factors reveals the minimal prime factor exponents required for

x^2

.

2

Determine the prime factors required for

x^2

to be divisible by 120.

The prime factorization of

x^2

must contain even exponents for all its prime factors and must be divisible by

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

. Therefore,

x^2

must contain at least

2^4 \times 3^2 \times 5^2

.

Because

x^2

is a perfect square, every prime factor in its prime factorization must have an even exponent.

3

Calculate the minimum value of

x

.

x = \sqrt{2^4 \times 3^2 \times 5^2} = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60

Taking the square root of

2^4 \times 3^2 \times 5^2

gives the least positive integer

x

satisfying the condition.

Key Concept

Prime Factorization and Perfect Squares

Question 1342Question →

In her treatise on nineteenth-century jurisprudence, legal scholar Elena Rostova observes that although formal statutory codes were enacted to centralize judicial authority, informal customary arbitration continued to obtain in provincial courts well into the modern era.

In the context of the passage, which of the following words is closest in meaning to 'obtain'?

prevail

acquire

deteriorate

transform

originate

Show answer & explanation

Answer: prevail

Answer

prevail

The word 'obtain' is used in its intransitive secondary sense meaning to be established, accepted, or in customary practice ('to prevail'). The sentence indicates that despite new statutory codes, informal arbitration continued to exist and remain active ('obtain') in provincial courts.

Step-by-Step Solution

1

Analyze the sentence structure and contextual transition signals.

The clause begins with 'although formal statutory codes were enacted...', signaling a contrast between formal centralization efforts and the persistence of informal customary arbitration.

Understanding the structural contrast illuminates the function of the target word in the sentence.

2

Evaluate the secondary definition of 'obtain' required by the passage context.

In formal and academic contexts, 'obtain' frequently functions as an intransitive verb meaning to be prevalent, customary, or in effect (e.g., 'the rule still obtains').

The standard definition of 'obtain' (to acquire) creates an ungrammatical and illogical sentence in this context.

3

Match the contextual definition with the option choices.

'Prevail' means to exist widely or be current, perfectly matching the contextual meaning of 'obtain'.

Selecting the synonym that retains the semantic integrity of the passage.

Key Concept

Secondary Meanings of High-Frequency Words

Question 1343Question →

Passage:
In 1902, French linguist Jules Gilliéron, alongside his assistant Edmond Edmont, published the first fascicles of the Atlas Linguistique de la France, a landmark work that fundamentally altered the study of dialectology. Unlike previous dialectologists who relied on self-administered questionnaires sent to local schoolteachers or educated elites, Gilliéron dispatched Edmont to 639 survey points across French-speaking regions. Armed with a standardized questionnaire of 1,920 words and phrases, Edmont recorded responses directly from uneducated, lifelong rural residents using a unified phonetic transcription system. Gilliéron deliberately selected Edmont—a non-linguist with an extraordinarily trained ear—to prevent theoretical bias from influencing phonetic notation. Furthermore, Edmont conducted all interviews single-handedly over four years, thereby eliminating inter-observer variance, a persistent flaw in earlier multi-investigator projects. Critics initially claimed that relying on a single informant per location compromised statistical validity. However, Gilliéron contended that his primary objective was not comprehensive demographic sampling, but mapping geographical boundaries of specific sound shifts (isoglosses).

According to the passage, for which of the following reasons did Gilliéron select Edmond Edmont to conduct the field interviews?

He possessed exceptional auditory acute skills while lacking theoretical linguistic preconceptions.

He had extensive experience training local schoolteachers to administer standardized dialect questionnaires.

He was an educated resident who belonged to the local elite of the rural survey points.

He intended to compile statistically representative demographic samples across all 639 regions.

He organized a multi-investigator team to minimize individual observer variance across interviews.

Show answer & explanation

Answer: He possessed exceptional auditory acute skills while lacking theoretical linguistic preconceptions.

Answer

Gilliéron selected Edmond Edmont because Edmont possessed exceptional auditory acute skills while lacking theoretical linguistic preconceptions.

The passage explicitly answers why Edmont was chosen: 'Gilliéron deliberately selected Edmont—a non-linguist with an extraordinarily trained ear—to prevent theoretical bias from influencing phonetic notation.' The option stating that he possessed exceptional auditory acute skills without holding pre-existing theoretical linguistic biases directly paraphrases these two stated points.

Step-by-Step Solution

1

Identify the target detail in the question stem.

The question asks for the specific reason why Gilliéron chose Edmond Edmont to perform the field interviews.

Explicit detail questions require locating the specific sentence in the text that directly provides the cause or rationale requested.

2

Locate the explicit reference to Edmont's selection in the passage.

Found in the text: 'Gilliéron deliberately selected Edmont—a non-linguist with an extraordinarily trained ear—to prevent theoretical bias from influencing phonetic notation.'

Direct text retrieval requires finding exact facts rather than making broad inferences.

3

Match the explicit fact to the option that accurately paraphrases it.

The statement specifying that Edmont possessed exceptional auditory acute skills ('extraordinarily trained ear') while lacking theoretical linguistic preconceptions ('a non-linguist... to prevent theoretical bias') is an accurate paraphrase.

GRE explicit detail correct choices paraphrase key terms without changing the factual scope.

