All practice questions

2195 questions

All types2,195 Multiple choice1,339 Multiple select37 True / False283 Numeric387 Matching111 Ordering25 Fill in the blank13

Question 581Question →

Read the following short argument and match each boldfaced statement to its specific structural role within the overall argument:

Telemedicine services expanded rapidly during recent public health initiatives. Many healthcare analysts predicted that this expansion would permanently reduce hospital emergency room visits. However, recent hospital administration data indicates that emergency room visits have returned to pre-expansion levels. Consequently, the expansion of telemedicine has not reduced the overall demand for emergency hospital care.

Match each boldfaced statement on the left with its corresponding role on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The first boldfaced statement matches the opposing prediction that the argument challenges, the second boldfaced statement matches the factual evidence offered to counter that prediction, and the third boldfaced statement matches the main conclusion of the author.

The argument follows a classic rebuttal structure: it presents an outside prediction, introduces counter-evidence using the pivot 'However', and concludes with a main claim that contradicts the original prediction. Thus, the first statement is the opposed prediction, the second statement is the empirical premise/evidence, and the third statement is the main conclusion.

Step-by-Step Solution

Analyze the structural role of the first boldfaced statement.

Identified as an opposing prediction.

It presents the view of healthcare analysts which the rest of the passage argues against.

Analyze the structural role of the second boldfaced statement.

Identified as supporting premise/evidence.

It provides factual data regarding hospital ER visits to disprove the analysts' expectation.

Analyze the structural role of the third boldfaced statement.

Identified as the main conclusion.

It follows the indicator word 'Consequently' and summarizes the primary assertion of the passage.

Key Concept

Analyzing Boldface Statement Roles and Argument Structure

Question 582Question →

What is the smallest positive integer greater than $100$ that is divisible by $9$ ?

Show answer & explanation

Answer: 108

Answer

The smallest positive integer greater than

100

that is divisible by

9

108

An integer is divisible by 9 if it is an integer multiple of 9. Multiples of 9 around 100 are

9 \times 11 = 99

and

9 \times 12 = 108

. Since 99 is not greater than 100, the smallest integer meeting the condition is 108.

Step-by-Step Solution

Divide 100 by 9 to locate the adjacent multiples of 9.

100 = 9 \times 11 + 1

This shows that

9 \times 11 = 99

is the largest multiple of 9 that is less than or equal to 100.

Determine the next multiple of 9 by adding 9 to 99 (or evaluating

9 \times 12

99 + 9 = 108

Since 99 is less than 100, the next consecutive multiple of 9 must be the smallest multiple strictly greater than 100.

Key Concept

Divisibility and Multiples of Integers

Question 583Question →

If $p$ , $q$ , and $r$ are integers such that $3p + 2q + r^2 = 17$ , and $p$ is an odd integer, which of the following statements MUST be true?

r

is an even integer

q

must be an odd integer

p + r

is an even integer

r^2 + 1

is an even integer

p \cdot q \cdot r

must be an odd integer

Show answer & explanation

Answer: $r$ is an even integer

Answer

r

is an even integer

Because

p

is odd,

3p

is odd. The term

2q

is always even for any integer

q

. Adding an odd and an even number gives an odd sum (

3p + 2q

). Since the total sum

3p + 2q + r^2

equals

17

, which is an odd number,

r^2

must be even. An integer whose square is even must be even itself, so the statement that

r

is an even integer must be true.

Step-by-Step Solution

Analyze the parity of the term

3p

Since

p

is given as an odd integer,

\text{odd} \times \text{odd} = \text{odd}

, so

3p

is an odd integer.

Multiplying an odd integer by an odd integer yields an odd integer.

Analyze the parity of the term

2q

2q

is an even integer for any integer

q

Any integer multiplied by

2

produces an even integer.

Determine the parity of the sum

3p + 2q

3p + 2q = \text{odd} + \text{even} = \text{odd}

The sum of an odd integer and an even integer is always odd.

Evaluate the equation

(3p + 2q) + r^2 = 17

to find the parity of

r^2

and

r

\text{odd} + r^2 = 17\ (\text{odd}) \implies r^2

must be even

\implies r

must be an even integer.

For the sum of an odd integer and

r^2

to equal an odd integer (

17

r^2

must be even. An integer whose square is even must itself be even.

Key Concept

Parity rules of addition and multiplication of integers:

\text{odd} + \text{even} = \text{odd}

and

\text{even} \times \text{any integer} = \text{even}

Estimated Time:1m 30s

Question 584Question →

The original price of a sweater is $\$40$ . If the price is increased by $25\%$ , and then the new price is decreased by $10\%$ , what is the final price of the sweater?

\$44

\$45

\$46

\$50

\$36

Show answer & explanation

Answer: $\$45$

Answer

The final price of the sweater is

\$45

Increasing the original price of

\$40

25\%

yields an intermediate price of

\$50

(since

25\%

\$40

\$10

). Decreasing

\$50

10\%

reduces the price by

\$5

(since

10\%

\$50

\$5

), resulting in a final price of

\$45

Step-by-Step Solution

Calculate the price after the initial

25\%

increase.

The price increases by

25\%

\$40

, which is

0.25 \times \$40 = \$10

. The new intermediate price is

\$40 + \$10 = \$50

Percentage increases must be calculated using the starting base value.

Calculate the final price after the

10\%

decrease.

The discount is

10\%

of the intermediate price of

\$50

, which is

0.10 \times \$50 = \$5

. Subtracting this from the intermediate price gives

\$50 - \$5 = \$45

Successive percentage changes apply to the updated base value, not the original starting value.

Key Concept

Successive Percentage Changes and Base Value Alignment

Question 585Question →

What is the smallest positive integer $n$ such that $n$ is divisible by both $12$ and $18$ , and $n$ has exactly $12$ positive divisors?

Show answer & explanation

Answer: 72

Answer

The smallest positive integer satisfying all given conditions is 72.

To satisfy the divisibility requirements,

n

must be a multiple of

\text{LCM}(12, 18) = 36 = 2^2 \times 3^2

. Thus,

n = 2^a \times 3^b \times \dots

where

a \geq 2

and

b \geq 2

. The total number of positive divisors of

n

is given by

(a+1)(b+1)\dots = 12

. Since

a+1 \geq 3

and

b+1 \geq 3

n

cannot have any additional prime factors, as that would yield at least

3 \times 3 \times 2 = 18

divisors. Factoring 12 into two integers each at least 3 gives

3 \times 4

4 \times 3

. Setting

(a+1, b+1) = (3, 4)

yields

a = 2, b = 3

, giving

n = 2^2 \times 3^3 = 108

. Setting

(a+1, b+1) = (4, 3)

yields

a = 3, b = 2

, giving

n = 2^3 \times 3^2 = 72

. The smallest value is 72.

Step-by-Step Solution

Determine the prime factor constraints on

n

n

must be divisible by

2^2

and

3^2

, so

n = 2^a \times 3^b \times \dots

with

a \geq 2

and

b \geq 2

For

n

to be divisible by

12 = 2^2 \times 3^1

and

18 = 2^1 \times 3^2

, its prime factorization must contain at least the maximum power of each prime appearing in either 12 or 18.

Set up the divisor count equation

(a+1)(b+1) = 12

with

a+1 \geq 3

and

b+1 \geq 3

, and no additional prime factors.

The number of divisors of

n = p_1^{e_1} p_2^{e_2} \dots

(e_1+1)(e_2+1)\dots

. Since

(a+1) \geq 3

and

(b+1) \geq 3

, adding another prime factor would make the product at least

3 \times 3 \times 2 = 18 > 12

Find all possible pairs of exponents

(a, b)

and calculate candidate values for

n

Candidate 1:

a=2, b=3 \implies n = 2^2 \times 3^3 = 108

. Candidate 2:

a=3, b=2 \implies n = 2^3 \times 3^2 = 72

The only factor pairs of 12 into integers

\geq 3

are

3 \times 4

and

4 \times 3

Identify the minimum value

n = 72

72 < 108

, so 72 is the smallest positive integer fulfilling all criteria.

Key Concept

Divisor Count Formula & Least Common Multiple constraints

Question 586Question →

Consider the following statement from a history of linguistics text:

"In his 1952 monograph on the decipherment of Linear B, Michael Ventris argued that despite the prevailing scholarly consensus attributing the tablets' script to an indigenous, non-Greek Aegean language, the structural frequency of specific sign combinations strongly indicated an inflected Indo-European language—a hypothesis that was initially dismissed by classicists until Ventris identified distinct phonetic values that consistently yielded archaic Greek vocabulary."

Based on the statement above, which of the following regarding the scholarly view of Linear B prior to Ventris's identification of phonetic values can be most reliably inferred?

The dominant opinion among scholars was that the language encoded by the Linear B tablets originated in the Aegean region and was not Greek.

Classicists accepted Ventris's structural frequency analysis as valid immediately upon the publication of his 1952 monograph.

Ventris himself originally believed that Linear B was an indigenous Aegean language before revising his position during his structural research.

The mainstream academic community rejected Ventris's hypothesis primarily because classicists held a dogmatically hostile stance against applying quantitative structural methods to ancient scripts.

Scholars universally agreed that Linear B was an uninflected writing system unrelated to any known European language family.

Show answer & explanation

Answer: The dominant opinion among scholars was that the language encoded by the Linear B tablets originated in the Aegean region and was not Greek.

Answer

The dominant opinion among scholars was that the language encoded by the Linear B tablets originated in the Aegean region and was not Greek.

The sentence explicitly notes that there was a 'prevailing scholarly consensus attributing the tablets' script to an indigenous, non-Greek Aegean language' before Ventris's findings persuaded classicists otherwise. Therefore, inferring that the mainstream opinion viewed the language as non-Greek and native to the Aegean is directly supported.

Step-by-Step Solution

Identify the target statement and break down its structural components

The target sentence contrasts the 'prevailing scholarly consensus' (which viewed the script as an indigenous, non-Greek Aegean language) with Ventris's hypothesis (that it was an inflected Indo-European language).

Single-sentence inference questions require strict deduction grounded exclusively in the provided sentence structure and qualifiers.

Evaluate the condition 'prior to Ventris's identification of phonetic values'

The sentence states that classicists initially dismissed Ventris's hypothesis until he identified distinct phonetic values. Prior to that identification, the prevailing scholarly consensus held.