Key Concept

Explicit Detail Retrieval

Question 1344Question →

Complete the passage by supplying a word in the blank that correctly completes the sentence based on the structural contrast clues.

Fill in the blanks below

Far from being a neutral record of physical geography, the sixteenth-century atlas was a thoroughly document, calculated to promote imperial ambitions and subtly manipulate territorial claims.

Show answer & explanation

Answer

The word filling the blank must contrast directly with 'neutral record' and align with 'calculated to promote imperial ambitions'. Words such as 'tendentious', 'ideological', or 'partisan' correctly complete the sentence.

The introductory structural signal 'Far from being a neutral record' dictates that the missing word must express the opposite of neutrality. Because the text specifies that the atlas was designed to promote imperial goals, a term signifying bias or political motivation—such as 'tendentious', 'ideological', or 'partisan'—properly completes the contrast.

Step-by-Step Solution

1

Locate the contrast pivot in the sentence

The opening phrase 'Far from being...' establishes an explicit reversal between the expected trait ('neutral record') and the actual nature of the atlas.

Contrast pivot phrases signal that the missing word will have an opposite valence or meaning to the benchmark descriptor.

2

Analyze context clues following the blank

The phrase 'calculated to promote imperial ambitions and subtly manipulate territorial claims' indicates an intentional political agenda.

The elaboration provides specific semantic content confirming that the document served biased interests.

3

Synthesize the required meaning

The correct term must mean biased, partisan, or expressing a deliberate political stance (e.g., 'tendentious' or 'ideological').

This satisfies both the negation of neutrality and the alignment with promoting imperial motives.

Key Concept

Identifying semantic reversal driven by contrast pivots such as 'Far from being'

Estimated Time:1m 0s

Question 1345Question →

At the start of a fiscal year, a venture capital fund divided its total investment capital between Asset Class $X$ and Asset Class $Y$ . Over the course of the year, the value of Asset Class $X$ increased by $25\%$ , while the value of Asset Class $Y$ decreased by $40\%$ . At the end of the year, the total value of the fund was exactly equal to its total value at the start of the year. Which of the following statements must be true? Select all that apply.

Select all that apply

At the start of the year, the value of Asset Class

X

was

60\%

greater than the value of Asset Class

Y

.

At the start of the year, Asset Class

X

accounted for exactly

60\%

of the total capital of the fund.

At the end of the year, Asset Class

X

represented more than

75\%

of the total value of the fund.

The ratio of the final value of Asset Class

X

to the final value of Asset Class

Y

was

5

to

2

.

The dollar amount by which Asset Class

X

increased was equal to the dollar amount by which Asset Class

Y

decreased.

Show answer & explanation

Answer: At the start of the year, the value of Asset Class $X$ was $60\%$ greater than the value of Asset Class $Y$ .; At the end of the year, Asset Class $X$ represented more than $75\%$ of the total value of the fund.; The dollar amount by which Asset Class $X$ increased was equal to the dollar amount by which Asset Class $Y$ decreased.

Answer

The statements that must be true are: at the start of the year, the value of Asset Class X was 60% greater than the value of Asset Class Y; at the end of the year, Asset Class X represented more than 75% of the total value of the fund; and the dollar amount by which Asset Class X increased was equal to the dollar amount by which Asset Class Y decreased.

The problem establishes that

0.25X = 0.40Y

, which yields

X = 1.60Y

. This confirms that at the start of the year, the value of Asset Class

X

was

60\%

greater than Asset Class

Y

. Furthermore, the final value of Asset Class

X

becomes

2.00Y

out of a total final fund value of

2.60Y

, giving it a share of

\frac{10}{13} \approx 76.92\%

, which is strictly greater than

75\%

. Finally, because the total portfolio value is unchanged, the exact dollar increase in Asset Class

X

(

0.25X

) must balance the dollar decrease in Asset Class

Y

(

0.40Y

).

Step-by-Step Solution

1

Set up an equation using initial variables

X

and

Y

for the two asset classes.

Initial total value =

X + Y

. Final value of

X = 1.25X

, final value of

Y = 0.60Y

. Final total value =

1.25X + 0.60Y

.

Percentage increases and decreases apply directly as multiplier factors to their respective initial base values.

2

Equate the initial and final total fund values to find the relationship between

X

and

Y

.

1.25X + 0.60Y = X + Y \implies 0.25X = 0.40Y \implies X = 1.60Y

.

The problem states the net total value of the fund remained unchanged over the year.

3

Evaluate the initial relationship between Asset Class

X

and Asset Class

Y

.

Since

X = 1.60Y = (1 + 0.60)Y

, Asset Class

X

was

60\%

greater than Asset Class

Y

at the start of the year.

A multiplier of

1.60

corresponds to a

60\%

increase over the base value

Y

.

4

Determine the initial and final percentage allocations of Asset Class

X

relative to the total fund.

Initial share =

\frac{1.60Y}{2.60Y} = \frac{8}{13} \approx 61.54\%

. Final share =

\frac{1.25(1.60Y)}{1.25(1.60Y) + 0.60Y} = \frac{2.00Y}{2.60Y} = \frac{10}{13} \approx 76.92\%

.

Evaluating part-to-whole fractions demonstrates that the final share of Asset Class

X

(

76.92\%

) exceeds

75\%

.

5

Analyze dollar change equality between the assets.