Understanding the timeline established by the modifiers allows us to determine what was believed before the turning point.

Match the logical deduction to the options

The claim that the dominant scholarly view considered the script to be an indigenous, non-Greek Aegean language directly paraphrases the explicit consensus mentioned in the sentence.

Valid GMAT Reading Comprehension inferences must be strictly supported without bringing in external assumptions or exaggerating claims.

Key Concept

Single-Sentence Inferences

Question 587Question →

Environmental scientists recently deployed underwater acoustic speakers broadcasting healthy reef soundscapes along a degraded coastline to attract free-swimming fish larvae, hoping to regenerate local kelp forests. Within six months of continuous broadcast, fish larval settlement along the treated coastline tripled, and local kelp canopy density increased by 40 percent. The scientists concluded that the soundscape-induced influx of fish larvae directly accelerated the recovery of the kelp forest. Which of the following, if true, most strengthens the scientists' argument?

The predominant species of fish larvae attracted by the soundscapes feed aggressively on juvenile sea urchins, which are the primary herbivores responsible for destroying kelp holdfasts in the region.

The artificial low-frequency soundscapes also attract adult herbivorous fish that feed extensively on young kelp fronds before the plants reach maturity.

Coastal tourism operators in the vicinity recorded a substantial increase in diving bookings following the announcement of the reef soundscape initiative.

Unusually cool ocean water temperatures, which are known to promote rapid kelp proliferation, prevailed throughout the entire six-month trial period.

The audio tracks used for the acoustic broadcasts were recorded at pristine coral reefs located thousands of miles away from the test coastline.

Show answer & explanation

Answer: The predominant species of fish larvae attracted by the soundscapes feed aggressively on juvenile sea urchins, which are the primary herbivores responsible for destroying kelp holdfasts in the region.

Answer

The argument is most strengthened by the statement establishing that the attracted fish larvae consume juvenile sea urchins, the primary destroyers of kelp holdfasts.

The conclusion claims that the influx of fish larvae directly caused the kelp forest's recovery. The statement about fish larvae preying on juvenile sea urchins supplies a direct biological mechanism connecting fish larvae to kelp survival: by consuming sea urchins (which destroy kelp holdfasts), the larvae reduce kelp mortality, directly explaining how their presence accelerates kelp canopy growth.

Step-by-Step Solution

Analyze the core argument structure.

Premise 1: Soundscapes increased fish larvae settlement threefold. Premise 2: Kelp canopy density increased by 40%. Conclusion: The influx of fish larvae directly accelerated the kelp forest recovery.

Identifying the leap from correlation (larvae increase coincided with kelp increase) to causation (larvae caused kelp increase) is necessary to determine what support is required.

Identify the logical gap or missing link.

The argument assumes a causal connection between the presence of fish larvae and the growth of kelp without explicitly stating how fish larvae benefit kelp.

To strengthen a causal argument, an option must provide a plausible biological mechanism connecting the cause to the effect or rule out alternative causes.

Evaluate the choices against the logical gap.

The option stating that the larvae feed on sea urchins (which destroy kelp) supplies the exact causal mechanism needed to show that fish larvae actively protect kelp.

Connecting fish larvae behavior directly to the suppression of kelp predators validates the author's causal conclusion.

Key Concept

Strengthening Causal Arguments by Supplying a Causal Mechanism

Question 588Question →

If $x$ is a real number, is $|x - 3| < 5$ ?

(1) $1 < x < 6$
(2) $x > 0$

Which of the following describes the sufficiency of the statements?

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Show answer & explanation

Answer: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

The correct choice is the option stating that Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Rephrasing

|x - 3| < 5

yields

-2 < x < 8

. Statement (1) restricts

x

(1, 6)

, which is completely inside

(-2, 8)

, guaranteeing a 'Yes' answer. Statement (2) allows values like

x = 2

('Yes') and

x = 10

('No'), so it is not sufficient.

Step-by-Step Solution

Rephrase the target inequality from the stem.

The absolute value inequality

|x - 3| < 5

is equivalent to

-5 < x - 3 < 5

. Adding 3 to all parts gives

-2 < x < 8

. The question asks: 'Is

x

strictly between

-2

and

8

Simplifying the stem into a clear range for

x

makes evaluating sufficiency straightforward.

Evaluate Statement (1):

1 < x < 6

Every number in the interval

(1, 6)

is strictly between

-2

and

8

. Thus, the answer to 'Is

-2 < x < 8

?' is a definitive 'Yes'. Statement (1) alone is sufficient.

Since the entire set of allowed values under statement (1) is a subset of

(-2, 8)

, statement (1) provides a conclusive answer.

Evaluate Statement (2):

x > 0

x = 2

, then

-2 < 2 < 8

is True (Yes). However, if

x = 10

, then

-2 < 10 < 8

is False (No). Because both 'Yes' and 'No' are possible, Statement (2) alone is not sufficient.

A statement is insufficient if it permits values that produce conflicting answers to the target question.