Dollar gain in

X = 0.25X

. Dollar loss in

Y = 0.40Y

. Since

0.25X = 0.40Y

, the dollar gain in

X

equals the dollar loss in

Y

.

Zero net change in total fund value guarantees that positive dollar changes cancel negative dollar changes exactly.

Key Concept

Weighted Percentage Changes and Base Value Shifting

Estimated Time:3m 0s

Question 1346Question →

A retail store tracks the price of a commercial oven across three consecutive quarters.

- In Quarter 1, the original price $P$ was increased by $x\%$ .
- In Quarter 2, the price was decreased by $x\%$ from its Quarter 1 price.
- In Quarter 3, the price was increased by $25\%$ from its Quarter 2 price.

If the price at the end of Quarter 3 is $20\%$ greater than the original price $P$ , which of the following statements must be true? Select all such statements.

Select all that apply

The value of

x

is

20

.

The price at the end of Quarter 2 was

4\%

less than the original price

P

.

The dollar amount of the price decrease in Quarter 2 was equal to the dollar amount of the price increase in Quarter 1.

The overall net percent change from the original price

P

to the price at the end of Quarter 2 was

0\%

.

The price at the end of Quarter 1 was

20\%

greater than the price at the end of Quarter 2.

Show answer & explanation

Answer: The value of $x$ is $20$ .; The price at the end of Quarter 2 was $4\%$ less than the original price $P$ .

Answer

The statements holding that the value of

x

is

20

and that the price at the end of Quarter 2 was

4\%

less than the original price

P

are both true.

The statement showing

x = 20

is correct because solving the multi-stage percent equation

1.25 P (1 - \frac{x^2}{10,000}) = 1.20P

yields

x = 20

. The statement showing that the Quarter 2 price was

4\%

less than

P

is correct because

P_2 = P(1 - \frac{400}{10,000}) = 0.96P

, which represents a

4\%

reduction relative to

P

.

Step-by-Step Solution

1

Express the price after each quarter algebraically in terms of initial price

P

and rate

x

.

Quarter 1 price:

P_1 = P\left(1 + \frac{x}{100}\right)

. Quarter 2 price:

P_2 = P_1\left(1 - \frac{x}{100}\right) = P\left(1 - \frac{x^2}{10,000}\right)

. Quarter 3 price:

P_3 = 1.25 P_2 = 1.25 P\left(1 - \frac{x^2}{10,000}\right)

.

Successive percentage changes compound sequentially on updated base values.

2

Set the Quarter 3 price expression equal to

1.20P

and solve for

x

.

1.25 P\left(1 - \frac{x^2}{10,000}\right) = 1.20 P \implies 1 - \frac{x^2}{10,000} = \frac{1.20}{1.25} = 0.96 \implies \frac{x^2}{10,000} = 0.04 \implies x^2 = 400 \implies x = 20

.

A price

20\%

greater than

P

equals

1.20P

.

3

Evaluate intermediate values to test each statement.

P_1 = 1.20P

,

P_2 = 0.96P

. The Quarter 1 increase is

0.20P

, while the Quarter 2 decrease is

0.20 \times 1.20P = 0.24P

.

Comparing exact calculated dollar and percentage values allows for direct validation of each option.

Key Concept

Successive Percentage Changes and Base Shift Dependencies

Question 1347Question →

Let $a$ and $b$ be positive integers such that $\gcd(a, b) = 60$ and $\text{lcm}(a, b) = 75,600$ . Which of the following statements must be true? Select all that apply.

Select all that apply

The product

ab

is equal to

4,536,000

.

Neither

a

nor

b

can be divisible by

49

.

There are exactly

8

distinct unordered pairs of positive integers

\{a, b\}

that satisfy the given conditions.

Both

a

and

b

must be multiples of

9

.

The greatest common divisor of

(a + b)

and

60

is equal to

30

.

Show answer & explanation

Answer: The product $ab$ is equal to $4,536,000$ .; Neither $a$ nor $b$ can be divisible by $49$ .; There are exactly $8$ distinct unordered pairs of positive integers $\{a, b\}$ that satisfy the given conditions.

Answer

The statements asserting that

ab = 4,536,000

, that neither number is divisible by

49

, and that there are exactly

8

distinct unordered pairs

\{a, b\}

are all correct.

The product of the GCD and LCM of two numbers always yields their product, confirming

ab = 4,536,000

. The prime factorization of the LCM shows that

7

appears only to the first power, making divisibility by

49

impossible for either number. Finally, assigning the minimum and maximum prime exponents across the four distinct prime factors

(2, 3, 5, 7)

yields

2^4 = 16

ordered pairs, which corresponds to exactly

8

unordered pairs.

Step-by-Step Solution

1

Apply the product identity for GCD and LCM.

ab = \gcd(a, b) \times \text{lcm}(a, b) = 60 \times 75,600 = 4,536,000

.

The product of two positive integers is always equal to the product of their greatest common divisor and least common multiple.

2

Find the prime factorizations of

\gcd(a, b)

and

\text{lcm}(a, b)

to determine exponent bounds.

\gcd(a, b) = 2^2 \times 3^1 \times 5^1 \times 7^0

and

\text{lcm}(a, b) = 2^4 \times 3^3 \times 5^2 \times 7^1

.