Key Concept

Absolute Value Inequalities and Range Containment in Data Sufficiency

Question 589Question →

In a GMAT Data Sufficiency 'Yes/No' question, if a statement permits multiple numerical values for a variable, but every permitted value yields a conclusive 'No' to the question stem, the statement is sufficient to answer the question.

True

False

Show answer & explanation

Answer: True

Answer

True

In GMAT Data Sufficiency 'Yes/No' questions, sufficiency requires a single, conclusive answer to the question asked. A statement that guarantees a 'No' answer under all valid cases is completely sufficient, even if the underlying variables can take on multiple numerical values.

Step-by-Step Solution

Analyze the core rule of Yes/No Data Sufficiency questions.

A statement is sufficient if it leads to a definitive, unambiguous 'Yes' or a definitive, unambiguous 'No' answer.

Data Sufficiency evaluates whether the provided data leads to one consistent answer.

Evaluate the condition described in the statement.

Although multiple numerical values are possible, all permitted values consistently yield 'No'.

Because there are no scenario outcomes that yield 'Yes', there is zero ambiguity in answering the question stem.

Conclude sufficiency.

The statement is sufficient.

A consistent 'No' satisfies the requirement of data sufficiency just as effectively as a consistent 'Yes'.

Key Concept

Definitive Yes/No Sufficiency Rule

Question 590Question →

In paleoceanographic reconstructions of Cenozoic surface ocean productivity, the accumulation rate of biogenic opal—primarily composed of the siliceous tests of radiolarians and diatoms—has long served as a primary proxy for silica export fluxes. However, oceanographer Elena Rostova demonstrated that raw biogenic opal accumulation rates in deep-sea sediments often fail to correlate with upper-ocean biological productivity due to differential postsedimentary dissolution. In oligotrophic ocean gyres, where bottom waters are strongly undersaturated with respect to amorphous silica, the dissolution rate of radiolarian tests is dictated primarily by the ratio of surface area to structural mass in individual microskeletal frameworks rather than by ambient water temperature. Specifically, Rostova observed that delicate, highly porous lattice structures undergo rapid dissolution in the upper sediment column, whereas robust, thick-walled polycystine shells survive intact, artificially skewing the fossil assemblage toward heavy-bodied taxa. Furthermore, Rostova identified that trace concentrations of adsorbed aluminum ions within the sediment pore waters can passivate the silica surface, reducing dissolution rates by up to two orders of magnitude even in highly undersaturated bottom waters. Consequently, when assessing past silica productivity, researchers who rely solely on total opal weight without accounting for species-specific skeletal density or pore-water aluminum geochemistry risk misinterpreting sediment layers characterized by low opal mass as periods of diminished surface biological activity when, in reality, intense post-depositional dissolution or insufficient aluminum passivation destroyed the lighter siliceous fraction.

According to the passage, Rostova's research explicitly indicates that the preservation of radiolarian tests in undersaturated deep-sea sediments is directly promoted by which of the following factors?

The presence of adsorbed aluminum ions in sediment pore waters that reduce silica dissolution rates.

Elevated ambient water temperatures surrounding the deep-sea sediment column.

A high ratio of surface area to structural mass within individual skeletal frameworks.

The overall total weight of biogenic opal accumulated within sediment layers.

High levels of upper-ocean biological productivity occurring during post-depositional periods.

Show answer & explanation

Answer: The presence of adsorbed aluminum ions in sediment pore waters that reduce silica dissolution rates.

Answer

The presence of adsorbed aluminum ions in sediment pore waters that reduce silica dissolution rates.

The correct answer accurately reflects the explicit text statement that adsorbed aluminum ions in sediment pore waters passivate the silica surface and decrease dissolution rates by up to two orders of magnitude, thereby promoting test preservation.

Step-by-Step Solution

Analyze the prompt to locate the specific detail requested

The prompt asks for a factor explicitly cited in the passage that directly promotes the preservation (reduces dissolution) of radiolarian tests in undersaturated ocean sediments.

Direct factual retrieval requires finding explicit text evidence without making external inferences.

Scan the passage for explicit statements detailing preservation factors

The text states that 'trace concentrations of adsorbed aluminum ions within the sediment pore waters can passivate the silica surface, reducing dissolution rates by up to two orders of magnitude'.

This sentence provides the exact mechanism by which radiolarian tests are protected from dissolution.

Evaluate the answer options against the explicit text evidence

The option referring to adsorbed aluminum ions in sediment pore waters accurately paraphrases this explicit finding.

Matching semantic equivalents confirms the correct direct factual answer choice.

Key Concept

Direct Factual Retrieval from Academic Text

Estimated Time:2m 0s

Question 591Question →

Read the following argument regarding environmental economic policy carefully, and match each boldfaced statement to its specific structural role within the overall argument:

Many economic analysts contend that imposing a carbon tax on domestic manufacturing will severely undermine international competitiveness. Data from pilot tax programs show that domestic manufacturers offset compliance costs by improving energy efficiency. Based on this finding, environmental advocates argue that carbon taxation yields net environmental gains without hurting economic output. However, this argument falsely assumes that energy efficiency gains can be scaled indefinitely across all manufacturing sectors. Therefore, implementing a comprehensive carbon tax under current conditions is likely to cause substantial net harm to domestic industry.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The first boldfaced statement matches 'Evidence cited to support a position that the author ultimately criticizes.', the second boldfaced statement matches 'A premise offered by the author to undermine the reasoning of an opposing group.', and the third boldfaced statement matches 'The main conclusion reached by the author of the argument.'

The first boldfaced statement introduces empirical evidence from pilot programs that supports the environmental advocates' view, which the author subsequently refutes. The second boldfaced statement serves as a counter-premise directly targeting an unstated assumption of those advocates. The third boldfaced statement is the final claim supported by the author's rebuttal, making it the main conclusion.

Step-by-Step Solution

Analyze the main argument flow and identify the author's stance.

The author concludes that implementing a comprehensive carbon tax under current conditions is likely to cause substantial net harm to domestic industry.

Establishing the main conclusion anchors the overall structural organization of the passage.

Determine the role of the first boldface statement.

It describes empirical data showing energy efficiency improvements, which environmental advocates use to support carbon taxation. The author later refutes this advocacy.

Recognizing that this evidence supports an opposing view helps classify it as evidence for a criticized position.

Determine the role of the second boldface statement.

It directly attacks the environmental advocates' argument by highlighting an unviable assumption regarding scaling.

This statement functions as the author's premise used to weaken the intermediate counter-position.

Determine the role of the third boldface statement.

Introduced by 'Therefore', it states the final judgment of the author.

This statement represents the author's main conclusion.

Key Concept

Analyzing Boldface Statement Roles and Argument Structure

Question 592Question →

A small local bakery introduced a new sugar-free pastry line last month, hoping to attract health-conscious customers. During that same month, the bakery's total sales increased by 20 percent. The owner concludes that introducing the sugar-free pastry line was the main cause of the increase in total sales. Which of the following, if true, most strengthens the owner's conclusion?

Customer surveys conducted last month showed that the majority of new customers visited the bakery specifically to purchase the new sugar-free pastries.

A nearby competing bakery closed permanently at the start of last month, redirecting its regular customer traffic to this bakery.

Sugar-free pastries typically contain fewer total calories than traditional baked goods.

The bakery owner plans to introduce a line of sugar-free bottled teas early next year.

The wholesale price of flour used in the bakery's traditional pastries increased slightly last month.

Show answer & explanation

Answer: Customer surveys conducted last month showed that the majority of new customers visited the bakery specifically to purchase the new sugar-free pastries.

Answer

Customer surveys conducted last month showed that the majority of new customers visited the bakery specifically to purchase the new sugar-free pastries.

The conclusion asserts a causal relationship between the launch of sugar-free pastries and the 20 percent sales increase. Showing that most new customers were drawn to the shop specifically by the sugar-free pastries provides direct evidence that the new line was indeed the driver of the increased sales.

Step-by-Step Solution

Identify the argument's premises and conclusion.

Premises: Sugar-free pastries introduced last month; total sales rose 20% that month. Conclusion: The sugar-free line caused the sales increase.

To strengthen an argument, one must first isolate the core gap between evidence and conclusion.

Identify the assumption or missing link.

The argument assumes the sales growth came from buyers of the new sugar-free pastries rather than external factors or increased sales of traditional items.

A strengthening statement will confirm this link or eliminate major alternative explanations.

Evaluate the choices to find the one that directly supports the causal link.

The statement showing that most new customers came specifically for the sugar-free pastries directly confirms that the new line drove the sales increase.

Direct evidence of consumer motivation confirms the proposed cause-and-effect relationship.

Key Concept

Strengthening Causal Arguments

Estimated Time:1m 0s

Question 593Question →

If $x$ and $y$ are positive real numbers, is $\frac{1}{x} < \frac{1}{y}$ ?

(1) $x^2 > y^2$
(2) $x - y > 0$

Which of the following describes the sufficiency of the statements to answer the question?

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Show answer & explanation

Answer: EACH statement ALONE is sufficient.

Answer

EACH statement ALONE is sufficient.

Rephrasing the question stem

\frac{1}{x} < \frac{1}{y}

for positive numbers

x

and

y

yields

x > y

. Statement (1) states

x^2 > y^2

, which for positive numbers implies

x > y

(sufficient). Statement (2) states

x - y > 0

, which simplifies directly to

x > y

(sufficient). Therefore, each statement alone is sufficient.

Step-by-Step Solution

Rephrase the question stem target inequality.

Since

x

and

y

are both positive, multiplying

\frac{1}{x} < \frac{1}{y}

xy

preserves the inequality sign, yielding

y < x

, which is equivalent to

x > y

. The target question simplifies to: 'Is

x > y

Simplifying the target question stem allows direct evaluation of each statement.

Evaluate Statement (1):

x^2 > y^2

Since

x

and

y

are positive real numbers, taking the positive square root of both sides of

x^2 > y^2

yields

x > y

. This gives a definitive 'Yes' to the rephrased question.

Statement (1) alone provides sufficient information.

Evaluate Statement (2):

x - y > 0

Adding

y

to both sides of

x - y > 0

gives

x > y

. This gives a definitive 'Yes' to the rephrased question.

Statement (2) alone provides sufficient information.