The exponent of each prime factor in

\gcd(a, b)

gives the minimum exponent in

a

and

b

, while the exponent in

\text{lcm}(a, b)

gives the maximum exponent.

3

Evaluate prime factor constraints for prime

7

and prime

3

.

Maximum power of

7

in

a

or

b

is

7^1 = 7

, so neither can be divisible by

49

. For prime

3

, one integer has

3^1

(not divisible by

9

) and the other has

3^3 = 27

.

An integer is divisible by

49 = 7^2

only if its prime factorization contains

7^2

or higher. Similarly, a number is a multiple of

9 = 3^2

only if its prime exponent for

3

is at least

2

.

4

Calculate the total number of distinct unordered pairs

\{a, b\}

.

For each of the

4

prime factors (

2, 3, 5, 7

), there are

2

choices for which integer gets the higher exponent. Total ordered pairs

(a, b) = 2^4 = 16

. Unordered pairs

\{a, b\} = 16 / 2 = 8

.

Since

\min < \max

for all prime factors,

a \neq b

for all pairs, allowing exact division by

2

to account for symmetry.

5

Analyze

\gcd(a + b, 60)

.

Since

60 \mid a

and

60 \mid b

, it follows that

60 \mid (a + b)

, making

\gcd(a + b, 60) = 60

.

If a number

k

divides both

a

and

b

, it must divide their linear combination

a + b

.

Key Concept

Prime Factorization, GCD-LCM Identities, and Counting Valid Integer Pairs

Question 1348Question →

If $|x - 4| = 9$ and $x < 0$ , what is the value of $x$ ?

Show answer & explanation

Answer: -5

Answer

The value of

x

is

-5

.

The absolute value equation

|x - 4| = 9

specifies that the distance between

x

and

4

on the real number line is equal to

9

. Moving

9

units to the left of

4

gives

4 - 9 = -5

, and moving

9

units to the right gives

4 + 9 = 13

. Because

x

is specified to be negative (

x < 0

), the correct value of

x

is

-5

.

Step-by-Step Solution

1

Set up the two linear equations representing the absolute value equation

|x - 4| = 9

.

x - 4 = 9

or

x - 4 = -9

By definition,

|A| = B

(where

B \ge 0

) implies

A = B

or

A = -B

.

2

Solve for

x

in both equations.

x = 13

or

x = -5

Adding

4

to both sides of

x - 4 = 9

gives

x = 13

, and adding

4

to both sides of

x - 4 = -9

gives

x = -5

.

3

Select the value of

x

that satisfies the given condition

x < 0

.

x = -5

The value

13

is positive, while

-5

is negative and fulfills

x < 0

.

Key Concept

Absolute Value as Distance and Solving Absolute Value Equations

Estimated Time:45s

Question 1349Question →

At the beginning of the year, a cloud storage service had a certain number of active paid subscriptions. During the first six months of the year, the number of active subscriptions increased by $20\%$ . During the second six months of the year, the number of active subscriptions decreased by $15\%$ relative to the total at the middle of the year. If the service had $12,240$ active subscriptions at the end of the year, what was the number of active subscriptions at the beginning of the year?

Show answer & explanation

Answer: 12000

Answer

12000

To find the initial subscription count, model the successive percentage changes sequentially. Increasing the initial amount

N

by

20\%

yields

1.20N

. Decreasing that intermediate total by

15\%

multiplies

1.20N

by

0.85

, giving

1.02N

. Setting

1.02N = 12,240

gives

N = 12,000

.

Step-by-Step Solution

1

Express the mid-year subscription total in terms of the initial subscription count

N

.

Mid-year subscriptions

= N \times (1 + 0.20) = 1.20N

A

20\%

increase scales the original quantity by a factor of

1.20

.

2

Express the end-of-year subscription total in terms of

N

after a

15\%

decrease from the mid-year total.

End-of-year subscriptions

= 1.20N \times (1 - 0.15) = 1.20N \times 0.85 = 1.02N

A

15\%

decrease reduces the new base quantity to

85\%

of its mid-year value.

3

Set the algebraic expression for the final total equal to the given numerical total and solve for

N

.

1.02N = 12,240 \implies N = 12,000

Dividing the final amount by the net multiplier

1.02

yields the original starting value.

Key Concept

Successive Percentage Changes and Base Shift

Estimated Time:1m 30s

Question 1350Question →

Fill in each blank in the passage below to complete the text in a logically coherent manner.

Fill in the blanks below

Although nineteenth-century naturalists initially dismissed the regional expedition logs as (i) observations of purely localized interest, subsequent statistical analysis revealed that the recorded microclimatic shifts correlated with continental weather patterns. Far from being (ii) to global climate studies, the logs provided indispensable empirical data that reshaped modern meteorology.

Show answer & explanation

Answer

Blank (i) should be filled with 'peripheral' (or equivalent terms denoting minor/secondary significance) and Blank (ii) with 'tangential' (or equivalent terms denoting irrelevance).

The sentence relies on two coordinated contrast signals. 'Although' sets up Blank (i) to match 'dismissed' and 'purely localized interest', making 'peripheral' (or 'inconsequential') correct. Then, 'Far from being' requires Blank (ii) to state a negative trait like 'tangential' (or 'irrelevant'), which is negated to affirm that the logs were in fact indispensable.

Step-by-Step Solution

1

Analyze structural transition signals in the first clause.

The opening concession word 'Although' and the phrase 'dismissed... as... of purely localized interest' indicate that Blank (i) must carry a negative or diminishing connotation describing the logs as minor or secondary.

Establishing the initial negative valuation of the logs sets up the contrast required by the concession structure.

2

Track inter-blank dependency into the second sentence.

The pivot phrase 'Far from being' signals a reversal of a negative characterization in Blank (ii), reinforcing that the logs were actually highly relevant ('provided indispensable empirical data').

Blank (ii) must mirror the initial misjudgment from Blank (i) so that the reversal 'Far from being [irrelevant/tangential]' aligns with their true importance.

Key Concept

Multi-Blank Dependency Tracking

Estimated Time:1m 30s

Question 1351Question →

Read the passage below. Based on the context provided, determine the precise meaning of the term register as employed by the author.

Fill in the blanks below

In his critique of structuralist historical narrative, Fernand Braudel argued that traditional historiography had failed by focusing exclusively on brief, dramatic events—the surface agitation of history—while ignoring the deep, slow-moving environmental and demographic currents that truly dictate societal transformation. To capture these underlying shifts, Braudel suggested that historians must recalibrate their analytical tools to record subtle structural transformations over centuries. In this methodological framework, to register an event requires looking past its immediate political sensationalism and instead measuring its enduring weight within long-term historical structures.

Based on the passage context, in the final sentence the word register most nearly means to .

Show answer & explanation

Answer

In the context of the passage, 'register' means to perceive, gauge, evaluate, or discern an event's true historical significance rather than merely noting its surface occurrence.

The passage establishes a contrast between superficial event-focused history and deep structural history. Braudel asserts that to truly 'register' an event, a historian must measure its long-term structural impact rather than react to immediate political drama. Thus, 'register' contextually signifies perceiving, evaluating, or discerning the true historical weight of an occurrence.

Step-by-Step Solution

1

Analyze the passage structure and contrasting concepts.

Braudel contrasts traditional historiography (focused on immediate, brief political events) with his preferred approach (focused on deep, slow-moving structural transformations over centuries).

Understanding the overarching thesis illuminates how specific vocabulary serves the author's methodological argument.

2

Examine the specific sentence containing the target word.

The sentence states that to 'register' an event requires looking past immediate sensationalism and measuring its enduring weight within long-term structures.

The direct context links 'registering' an event with active evaluation and discernment of structural weight, contrasting with superficial observation.

3

Determine the contextual meaning of 'register'.

Rather than its primary colloquial meaning (enrolling on an official list) or simple mechanical recording, 'register' here denotes analytical discernment, assessment, or perception of true significance.

The passage emphasizes analytical depth and measurement of impact over formal or superficial entry.

Key Concept

Passage-Based Word-in-Context Analysis

Estimated Time:2m 0s

Question 1352Question →

Far from being a __________ account of the maritime silk route, the historian's multi-volume treatise meticulously documents even the most minor transaction ledgers and localized cultural exchanges. Which TWO of the following answer choices, when inserted into the blank, produce sentences that are equivalent in meaning?

Select all that apply

cursory

exhaustive

perfunctory

comprehensive

biased

unprecedented

Show answer & explanation

Answer: cursory; perfunctory

Answer

The correct selections are 'cursory' and 'perfunctory'. Both words mean hasty, superficial, or brief, creating a logical contrast with the subsequent clause describing a treatise that 'meticulously documents even the most minor transaction ledgers.'

The sentence uses the contrast structural clue 'Far from being a __________ account', which signals that the word in the blank must be opposite in meaning to the description of the treatise later in the sentence ('meticulously documents even the most minor transaction ledgers'). The words 'cursory' and 'perfunctory' both mean superficial, hasty, or carried out with minimal effort. Inserting either word produces two sentences with identical, coherent meanings.

Step-by-Step Solution

1

Analyze structural clues and sentence polarity

The pivot phrase 'Far from being a [blank] account' establishes a direct contrast between the target word and the subsequent description of the treatise ('meticulously documents even the most minor transaction ledgers').

Understanding structural signals dictates whether the blank requires a positive, negative, or contrasting word relative to the main clause.

2

Determine the required target meaning

Since the treatise is meticulous and thorough, the blank must mean superficial, hasty, or brief.

The contrast established by 'Far from being' means the blank is the opposite of thorough and detailed.

3

Evaluate choices for synonym pairs and contextual fit

'Cursory' and 'perfunctory' both mean brief, superficial, or executed with minimal care, fitting the context precisely and creating equivalent sentences.

GRE Sentence Equivalence requires choosing two options that complete the blank with logically coherent and equivalent overall sentence meanings.

Key Concept

Identifying Contextual Synonym Pairs via Contrast Signals

Question 1353Question →

Read the following passage from an essay on the history of science:

"In late nineteenth-century evolutionary biology, many researchers refused to endorse Lamarckian mechanisms of inheritance outright; nevertheless, they continued to entertain such hypotheses whenever Mendelian models failed to account for rapid phenotypic adaptation under severe environmental stress. Far from signaling a permanent return to vitalist doctrines, this willingness to give serious consideration to soft inheritance was strictly provisional, serving merely as an empirical placeholder until sub-cellular processes could be fully elucidated."