Key Concept

Question Stem Simplification and Target Rephrasing

Question 594Question →

Under municipal heritage protection rules, a private conservation laboratory is granted an Elite Restoration License only if it maintains a continuous remote environmental monitoring system. A laboratory maintains a continuous remote environmental monitoring system whenever it operates an automated climate regulation system certified by the Standards Bureau. Furthermore, a laboratory requires an Elite Restoration License to be eligible to bid on state-funded artifact restoration contracts.

If the statements above are true, which of the following must also be true?

A laboratory that is eligible to bid on state-funded artifact restoration contracts maintains a continuous remote environmental monitoring system.

Any laboratory that maintains a continuous remote environmental monitoring system is eligible to bid on state-funded artifact restoration contracts.

A laboratory that operates a certified automated climate regulation system is guaranteed to receive an Elite Restoration License.

Operating a certified automated climate regulation system is the only method by which a laboratory can maintain a continuous remote environmental monitoring system.

A laboratory that lacks an Elite Restoration License must not be operating a certified automated climate regulation system.

Show answer & explanation

Answer: A laboratory that is eligible to bid on state-funded artifact restoration contracts maintains a continuous remote environmental monitoring system.

Answer

A laboratory that is eligible to bid on state-funded artifact restoration contracts maintains a continuous remote environmental monitoring system.

The passage establishes that eligibility to bid on state-funded contracts requires an Elite Restoration License, which in turn requires maintaining a continuous remote environmental monitoring system. Linking these two necessary conditions creates a valid transitive chain: Bidding Eligibility -> Elite Restoration License -> Remote Environmental Monitoring. Thus, any laboratory eligible to bid must maintain a continuous remote environmental monitoring system.

Step-by-Step Solution

Formalize the conditional premises from the passage.

Premise 1: Bidding Eligibility -> Elite License. Premise 2: Elite License -> Remote Monitoring. Premise 3: Certified Climate System -> Remote Monitoring.

Translating natural language indicators ('only if', 'whenever', 'requires') into formal logic enables valid transitive deductions.

Chain the conditional statements involving Bidding Eligibility.

Bidding Eligibility -> Elite License -> Remote Monitoring.

Using hypothetical syllogism, if A requires B and B requires C, then A requires C.

Deduce the necessary inference.

Any laboratory eligible to bid on state-funded artifact restoration contracts must maintain a continuous remote environmental monitoring system.

This conclusion follows with formal logical certainty from the premise chain.

Key Concept

Conditional Logic Chaining and Valid Transitive Deductions

Question 595Question →

If $x$ and $y$ are real numbers, is $x > y$ ?

(1) $y - x = |x + 3| + 1$
(2) $x + y = 10$

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Show answer & explanation

Answer: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

The option stating that Statement (1) alone is sufficient while Statement (2) alone is not is correct. Statement (1) demonstrates that

y - x = |x + 3| + 1 \ge 1

, which proves

y > x

. Consequently, the answer to 'Is

x > y

?' is a guaranteed, definitive 'No'. In GMAT Yes/No Data Sufficiency questions, any statement that yields a conclusive 'No' is sufficient. Statement (2) allows multiple relative orderings of

x

and

y

, making it insufficient.

Step-by-Step Solution

Analyze the question stem

The target is a Yes/No question: 'Is

x > y

?' Any statement that yields a definitive 'Yes' OR a definitive 'No' is sufficient.

Data Sufficiency Yes/No decision logic requires evaluating whether a statement yields a single consistent truth value.

Evaluate Statement (1):

y - x = |x + 3| + 1

Since absolute value is always non-negative (

|x + 3| \ge 0

), we have

y - x \ge 0 + 1 = 1 > 0

. Thus,

y - x > 0 \implies y > x

Because

y > x

is always true under Statement (1), the answer to 'Is

x > y

?' is a definitive 'No'.

Conclude sufficiency for Statement (1)

A definitive 'No' is SUFFICIENT. Statement (1) alone is sufficient.

In GMAT Data Sufficiency, a consistent negative answer resolves the question completely.

Evaluate Statement (2):

x + y = 10

x = 6

and

y = 4

, then

x > y

is 'Yes'. If

x = 4

and

y = 6

, then

x > y

is 'No'.

Since both 'Yes' and 'No' are possible, Statement (2) alone is NOT sufficient.

Key Concept

Definitive Yes/No Decision Logic in Data Sufficiency

Question 596Question →

In 2025, every commercial solar farm operated by Helios Power produced more electricity than it did in 2024. During the same period, Helios Power neither acquired any new solar farms nor decommissioned any existing ones. Which of the following statements must be true based on the information above?

The total electricity produced by all of Helios Power's commercial solar farms combined was greater in 2025 than in 2024.

Helios Power generated higher financial profits from its commercial solar farms in 2025 than it did in 2024.

Technological improvements to equipment were the primary reason for the increased electricity output at Helios Power's solar farms.

Every commercial solar farm in the country experienced an increase in electricity production in 2025.

Any commercial solar farm that increased its electricity production in 2025 was operated by Helios Power.

Show answer & explanation

Answer: The total electricity produced by all of Helios Power's commercial solar farms combined was greater in 2025 than in 2024.

Answer

The total electricity produced by all of Helios Power's commercial solar farms combined was greater in 2025 than in 2024.