In the context in which it appears, which of the following best captures the meaning of the word "entertain"?

amuse or provide diversion for

give serious consideration to

harbor secret or illicit beliefs

definitively prove or validate

host or receive as guests

Show answer & explanation

Answer: give serious consideration to

Answer

In the passage, "entertain" most nearly means to give serious consideration to.

The correct answer is 'give serious consideration to'. The passage sets up a contrast using 'nevertheless' after stating that scientists 'refused to endorse' the hypotheses outright, indicating that they were still open to contemplating them. Furthermore, the very next sentence directly restates this action as 'this willingness to give serious consideration', providing a structural definition clue.

Step-by-Step Solution

1

Analyze the structural signals and sentence context surrounding the target word.

The clause opens with a concession: researchers 'refused to endorse Lamarckian mechanisms... outright', followed by the contrast signal 'nevertheless, they continued to entertain such hypotheses'.

Contrast signals indicate a shift from total rejection ('refused to endorse') to a degree of open-minded evaluation ('entertain').

2

Identify structural elaboration clues in the subsequent sentence.

The following sentence rephrases the action as 'this willingness to give serious consideration to soft inheritance'.

Authors frequently clarify polysemous terms by elaborating on or restating them in adjacent sentences.

3

Match the synthesized contextual definition against the available options.

The phrase 'give serious consideration to' aligns precisely with both the contrast clue and the explicit restatement clue.

Selecting the meaning derived from contextual structural signals ensures accuracy over primary dictionary definitions.

Key Concept

Deciphering Meaning via Structural Clues and Contrast/Continuation Signals

Estimated Time:1m 30s

Question 1354Question →

A specialty baking recipe consists of three ingredients: flour, sugar, and butter. By weight, $\frac{1}{2}$ of the recipe is flour and $\frac{1}{3}$ of the recipe is sugar, with the remaining portion consisting entirely of butter. Which of the following statements about the ingredients in the recipe must be true? Select all such statements.

Select all that apply

The butter accounts for

\frac{1}{6}

of the total weight of the recipe.

The ratio of the weight of sugar to the weight of butter is

2 : 1

.

The combined weight of flour and sugar accounts for

\frac{2}{5}

of the total weight of the recipe.

The weight of sugar is

50\%

less than the weight of flour.

The ratio of the weight of flour to the combined weight of the remaining ingredients is

1 : 2

.

Show answer & explanation

Answer: The butter accounts for $\frac{1}{6}$ of the total weight of the recipe.; The ratio of the weight of sugar to the weight of butter is $2 : 1$ .

Answer

The statement that butter accounts for 1/6 of the total weight of the recipe and the statement that the ratio of the weight of sugar to the weight of butter is 2:1 are both correct.

The statement asserting that butter accounts for 1/6 of the total weight is correct because subtracting the combined fraction of flour and sugar (5/6) from the total (1) yields 1/6. The statement asserting that the ratio of sugar to butter is 2:1 is correct because dividing 1/3 by 1/6 equals 2.

Step-by-Step Solution

1

Calculate the fraction of the recipe that is butter.

Butter fraction =

1 - \left(\frac{1}{2} + \frac{1}{3}\right) = 1 - \frac{5}{6} = \frac{1}{6}

.

The total of all constituent fractions must sum to 1.

2

Calculate the ratio of sugar to butter.

\text{Ratio} = \frac{1/3}{1/6} = \frac{1}{3} \times \frac{6}{1} = \frac{2}{1} = 2 : 1

.

Divide the fraction representing sugar by the fraction representing butter.

3

Evaluate the statement regarding combined flour and sugar weight.

Combined fraction =

\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \neq \frac{2}{5}

.

Adding fractions requires finding a common denominator (6).

4

Evaluate the statement regarding percentage difference between sugar and flour.

Percent less =

\frac{1/2 - 1/3}{1/2} \times 100\% = \frac{1/6}{1/2} \times 100\% = \frac{1}{3} \times 100\% = 33.33\% \neq 50\%

.

Percent decrease must use the original reference quantity (flour) as the denominator.

5

Evaluate the ratio of flour to the combined remaining ingredients.

Remaining ingredients fraction =

1/3 + 1/6 = 1/2

. Ratio of flour (1/2) to remaining (1/2) =

1 : 1 \neq 1 : 2

.

Compare the part (flour) to the other part (sugar + butter), not to the whole.

Key Concept

Operations on rational numbers, fraction subtraction/addition using common denominators, part-to-part ratio comparisons, and percentage change base selection.

Question 1355Question →

How many positive integers $n$ less than $1,000$ are divisible by $12$ , leave a remainder of $4$ when divided by $5$ , and are not divisible by $9$ ?

11

12

13

15

17

Show answer & explanation

Answer: 12

Answer

12

The problem asks for positive integers

n < 1,000

that satisfy three conditions:

n = 12k

,

n \equiv 4 \pmod 5

, and

9 \nmid n

. Expressing

n = 12k

and substituting into the modular equation yields

2k \equiv 4 \pmod 5

, which simplifies to

k \equiv 2 \pmod 5

. For

k \le 83

, setting

k = 5m + 2

yields

17

values for

m \in \{0, 1, \dots, 16\}

. Furthermore,

12k

is divisible by

9

if and only if

k

is a multiple of

3

, which corresponds to

m \equiv 2 \pmod 3

. The values

m = 2, 5, 8, 11, 14

(

5

values) must be excluded. Subtracting

5

from

17

leaves exactly

12

valid integers.

Step-by-Step Solution

1

Express

n

in terms of its divisibility by

12

and set the upper bound.

n = 12k

for a positive integer

k

. Since

n < 1,000

, we have

12k < 1,000

, which implies

k \le 83

.

Any positive integer divisible by

12

must be a positive integer multiple of

12

.

2

Apply the modular remainder condition modulo

5

.

12k \equiv 4 \pmod 5 \implies 2k \equiv 4 \pmod 5 \implies k \equiv 2 \pmod 5

.

Since

12 \equiv 2 \pmod 5

, simplifying the congruence gives

k \equiv 2 \pmod 5

.

3

Determine the candidate set of values for

k

.

k

can be written as

k = 5m + 2

. For

1 \le k \le 83

, the non-negative integer

m

ranges from

0

to

16

inclusive, yielding

17

possible values.

The maximum value

5m + 2 \le 83

gives

5m \le 81 \implies m \le 16

.

4

Apply the condition that

n

is not divisible by

9

.

12k = 3 \times 4 \times k

is divisible by

9

if and only if

k

is divisible by

3

.

5m + 2 \equiv 2m + 2 \pmod 3

, so

2m + 2 \equiv 0 \pmod 3 \implies m \equiv 2 \pmod 3

.

Since

12

already contains one factor of

3

,

12k

needs

k

to supply another factor of

3

to be divisible by

9

.

5

Filter out the excluded values of

m

and calculate the final count.

Values of

m \in \{0, 1, \dots, 16\}

with

m \equiv 2 \pmod 3

are

m \in \{2, 5, 8, 11, 14\}

(

5

values). The number of valid integers is

17 - 5 = 12

.

Subtracting the excluded multiples of

9

from the candidate set leaves the exact number of valid integers.

Key Concept

Modular arithmetic, linear congruences, and counting integer multiples with divisibility constraints

Estimated Time:2m 0s

Question 1356Question →

A supercomputer processor operates at a standard speed of $1.25 \times 10^9$ calculations per second. During a maintenance diagnostic, the processor's operational speed is reduced by $96\%$ . Operating exclusively at this reduced speed, how many seconds will it take the processor to complete a workload of $1.8 \times 10^{13}$ calculations?

3.6 \times 10^4

1.5 \times 10^4

3.6 \times 10^5

1.44 \times 10^5

3.6 \times 10^6

Show answer & explanation

Answer: $3.6 \times 10^5$

Answer

3.6 \times 10^5

seconds

The correct answer is derived by first finding the reduced processing speed:

4\%

of

1.25 \times 10^9

equals

0.04 \times 1.25 \times 10^9 = 5.0 \times 10^7

calculations per second. Dividing the target workload of

1.8 \times 10^{13}

by

5.0 \times 10^7

yields

\frac{1.8}{5.0} \times 10^{13-7} = 0.36 \times 10^6 = 3.6 \times 10^5

seconds.

Step-by-Step Solution

1

Determine the reduced operational speed percentage.

Remaining speed percentage is

100\% - 96\% = 4\% = 0.04

.

A

96\%

reduction means the processor operates at

4\%

of its original capacity.

2

Calculate the reduced operational speed in scientific notation.

Reduced speed

= 0.04 \times (1.25 \times 10^9) = 0.05 \times 10^9 = 5.0 \times 10^7

calculations per second.

Multiplying the decimal coefficient

0.04

by

1.25

gives

0.05

, which adjusts to

5.0 \times 10^7

in scientific notation.

3

Divide total workload by reduced speed to compute time in seconds.

Time

= \frac{1.8 \times 10^{13}}{5.0 \times 10^7} = \left(\frac{1.8}{5.0}\right) \times 10^{13 - 7} = 0.36 \times 10^6

seconds.

Workload divided by rate gives total duration. Exponents are subtracted when dividing powers of ten.

4

Convert the final result to standard scientific notation.

0.36 \times 10^6 = 3.6 \times 10^5

seconds.

Moving the decimal point one place to the right requires decreasing the exponent of 10 by 1.

Key Concept

Decimals and Scientific Notation Operations

Estimated Time:2m 0s

Question 1357Question →

A bakery uses flour and sugar in a ratio of $5:2$ by weight to make a cake batter. If a baker needs to prepare a batch using a total of $28$ pounds of flour and sugar combined, how many pounds of flour are needed?

8

pounds

14

pounds

20

pounds

35

pounds

70

pounds

Show answer & explanation

Answer: $20$ pounds

Answer

20

pounds

To find the amount of flour, determine the fraction of the total mixture that consists of flour. The ratio of flour to sugar is

5:2

, meaning flour makes up

5

out of

5 + 2 = 7

total parts. Multiplying this fraction by the total weight gives

\frac{5}{7} \times 28 = 20

pounds.

Step-by-Step Solution

1

Determine the total number of ratio parts

Total ratio parts =

5 + 2 = 7

The ratio

5:2

means that for every

5

parts of flour, there are

2

parts of sugar, giving a total of

7

parts.

2

Calculate the weight of one ratio part

Weight per part =

28 \text{ pounds} \div 7 = 4 \text{ pounds}

Dividing the total weight by the total number of parts yields the weight of a single part.

3

Multiply the weight per part by the number of flour parts

Flour weight =

5 \times 4 \text{ pounds} = 20 \text{ pounds}

Since flour represents

5

of the

7

parts, multiplying

5

by

4

gives the total weight of flour required.

Key Concept

Part-to-Whole Ratios

Estimated Time:45s

Question 1358Question →

Read the sentence below and fill in the blank with the single word that best completes the passage based on its secondary academic meaning.

Fill in the blanks below

In her study of ecosystem resilience, the environmental scientist observed that unseasonal temperature spikes inevitably even the most robust plant species, placing severe demands on their energy reserves and straining their physiological limits.

Show answer & explanation

Answer

tax

In academic writing, the verb 'tax' frequently carries the secondary meaning of placing heavy demands upon, straining, or exhausting the resources of a system or organism. In this passage, unseasonal temperature spikes strain biological energy reserves, making 'tax' the precise contextual fit.

Step-by-Step Solution

1

Analyze the context of the blank within the passage.

The passage describes environmental stressors placing 'severe demands' and 'straining... physiological limits' on plant species.

The surrounding context requires a verb that means to overburden, strain, or place heavy demands upon an organism or system.

2

Identify the word that fits this context via its secondary meaning.

The word 'tax' primarily refers to levying financial duties, but in an academic context it functions as a high-frequency secondary verb meaning to burden or strain severely.

Using 'tax' fits both the syntactic requirement of the plural subject ('spikes inevitably tax...') and the semantic requirement of placing severe physical demands on energy reserves.

Key Concept

Secondary and High-Frequency Alternative Meanings

Estimated Time:1m 0s

Question 1359Question →

If $2^x \times 4^3 = 2^9$ , what is the value of $x$ ?

Show answer & explanation

Answer: 3

Answer

The value of

x

is 3.

By rewriting

4^3

as

(2^2)^3 = 2^6

, the equation becomes

2^x \cdot 2^6 = 2^9

. Applying the product rule gives

2^{x+6} = 2^9

, which simplifies to

x + 6 = 9

, yielding

x = 3

.

Step-by-Step Solution

1

Convert all terms to base 2

4^3 = (2^2)^3 = 2^{2 \times 3} = 2^6

To apply exponent rules, expressions should share a common base.

2

Apply product rule of exponents to the left side of the equation

2^x \times 2^6 = 2^{x+6}

When multiplying exponential terms with the same base, add their exponents:

a^m \cdot a^n = a^{m+n}

.

3

Equate the exponents from both sides

x + 6 = 9

Since the bases are identical and non-zero, the exponents must be equal.

4

Solve the linear equation for

x

x = 3

Subtract 6 from both sides of the equation.

Key Concept

Combining exponential terms with equal bases using power rules (

a^m \cdot a^n = a^{m+n}

and

(a^m)^n = a^{mn}

).

Question 1360Question →

Passage:
In 1989, maritime archaeologist Ole Crumlin-Pedersen analyzed timber samples from five 11th-century shipwrecks excavated in Denmark's Roskilde Fjord. Using dendrochronology—a technique measuring annual tree-ring growth variations—he established that the vessel designated Skuldelev 2 was constructed not from native Danish oak, as long hypothesized, but from timber harvested in the vicinity of Dublin, Ireland, around 1042 CE. Crucially, the growth ring patterns in the oak exhibited an abrupt reduction in ring width occurring precisely during the 1020s, a period coinciding with documented severe droughts in eastern Ireland. Furthermore, while the hull planking consisted exclusively of Irish oak, the vessel's internal framing components comprised Scandinavian pine, indicating that the ship underwent structural refitting in a Nordic shipyard prior to its scuttling.

Consider each of the choices separately and select all that apply.

According to the passage, which of the following statements regarding the vessel designated Skuldelev 2 are explicitly supported?

Select all that apply

Its hull planking was constructed from oak trees harvested near Dublin.

The tree-ring patterns of its pine framing components exhibited a marked growth reduction in the 1020s.

Its internal framing contained timber that originated outside of Ireland.

Show answer & explanation

Answer: Its hull planking was constructed from oak trees harvested near Dublin.; Its internal framing contained timber that originated outside of Ireland.

Answer

The correct choices are the statement regarding the Dublin harvest location for the hull planking oak and the statement concerning the non-Irish origin of the internal framing timber.

The passage explicitly confirms that the hull planking was made of oak harvested near Dublin and that the internal framing consisted of Scandinavian pine, which originated outside Ireland.

Step-by-Step Solution

1

Identify passage statements regarding the hull planking origin.

The text states that Skuldelev 2's hull planking consisted of oak harvested in the vicinity of Dublin, Ireland.

Direct text alignment confirms that the hull planking was harvested near Dublin.

2

Locate text details regarding the tree-ring growth reduction during the 1020s.

The text links the 1020s tree-ring width reduction to Irish oak affected by regional droughts, not to the Scandinavian pine framing.

Misattributing the oak tree-ring pattern to the pine framing components contradicts explicit passage statements.

3

Identify passage statements regarding the internal structural framing.

The text explicitly specifies that the internal framing comprised Scandinavian pine.

Because the pine is Scandinavian, the framing timber originated outside of Ireland.

Key Concept

Explicit Detail Retrieval

Answer

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Key Concept

Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

Answer

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Key Concept