The correct option is strictly guaranteed by combining the two premises. Since every farm in a fixed portfolio increased its electricity output from 2024 to 2025, the combined total output of that portfolio necessarily increased in 2025.

Step-by-Step Solution

Analyze the given premises

Identified two key facts: (1) Each individual farm operated by Helios Power produced more electricity in 2025 than in 2024; (2) The roster of farms remained identical between both years.

Establishing the precise scope of facts prevents falling into out-of-scope or speculative inference traps.

Deduce the necessary conclusion

If every component of a fixed set increases in value, the total sum of the set must strictly increase.

A valid GMAT inference must be mathematically or logically guaranteed by the text without relying on external assumptions.

Evaluate the answer choices against strict logical necessity

The statement regarding total combined electricity output is guaranteed. All other choices introduce unstated causes, financial metrics, external entities, or invalid logical reversals.

Eliminating options that 'could be true' or fall outside the stated facts leaves the single 'must be true' statement.

Key Concept

Avoiding Out-of-Scope and 'Could Be True' Inference Traps

Question 597Question →

A recent municipal study observed that residents living within walking distance of public parks report significantly lower average stress levels than residents living in urban areas without green space. Based on this observation, city planners concluded that creating more public parks directly causes a reduction in the stress levels of nearby residents. Which of the following would be most important to determine in evaluating the city planners' conclusion?

Whether the city plans to construct additional public parks in high-density commercial districts over the next five years.

Whether residents living near public parks also report higher satisfaction with city public transportation services than other residents do.

Whether individuals with naturally lower stress levels are more likely to select housing locations near public parks.

Whether living near a public park guarantees a complete elimination of stress for every single resident.

Whether reducing resident stress levels is the single most effective way to improve overall urban public health outcomes.

Show answer & explanation

Answer: Whether individuals with naturally lower stress levels are more likely to select housing locations near public parks.

Answer

Determining whether individuals with lower stress levels naturally choose to live near parks evaluates the possibility of reverse causality.

The argument infers a direct causal link (proximity to parks reduces stress) from an observed correlation. To evaluate this claim, one must consider alternative explanations, such as reverse causality or self-selection. Determining whether lower-stress individuals systematically choose to live near parks tests whether pre-existing low stress determines housing choice rather than park proximity causing stress reduction.

Step-by-Step Solution

Identify the Premise and Conclusion in the argument

Premise: People near parks have lower stress than people far from parks. Conclusion: Parks directly cause lower stress.

The argument concludes causation based solely on an observed correlation between proximity to parks and lower stress.

Identify the key causal vulnerability

The argument assumes directionality (Park

\rightarrow

Lower Stress) without ruling out reverse causality (Lower Stress / Preference

\rightarrow

Choosing to live near a Park) or confounding variables.

A standard method for evaluating a causal claim is to test whether the presumed effect actually caused the presumed cause.

Evaluate the impact of self-selection

If stressed-free or health-conscious people move near parks, the correlation exists because of self-selection, invalidating the claim that parks cause the lower stress.

Determining this alternative direction directly tests the validity of the author's causal leap.

Key Concept

Evaluating Causal Arguments and Alternative Explanations

Estimated Time:1m 30s

Question 598Question →

Over the past two years, an agricultural cooperative in an arid valley replaced traditional flood irrigation with an advanced drip-irrigation system across all its member farms. Although the new system reduced water usage per cultivated acre by 30 percent, total agricultural water consumption across the valley rose substantially during the same period. This increase occurred despite stable weather conditions and no changes in non-agricultural water demands.

Which of the following, if true, most helps to resolve the apparent discrepancy described above?

Traditional flood irrigation lost a much larger volume of water to evaporation than the new drip-irrigation system does.

Farmers in the valley switched to newly developed crop varieties that require even less water per plant than traditional varieties.

The lower water cost per acre made farming profitable enough for member farms to expand their total cultivated land significantly by planting previously uncultivated acreage.

Local industrial facilities in the surrounding area implemented strict water-recycling protocols during the same period.

The capital equipment costs of installing and maintaining the automated drip system exceeded the financial projections of many farm owners.

Show answer & explanation

Answer: The lower water cost per acre made farming profitable enough for member farms to expand their total cultivated land significantly by planting previously uncultivated acreage.

Answer

The correct answer is that the lower water cost per acre made farming profitable enough for farmers to expand their total cultivated land significantly by planting previously uncultivated acreage.

The correct answer resolves the paradox by bridging the rate-versus-total-volume gap. Total agricultural water consumption depends on both the water required per acre and the total number of acres farmed. If the per-acre water savings lower operating costs enough to induce farmers to cultivate significantly more land, total water usage across all land can increase even as each individual acre uses 30 percent less water.

Step-by-Step Solution

Identify the two contradictory empirical facts presented in the stimulus.

Fact 1: Water usage per cultivated acre decreased by 30%. Fact 2: Total agricultural water consumption in the region increased substantially.

Resolving a paradox requires finding a factor that allows both stated premises to remain true simultaneously.

Analyze the mathematical relationship between the rate (per acre) and the total volume.

Total Water Consumption = (Water Usage per Acre) × (Total Number of Acres). If per-acre usage drops, total volume can only increase if the total number of acres increases by a greater proportion.

Recognizing the underlying rate versus absolute total relationship highlights what missing variable is required.

Evaluate the answer choices to identify which one provides the necessary reconciling factor.

The option stating that farmers expanded their total cultivated land accounts for the increase in total water volume while preserving the fact that each acre used less water.

This supplies the missing cause for the overall volume increase without disputing either stated premise.

Key Concept

Resolving Paradoxes: Rate vs. Total Volume Discrepancy

Estimated Time:1m 40s

Question 599Question →

An enterprise software firm achieves ISO certification only if it implements end-to-end data encryption across all servers. Implementing end-to-end data encryption requires adopting a zero-trust network architecture. Furthermore, an enterprise software firm is permitted to bid on high-security municipal contracts only if it achieves ISO certification. Firm Apex is currently permitted to bid on high-security municipal contracts.

If the statements above are true, which of the following must also be true about Firm Apex?

Firm Apex has adopted a zero-trust network architecture.

If Firm Apex adopts a zero-trust network architecture, it will automatically be awarded a municipal contract.

Adopting a zero-trust network architecture is sufficient to grant a firm permission to bid on high-security municipal contracts.

Any firm that implements end-to-end data encryption is permitted to bid on high-security municipal contracts.

Firm Apex spends more on network security than other software firms competing for municipal contracts.

Show answer & explanation

Answer: Firm Apex has adopted a zero-trust network architecture.

Answer

Firm Apex has adopted a zero-trust network architecture.

The correct answer is derived from chaining the formal conditional rules provided: Permitted to Bid requires ISO Certification, which requires End-to-End Encryption, which requires Zero-Trust Architecture. Since Firm Apex is permitted to bid, it must satisfy all necessary prerequisites along the chain, including adopting a zero-trust network architecture.

Step-by-Step Solution

Analyze the conditional premises in the passage

Premise 1: ISO Certification → End-to-End Encryption
Premise 2: End-to-End Encryption → Zero-Trust Architecture
Premise 3: Permitted to Bid → ISO Certification

Indicator words like 'only if' and 'requires' establish necessary conditions.

Chain the conditional statements transitively

Permitted to Bid → ISO Certification → End-to-End Encryption → Zero-Trust Architecture

Since each necessary condition links to the next, we can form a valid transitive deduction chain.

Apply the given fact about Firm Apex to the chain

Firm Apex is Permitted to Bid → Firm Apex MUST have adopted Zero-Trust Architecture

If the sufficient condition (Permitted to Bid) is true, all necessary conditions in the chain must also be true.

Key Concept

Transitive Chaining of Necessary Conditions

Question 600Question →

While critics of municipal broadband networks contend that public investment inevitably depresses private telecom infrastructure expansion, recent fiscal audits from several mid-sized districts reveal that cities establishing utility-run fiber networks experienced a 40 percent surge in private fiber-optic deployments by commercial ISPs over five years. Because public fiber installations lower the initial capital expenditure of laying conduit in dense urban corridors, commercial providers can expand their local networks far more cost-effectively. Therefore, municipal broadband programs actually stimulate, rather than suppress, overall private telecommunications development.

In the argument above, which of the following statements functions as the primary underlying premise offered to support the main conclusion?

Public fiber installations lower the initial capital expenditure of laying conduit in dense urban corridors.

Public investment in municipal broadband networks inevitably depresses private telecommunications infrastructure expansion.

Cities establishing utility-run fiber networks experienced a 40 percent surge in private fiber-optic deployments over five years.

Municipal broadband programs actually stimulate, rather than suppress, overall private telecommunications development.

Commercial internet service providers are generally unable to fund network expansion in urban corridors without municipal subsidies.

Show answer & explanation

Answer: Public fiber installations lower the initial capital expenditure of laying conduit in dense urban corridors.

Answer

The statement that public fiber installations lower the initial capital expenditure of laying conduit in dense urban corridors.

The correct answer identifies the sentence beginning with 'Because public fiber installations lower...', which serves as the direct economic rationale for why commercial providers can expand cost-effectively. This logical bridge functions as the primary premise directly supporting the author's main conclusion that municipal broadband stimulates overall private telecom development.

Step-by-Step Solution

Deconstruct the argument into its structural components.

Opposing view: critics contend public investment depresses private expansion. Empirical evidence: audits show a 40% surge in private deployments. Explanatory mechanism: public fiber lowers initial capital expenditure for conduit laying. Main conclusion: municipal broadband stimulates overall private development.

Identifying the functional role of each sentence is essential for isolating the core premise.

Distinguish between empirical observation evidence and the core analytical premise.

The 40% surge statistic is background observational evidence. The reduction in initial capital expenditure is the logical bridge/premise explaining why that surge occurred.

Premises directly supply the causal or logical rationale supporting the author's claim.

Match the identified core analytical premise with the correct option.

The option stating that public fiber installations lower initial capital expenditures corresponds exactly to the primary premise.

This claim answers why commercial ISPs are able to expand cost-effectively, directly underpinning the main conclusion.

Key Concept

Identifying Premises vs. Background Evidence and Conclusions

PreviousPage 30 / 110Next

All practice questions

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept