All practice questions

Question 1381Question →

If $x$ and $y$ are positive real numbers, is $\frac{x + y}{2} - \sqrt{xy} > 1$ ?

(1) $(\sqrt{x} + \sqrt{y})^2 = 9$ and $xy = 4$
(2) $x + y = 8$ and $xy = 9$

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 shows that

\frac{x + y}{2} - \sqrt{xy} > 1

is equivalent to

(\sqrt{x} - \sqrt{y})^2 > 2

. Statement (1) establishes that

(\sqrt{x} - \sqrt{y})^2 = 1

, giving a definitive 'No' to the target question. Statement (2) establishes that

(\sqrt{x} - \sqrt{y})^2 = 2

, which also gives a definitive 'No' since 2 is not strictly greater than 2. Thus, each statement alone is sufficient.

Step-by-Step Solution

1

Rephrase the target question stem algebraically.

The target question 'Is

\frac{x + y}{2} - \sqrt{xy} > 1

?' simplifies to 'Is

x + y - 2\sqrt{xy} > 2

?', which is equivalent to 'Is

(\sqrt{x} - \sqrt{y})^2 > 2

?'

Since

x

and

y

are positive real numbers,

x + y - 2\sqrt{xy}

can be rewritten as the perfect square

(\sqrt{x} - \sqrt{y})^2

.

2

Evaluate Statement (1) using the rephrased target.

From

(\sqrt{x} + \sqrt{y})^2 = 9

and

xy = 4

, we have

\sqrt{xy} = 2

. Using the algebraic identity

(\sqrt{x} - \sqrt{y})^2 = (\sqrt{x} + \sqrt{y})^2 - 4\sqrt{xy}

, we find

(\sqrt{x} - \sqrt{y})^2 = 9 - 4(2) = 1

. Asking 'Is

1 > 2

?' yields a definitive 'No'.

A statement that yields a definitive 'No' to a Yes/No question is sufficient.

3

Evaluate Statement (2) using the rephrased target.

From

x + y = 8

and

xy = 9

, we have

\sqrt{xy} = 3

. Expanding

(\sqrt{x} - \sqrt{y})^2 = x + y - 2\sqrt{xy}

gives

8 - 2(3) = 2

. Asking 'Is

2 > 2

?' yields a definitive 'No'.

Since 2 is not strictly greater than 2, Statement (2) provides a definitive 'No' and is therefore sufficient.

4

Conclude the final sufficiency decision.

Because each statement independently provides a definitive 'No' answer, each statement alone is sufficient.

Both statements satisfy the Data Sufficiency requirements independently.

Key Concept

Question Stem Simplification and Target Rephrasing

Estimated Time:2m 0s

Question 1382Question →

Consider the following passage:

A three-year financial analysis of mid-sized manufacturing firms in Sector K revealed that every firm that fully automated its inventory tracking system achieved a reduction in warehousing overhead costs within twelve months. Furthermore, during those three years, no mid-sized manufacturing firm in Sector K that retained a fully manual inventory system achieved any reduction in warehousing overhead costs. Throughout the period of the analysis, overall energy costs for manufacturing facilities across Sector K decreased substantially.

Statement: Based solely on the information provided in the passage, it must be true that any mid-sized manufacturing firm in Sector K that achieved a reduction in warehousing overhead costs during the three-year period had automated its inventory tracking system at least partially.

True

False

Show answer & explanation

Answer: True

Answer

True

The evaluated statement is a mathematically valid deduction derived directly from the passage premises via contraposition. Because the passage asserts that no fully manual firm reduced overhead costs, any firm that did reduce overhead costs logically could not be fully manual. Therefore, such a firm must have implemented at least partial automation. This requires zero unstated assumptions or speculative leaps.

Step-by-Step Solution

1

Analyze the given premises and establish their formal logical structure.

Premise 1: Fully Automated Inventory System → Reduced Warehousing Overhead Costs.
Premise 2: Fully Manual Inventory System → NO Reduction in Warehousing Overhead Costs.
Premise 3: Energy costs across Sector K decreased substantially.

Deconstructing the passage into clear logical terms isolates facts from speculation.

2

Formulate the contrapositive of Premise 2.

The logical contrapositive of 'Fully Manual → NO Reduction' is 'Reduction → NOT Fully Manual'.

In formal logic, a conditional statement and its contrapositive are logically equivalent.

3

Evaluate the condition 'NOT Fully Manual'.

If an inventory tracking system is NOT fully manual, it must possess at least partial automation.

Binary categorization between fully manual and non-manual implies any non-manual system incorporates at least some degree of automation.

4

Compare the derived deduction with the evaluated statement.

The deduction confirms that any firm achieving a reduction in warehousing overhead costs MUST have automated its system at least partially. Thus, the statement is a valid logical inference ('Must Be True').

Valid inferences follow strictly from premises without requiring additional unstated assumptions.

Key Concept

Distinguishing Inferences from Assumptions and Speculations

Question 1383Question →

In an agricultural study of regional grain cooperatives, researchers monitored 200 wheat storage silos over twelve months. Every silo that maintained an internal relative humidity below 50% remained entirely free of Aspergillus mold contamination throughout the observation period. Furthermore, among the silos where Aspergillus mold was detected, none had been treated with specialized organic desiccant powders prior to storage. Which of the following statements must be true based solely on the information provided?

Any wheat storage silo monitored in the study that developed Aspergillus mold contamination maintained an internal relative humidity of at least 50% during the study period.

Any wheat storage silo in the study that maintained an internal relative humidity of 50% or higher developed Aspergillus mold contamination.

Treating a wheat storage silo with specialized organic desiccant powders guarantees that the silo will maintain an internal relative humidity below 50%.

Applying specialized organic desiccant powders to a wheat storage silo is sufficient to prevent all species of fungal contamination.

Silos treated with specialized organic desiccant powders contained higher quality wheat than silos that relied solely on humidity control.

Show answer & explanation

Answer: Any wheat storage silo monitored in the study that developed Aspergillus mold contamination maintained an internal relative humidity of at least 50% during the study period.

Answer

Any wheat storage silo monitored in the study that developed Aspergillus mold contamination maintained an internal relative humidity of at least 50% during the study period.

The passage establishes a strict conditional relationship: maintaining humidity below 50% guarantees that a silo remains entirely free of Aspergillus mold. The logical contrapositive of 'If Humidity < 50%, then No Mold' is 'If Mold is present, then Humidity was NOT < 50%' (meaning Humidity ≥ 50%). Therefore, any silo in which mold developed must have had a relative humidity of at least 50%.

Step-by-Step Solution

1

Analyze the formal conditional structure in the premises.

Premise 1: If Humidity < 50% → No Aspergillus Mold.

Establishing the explicit conditional rule provided in the passage.

2

Formulate the logically valid contrapositive of Premise 1.

Contrapositive: If Aspergillus Mold is present → Humidity ≥ 50%.

The contrapositive of any valid conditional statement must also be strictly true.

3

Evaluate the choices to find the statement that expresses this contrapositive deduction.

The statement asserting that any silo with Aspergillus mold maintained relative humidity of at least 50% matches the contrapositive perfectly.

Valid inference questions require deductions that are logically guaranteed without external assumptions.

Key Concept

Conditional Logic Contrapositive and Out-of-Scope Inference Traps

Estimated Time:1m 30s

Question 1384Question →

A water reservoir is filled by two pumps, Pump X and Pump Y, each operating continuously at its own constant rate. How many hours does it take for Pump X and Pump Y working together to fill the empty reservoir?

(1) Working alone at its constant rate, Pump X fills the reservoir in 6 hours.
(2) Working alone at its constant rate, Pump Y fills the reservoir in 12 hours.

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

Answer

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

The correct answer is that both statements together are sufficient, but neither statement alone is sufficient. Statement (1) gives only the rate of Pump X, and Statement (2) gives only the rate of Pump Y. Neither statement alone allows calculation of the combined rate. When used together, the combined rate is

\frac{1}{6} + \frac{1}{12} = \frac{1}{4}

reservoirs per hour, which yields a unique solution of 4 hours.

Step-by-Step Solution

1

Rephrase the question stem mathematically

Let

r_X

be the hourly rate of Pump X and

r_Y

be the hourly rate of Pump Y. The target combined time

T

is given by

T = \frac{1}{r_X + r_Y}

. We need the value of

r_X + r_Y

.

Simplifying the target variable helps determine what information is necessary for sufficiency.

2

Evaluate Statement (1) independently

Statement (1) states

r_X = \frac{1}{6}

reservoir per hour, but gives no information about

r_Y

. Therefore,

r_X + r_Y

cannot be calculated.

One variable in a two-variable sum remains unknown.

3

Evaluate Statement (2) independently

Statement (2) states

r_Y = \frac{1}{12}

reservoir per hour, but gives no information about

r_X

. Therefore,

r_X + r_Y

cannot be calculated.

One variable in a two-variable sum remains unknown.

4

Evaluate Statement (1) and Statement (2) together

Combining both statements:

r_X + r_Y = \frac{1}{6} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4}

. Thus,

T = \frac{1}{1/4} = 4

hours. A single, definitive numerical answer is obtained.

Both individual rates are known, allowing exact computation of the combined rate and total time.

Key Concept

Combined Work Rates in Data Sufficiency

Question 1385Question →

If $x$ is a real number, is $|x + 4| > 2x$ ?

(1) $|x - 1| < 3$
(2) $x^2 - x - 6 < 0$

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 shows that

|x + 4| > 2x

is equivalent to

x < 4

. Statement (1) establishes that

-2 < x < 4

, which guarantees

x < 4

(definitive Yes). Statement (2) establishes that

-2 < x < 3

, which also guarantees

x < 4

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

Step-by-Step Solution

1

Rephrase the target question stem algebraically.

The inequality

|x + 4| > 2x

simplifies to

x < 4

.

If

x \ge -4

, then

x + 4 > 2x \implies x < 4

. If

x < -4

,

|x + 4| = -(x + 4) > 2x \implies 3x < -4 \implies x < -4/3

, which holds for all

x < -4

. Thus,

|x + 4| > 2x

is true if and only if

x < 4

.

2

Evaluate Statement (1):

|x - 1| < 3

.

Statement (1) yields the range

-2 < x < 4

.

Unpacking

|x - 1| < 3

gives

-3 < x - 1 < 3 \implies -2 < x < 4

. Since every value in

(-2, 4)

is strictly less than

4

, the answer to 'Is

x < 4

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

3

Evaluate Statement (2):

x^2 - x - 6 < 0

.

Statement (2) yields the range

-2 < x < 3

.

Factoring gives

(x - 3)(x + 2) < 0 \implies -2 < x < 3

. Since every value in

(-2, 3)

is strictly less than

4

, the answer to 'Is

x < 4

?' is a definitive 'Yes'. Thus, Statement (2) alone is sufficient.

Key Concept

Rephrasing absolute value inequalities in Data Sufficiency Yes/No questions

Estimated Time:1m 30s

Question 1386Question →

To secure a promotion to senior analyst at Meridian Financial, an employee is required to complete the advanced risk modeling certification. David, a junior analyst, has successfully passed the final examination for this advanced certification this week. Therefore, the company's executive management committee will undoubtedly promote David to senior analyst during the upcoming annual performance review cycle.

Which of the following best describes the flaw in the argument's reasoning?

It treats a condition that is required for promotion as though it were sufficient to guarantee that promotion.

It mistakes a statistical correlation between certification and promotion for a direct causal relationship.

It assumes without evidence that David's exam performance reflects his overall day-to-day competence.

It ignores the possibility that preparing for the certification exam negatively impacted David's routine tasks.

It assumes that no junior analyst other than David has completed the advanced risk modeling certification.

Show answer & explanation

Answer: It treats a condition that is required for promotion as though it were sufficient to guarantee that promotion.

Answer

The argument's flaw is that it treats a condition necessary for promotion as sufficient to guarantee that promotion.

The argument states that completing the certification is required for a promotion (a necessary condition). However, the author concludes that because David met this requirement, he is guaranteed to be promoted. Meeting a necessary condition does not guarantee the outcome, as other unstated requirements may exist.

Step-by-Step Solution

1

Identify the premises and conclusion in the passage.

Premise: Completing the certification is required ('must/is required to') for promotion. Premise: David completed the certification. Conclusion: David will certainly be promoted.

Deconstructing the argument reveals the formal logical structure connecting the condition to the outcome.

2

Analyze the logical relationship between the condition and the outcome.

The phrase 'required to complete' indicates that certification is a necessary condition, not a sufficient one. Other factors (such as job performance or position availability) might also be required.

Differentiating between necessary (required) and sufficient (guaranteed) conditions exposes the leap in logic.

3

Select the option that accurately describes this conditional logic error.

The option stating that a required condition is mistaken as a guarantee accurately captures this flaw.

Mistaking a requirement for a guarantee is the classic definition of confusing necessary and sufficient conditions.

Key Concept

Confusing Necessary and Sufficient Conditions

Question 1387Question →

A city plans to introduce high-speed automated optical sorting machines at its primary municipal recycling facility to process post-consumer textile waste. Currently, textile recycling is limited because manual sorting cannot efficiently distinguish between pure cotton and synthetic-blend fabrics. City officials claim that deploying these optical sorters will double the annual volume of pure cotton recovered and sold to textile manufacturers. Which of the following, if true, provides the strongest support for the city officials' claim?

Operating high-speed optical sorting machines requires frequent calibration stops that reduce the facility's total daily processing hours.

The volume of textile waste delivered to the facility currently contains more than enough uncollected pure cotton to support a doubling of recovered output.

Textile manufacturers have recently increased their demand for recycled synthetic fibers to produce athletic performance apparel.

Manual sorting techniques for paper and plastic recycling in the same facility achieved high purity rates prior to automation.

The municipal recycling facility was originally constructed to handle only rigid plastics and glass containers.

Show answer & explanation

Answer: The volume of textile waste delivered to the facility currently contains more than enough uncollected pure cotton to support a doubling of recovered output.

Answer

The argument is most strengthened by establishing that the incoming waste stream contains a sufficient volume of pure cotton to allow the recovered output to double.

The city officials' claim relies on the assumption that the main bottleneck to recovering pure cotton is sorting efficiency rather than raw supply. Showing that incoming waste already contains sufficient pure cotton eliminates the possibility of a supply shortage, thereby directly strengthening the conclusion that output can double.

Step-by-Step Solution

1

Identify the premise and conclusion of the argument.

Premise: Manual sorting fails to distinguish pure cotton from synthetic blends. Conclusion: Automated optical sorting will double the volume of pure cotton recovered and sold.

Understanding the logic gap helps determine what assumption or missing link is necessary to support the conclusion.

2

Evaluate potential weaknesses or unstated assumptions in the reasoning.

The argument assumes that technology is the only limiting factor. If incoming waste lacks enough pure cotton, improved sorting technology alone cannot double output.

A valid strengthening statement must address a potential bottleneck or validate a core underlying assumption.

3

Select the option that confirms the necessary supply condition.

Confirming that the raw waste already contains enough uncollected pure cotton proves that doubling output is physically viable.

This directly strengthens the feasibility of the city officials' claim.

Key Concept

Strengthening Causal & Plan-Based Arguments by Confirming Key Assumptions

Question 1388Question →

To determine how to allocate regional transit development funds, a metropolitan planning committee surveyed passengers riding the city center express subway line during weekday morning rush hours. Ninety-two percent of the surveyed riders reported that they preferred increasing the frequency of express subway trains over expanding suburban feeder bus lines. On the basis of these survey results, the committee concluded that the metropolitan area's commuter population as a whole overwhelmingly favors rail transit enhancements over bus network expansions. The reasoning in the committee's argument is most vulnerable to criticism on the grounds that it

presumes without justification that the transit preferences of commuters during peak morning hours are identical to the preferences of off-peak commuters

bases a broad conclusion about the preferences of all regional commuters on a sample limited exclusively to individuals currently using express rail service

takes for granted that increasing express rail service frequency requires financial resources comparable to expanding suburban feeder bus lines

confuses a condition necessary for increasing overall commuter satisfaction with a condition that is sufficient to guarantee higher transit usage

mistakes a high percentage of survey respondents supporting rail improvements for an increase in the absolute number of daily transit passengers

Show answer & explanation

Answer: bases a broad conclusion about the preferences of all regional commuters on a sample limited exclusively to individuals currently using express rail service

Answer

The argument is flawed because it relies on an unrepresentative sample—surveying only existing express rail passengers during peak hours—to make a sweeping generalization about the preferences of the entire metropolitan commuter population.

The correct answer accurately points out that the argument draws a conclusion about all regional commuters based on data collected only from passengers already riding the express subway line. Because express rail users naturally favor rail transportation more than the general commuting population does, the survey sample is structurally unrepresentative, rendering the generalization invalid.

Step-by-Step Solution

1

Identify the Premise and Conclusion

Premise: 92% of surveyed express subway riders during weekday morning rush hours prefer more express trains over expanded suburban bus routes. Conclusion: The region's commuter population as a whole overwhelmingly favors rail transit improvements over bus expansions.

Isolating the structural components reveals the leap from the sampled subgroup to the target population.

2

Evaluate the Sample's Representativeness

The sample consists exclusively of people who already choose to take the express subway line.

A sample must accurately mirror the diverse demographics and preferences of the larger target group (all commuters, including suburban bus riders and motorists) to yield a valid inductive generalization.

3

Identify the Sampling Flaw

Self-selection and selection bias are present: express rail riders inherently value rail service and are far more likely to advocate for rail improvements than people who rely on suburban buses or cars.

Generalizing from a heavily biased sample to the broader population is a classic sampling flaw.

Key Concept

Sampling and Generalization Flaws (Selection / Unrepresentative Sample Bias)

Question 1389Question →

If $p$ and $q$ are numbers, what is the value of the product $pq$ ?

(1) $(p + q)^2 = 49$
(2) $p^2 + q^2 = 25$

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

Answer

Both statements together are sufficient to determine that

pq = 12

, but neither statement alone is sufficient.

The correct option states that both statements together are sufficient, but neither alone is sufficient. Expanding

(p+q)^2 = p^2 + 2pq + q^2

allows substituting

(p+q)^2 = 49

from statement (1) and

p^2 + q^2 = 25

from statement (2), yielding

49 = 25 + 2pq

, which uniquely determines

pq = 12

. Neither statement alone isolates

pq

.

Step-by-Step Solution

1

Rephrase the target question using algebraic identities

Recall the identity

(p + q)^2 = p^2 + 2pq + q^2

. Rearranging gives

2pq = (p + q)^2 - (p^2 + q^2)

. Thus, knowing both

(p + q)^2

and

(p^2 + q^2)

will determine

pq

.

Target rephrasing simplifies evaluating statement sufficiency.

2

Evaluate Statement (1) independently

Statement (1) gives

(p + q)^2 = 49

. If

p = 7

and

q = 0

, then

pq = 0

. If

p = 4

and

q = 3

, then

(4+3)^2 = 49

and

pq = 12

. Multiple values for

pq

exist.

A statement is sufficient only if it yields one unique value for the target expression.

3

Evaluate Statement (2) independently

Statement (2) gives

p^2 + q^2 = 25

. If

p = 5

and

q = 0

, then

pq = 0

. If

p = 4

and

q = 3

, then

4^2 + 3^2 = 25

and

pq = 12

. Multiple values for

pq

exist.

Statement (2) alone does not yield a unique product.

4

Combine Statement (1) and Statement (2)

Substitute

(p + q)^2 = 49

and

p^2 + q^2 = 25

into

(p + q)^2 = p^2 + 2pq + q^2

to get

49 = 25 + 2pq 2pq = 24 pq = 12

. A single, unique value is found.

Combining the statements provides enough information to determine the value of the target expression

pq

uniquely.

Key Concept

Algebraic Expression Manipulation via Quadratic Identities

Question 1390Question →

To combat the depletion of its primary freshwater aquifer, a coastal agricultural district plans to install solar-powered desalination micro-turbines along drainage channels. These turbines will convert brackish surface runoff into water suitable for crop irrigation. District officials project that because the converted water will meet 35 percent of the district's current annual irrigation volume, agricultural pumpage from the aquifer will decrease significantly over the next five years.

Which of the following, if true, most seriously weakens the district officials' projection?

Farmers in the district plan to use the converted runoff to cultivate high-yield crop varieties that require routine soil flushing with pure freshwater from the aquifer to prevent salt buildup.

The solar-powered turbines operate at maximum output during peak summer months when crop water demand and aquifer drawdown are highest.

The initial capital cost of purchasing and installing the micro-turbines will not be fully recouped by farmers within the five-year projection period.

Desalination facilities operating in adjacent inland agricultural districts rely on electrical grid power rather than solar energy.

Organic sediments present in brackish surface runoff slightly decrease the operational lifespan of the micro-turbine filtration membranes.

Show answer & explanation

Answer: Farmers in the district plan to use the converted runoff to cultivate high-yield crop varieties that require routine soil flushing with pure freshwater from the aquifer to prevent salt buildup.

Answer

The argument is most seriously weakened by the finding that using converted brackish runoff requires farmers to routinely flush soil with pure freshwater drawn from the aquifer. This unstated operational side effect directly undermines the expected net reduction in aquifer pumpage.

The correct answer identifies an unintended operational consequence: using desalinated brackish water increases salt accumulation in soil, which in turn requires farmers to pump pure freshwater from the aquifer to flush the crops. This extra freshwater demand counteracts the projected 35 percent savings, severely undermining the claim that total aquifer pumpage will decrease.

Step-by-Step Solution

1

Deconstruct the core argument

Premise: Micro-turbines will supply desalinated runoff equal to 35% of current irrigation volume. Conclusion: Aquifer pumpage will decrease significantly over the next five years.

Identifying the premise-to-conclusion leap reveals the author's unstated assumption that total freshwater demand from the aquifer will drop proportionately to the new water supply.

2

Identify the unstated assumption and vulnerability

The argument assumes that introducing desalinated runoff will not trigger secondary actions or requirements that increase freshwater consumption from the aquifer.

Weakening questions for plan-to-goal arguments often rely on identifying unexpected secondary consequences that negate the goal.

3

Evaluate the choices for logical impact

The finding that farmers must flush fields with aquifer freshwater to mitigate salt buildup from the converted runoff demonstrates that using the new water source directly causes additional freshwater pumpage, invalidating the net savings projection.

This provides new empirical evidence directly attacking the central assumption of net pumpage reduction.

Key Concept

Evaluating Plan Feasibility and Counterproductive Side Effects

Estimated Time:2m 0s

Question 1391Question →

Read the passage below and complete the argument logically by providing the missing conclusion in the blank.

Fill in the blanks below

A major commercial airline recently converted its legacy aircraft fleet to operate entirely on 100% synthetic aviation fuel, which contains zero aromatic hydrocarbons, replacing conventional jet fuel. While synthetic fuel burns cleaner and produces lower particulate emissions, the elastomer gaskets in legacy turbine fuel lines specifically require regular contact with aromatic hydrocarbons to maintain a slight physical swelling that prevents fuel line seepage. Because the airline did not add aromatic compounds to the synthetic fuel supply or replace the existing engine gaskets, aviation maintenance analysts concluded that operating the legacy fleet on unblended synthetic fuel will directly result in .

Show answer & explanation

Answer

increased fuel leaks due to gasket shrinkage

The passage establishes two key facts: legacy gaskets need aromatic hydrocarbons to swell and prevent fuel leaks, and the new synthetic fuel lacks these aromatic compounds. Because the airline neither added aromatics nor replaced the gaskets, the gaskets will fail to maintain their swell, directly resulting in fuel line leakage due to gasket shrinkage.

Step-by-Step Solution

1

Identify the core premises provided in the stimulus.

Premise 1: Legacy engine elastomer gaskets require exposure to aromatic hydrocarbons to swell and maintain a leak-free seal. Premise 2: Pure synthetic aviation fuel lacks aromatic hydrocarbons. Premise 3: The airline switched to pure synthetic fuel without adding aromatics or replacing legacy gaskets.

Establishing the precise factual foundation is necessary before drawing a valid logical deduction.

2

Synthesize the premises to determine the necessary physical outcome.

Without aromatic hydrocarbons in the fuel, the elastomer gaskets will lose their required swelling, failing to seal fuel line connections properly.

Combining the requirement of the gaskets with the absence of aromatics in the new fuel directly implies seal breakdown.

3

Formulate the logial completion that directly bridges the premise chain to its missing conclusion.

The operation will lead to increased fuel leakage or fuel system seepage resulting from gasket shrinkage.

The conclusion must follow directly from the premises without introducing unsupported assumptions about extraneous engine failures or economic variables.

Key Concept

Completing a logical passage requires synthesizing facts given in the premises to infer the necessary consequence, avoiding unwarranted assumptions or shifts in scope.

Question 1392Question →

Between 2018 and 2024, all commercial solar farms in Country X that integrated lithium-iron-phosphate (LFP) battery storage systems achieved continuous grid synchronization during peak demand hours. Conversely, no solar farm relying exclusively on nickel-manganese-cobalt (NMC) storage maintained uninterrupted grid connectivity throughout those same peak periods. During this six-year period, any solar farm in Country X that failed to maintain continuous grid synchronization during peak demand hours was assessed a regulatory surcharge. Furthermore, every commercial solar farm built in Country X after 2020 integrated either LFP or NMC storage systems, but never both.

Based on the information provided, which of the following statements must be logically true? Select all that apply.

Select all that apply

Every commercial solar farm in Country X relying exclusively on NMC battery storage between 2018 and 2024 was assessed a regulatory surcharge.

Commercial solar farms using NMC battery storage generated less total electricity than those using LFP battery storage.

Any commercial solar farm built in Country X in 2022 that integrated LFP storage achieved continuous grid synchronization during peak demand hours.

Integrating LFP battery storage was the sole method available for solar farms in Country X to avoid regulatory surcharges.

Any solar farm in Country X assessed a regulatory surcharge between 2018 and 2024 must have utilized an NMC battery storage system.

Show answer & explanation

Answer: Every commercial solar farm in Country X relying exclusively on NMC battery storage between 2018 and 2024 was assessed a regulatory surcharge.; Any commercial solar farm built in Country X in 2022 that integrated LFP storage achieved continuous grid synchronization during peak demand hours.

Answer

The correct statements are that every commercial solar farm relying exclusively on NMC battery storage between 2018 and 2024 was assessed a regulatory surcharge, and that any commercial solar farm built in 2022 that integrated LFP storage achieved continuous grid synchronization during peak demand hours.

The statement regarding exclusive NMC storage farms being assessed a regulatory surcharge directly synthesizes two explicit passage facts: exclusive NMC farms failed to maintain continuous connectivity during peak hours, and failing continuous connectivity resulted in a regulatory surcharge. The statement regarding 2022 LFP-integrated farms directly applies the universal premise about LFP farms operating between 2018 and 2024.

Step-by-Step Solution

1

Analyze the premise regarding NMC storage and regulatory surcharges.

No exclusive NMC farm maintained uninterrupted grid connectivity, and failing uninterrupted connectivity triggered a surcharge. Synthesizing these two premises proves that all exclusive NMC farms incurred surcharges.

Direct deduction from linked conditional premises.

2

Analyze the premise regarding LFP storage for farms built in 2022.

The year 2022 is within 2018–2024. All LFP farms in this period achieved continuous grid synchronization during peak demand hours.

Direct application of a general premise to a specific year within the defined timeframe.

3

Evaluate the incorrect choices for logical leaps or scope errors.

Statements introducing unmentioned metrics (total electricity generation), necessary/sufficient confusions (sole method), or formal conditional reversals are invalid inferences.

Valid inferences on the GMAT must be strictly supported without external assumptions or formal fallacies.

Key Concept

Drawing Valid Inferences via Premise Synthesis

Question 1393Question →

A bakery sells only vanilla cupcakes and chocolate cupcakes. On Monday, what was the ratio of the number of vanilla cupcakes sold to the number of chocolate cupcakes sold?

(1) On Monday, the bakery sold a total of 120 cupcakes.
(2) On Monday, 40% of the cupcakes sold were vanilla cupcakes.

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

Answer

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

The correct answer states that Statement (2) alone is sufficient while Statement (1) alone is not. Statement (1) gives only the sum of both types of cupcakes, which allows for infinite possible ratio combinations. Statement (2) specifies that vanilla cupcakes represent 40% of the total sales, meaning chocolate cupcakes represent the remaining 60%. The ratio of vanilla to chocolate cupcakes is therefore fixed at 40:60, or 2:3, providing a unique and definitive solution.

Step-by-Step Solution

1

Rephrase the question stem target algebraically

Let

V

be the number of vanilla cupcakes sold and

C

be the number of chocolate cupcakes sold. The goal is to find the value of the ratio

\frac{V}{C}

.

Simplifying the target helps determine what information is necessary to answer the question.

2

Evaluate Statement (1) independently

Statement (1) gives

V + C = 120

. With no information about

V

or

C

individually, the ratio

\frac{V}{C}

could be

1:1

(60 of each),

1:2

(40 vanilla, 80 chocolate), or many other values. Thus, Statement (1) is NOT sufficient.

A total count alone cannot determine a ratio without additional proportional constraints.

3

Evaluate Statement (2) independently

Statement (2) states

V = 0.40(V + C)

. Expanding gives

V = 0.40V + 0.40C \implies 0.60V = 0.40C \implies \frac{V}{C} = \frac{0.40}{0.60} = \frac{2}{3}

. A single, unique ratio of

2:3

is determined. Thus, Statement (2) IS sufficient.

Knowing the percentage component of a two-part total fixes the ratio regardless of total volume.

Key Concept

Determining ratios from component percentages versus absolute quantities in Data Sufficiency

Question 1394Question →

If $x$ is a real number and $x \neq -1$ , is $\frac{|x - 3|}{x + 1} < 1$ ?

(1) $|2x - 1| > 3$
(2) $x(x - 1) > 0$

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.

Rephrasing the question stem shows that

\frac{|x - 3|}{x + 1} < 1

is satisfied when

x < -1

or

x > 1

. Statement (1) solves to

x < -1

or

x > 2

. Since

(2, \infty)

is completely contained inside

(1, \infty)

, every value satisfying Statement (1) yields a definitive YES to the question. Statement (2) solves to

x < 0

or

x > 1

. Choosing

x = 2

gives a YES answer, while choosing

x = -0.5

gives a NO answer. Thus, Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Step-by-Step Solution

1

Rephrase the question stem by analyzing cases for the denominator

x + 1

.

Case 1 (

x > -1

):

x + 1 > 0

, so

|x - 3| < x + 1 \iff -(x + 1) < x - 3 < x + 1

. The right inequality

-3 < 1

is always true, and the left inequality

-x - 1 < x - 3

simplifies to

2x > 2 \iff x > 1

.
Case 2 (

x < -1

):

x + 1 < 0

. The numerator

|x - 3| > 0

while the denominator is negative, making the ratio negative, which is always

< 1

.
Combining both cases: The target inequality holds if and only if

x < -1

or

x > 1

.

Rephrasing the stem target simplifies complex absolute value expressions into clear number line intervals.

2

Evaluate Statement (1):

|2x - 1| > 3

.

2x - 1 > 3 \implies 2x > 4 \implies x > 2

, or

2x - 1 < -3 \implies 2x < -2 \implies x < -1

.
Range:

x \in (-\infty, -1) \cup (2, \infty)

. Every value in this range satisfies

x < -1

or

x > 1

, guaranteeing a definitive YES to the question.

Statement 1 specifies a subset of the valid target range, making it sufficient alone.

3

Evaluate Statement (2):

x(x - 1) > 0

.

Range:

x < 0

or

x > 1

. Testing values within this range:
- If

x = 2

:

2(1) = 2 > 0

, and

\frac{|2 - 3|}{2 + 1} = \frac{1}{3} < 1

(YES).
- If

x = -0.5

:

-0.5(-1.5) = 0.75 > 0

, but

\frac{|-0.5 - 3|}{-0.5 + 1} = \frac{3.5}{0.5} = 7 \not< 1

(NO).
Since both YES and NO outcomes are possible, Statement (2) is insufficient.

Finding a counterexample within the statement's solution set proves insufficiency.

Key Concept

Data Sufficiency evaluation for rational expressions containing absolute values and rephrasing inequality ranges.

Estimated Time:2m 0s

Question 1395Question →

A regional agricultural authority plans to subsidize the replacement of traditional flood irrigation with subsurface drip irrigation across farms in a drought-prone river basin. Because subsurface drip irrigation reduces per-acre water loss to evaporation by 35 percent, the authority concludes that implementing this technology region-wide will substantially increase the total volume of water remaining in the basin's underground aquifer each year. Which of the following, if true, most seriously weakens the agricultural authority's argument?

Subsurface drip irrigation systems require specialized filtration equipment that significantly increases annual energy consumption for participating farms.

A substantial portion of the unevaporated water applied during traditional flood irrigation percolates down through the soil and recharges the aquifer, whereas drip irrigation delivers water directly to roots with virtually no deep soil percolation.

Subsurface drip systems have been successfully adopted by commercial farms in adjacent agricultural districts that share similar soil compositions.

Projected changes in international trade policy over the next decade may prompt regional farmers to shift production toward crops that require more total water.

Farms utilizing subsurface drip irrigation report an average 15 percent increase in crop yields compared to farms using traditional flood irrigation.

Show answer & explanation

Answer: A substantial portion of the unevaporated water applied during traditional flood irrigation percolates down through the soil and recharges the aquifer, whereas drip irrigation delivers water directly to roots with virtually no deep soil percolation.

Answer

The argument is most seriously weakened by the statement that unevaporated flood irrigation water previously percolated down to recharge the aquifer, whereas drip irrigation eliminates this percolation.

The correct answer weakens the argument by demonstrating that traditional flood irrigation served a vital function in replenishing the aquifer through deep soil percolation. By replacing flood irrigation with drip irrigation—which supplies only enough water for plant absorption—the basin loses its primary mechanism for aquifer recharge. Thus, even though evaporation is reduced, the net input of water into the underground aquifer decreases, directly undermining the authority's conclusion.

Step-by-Step Solution

1

Deconstruct the argument core

Premise: Subsurface drip irrigation reduces per-acre water loss from evaporation by 35%. Conclusion: Region-wide adoption will substantially increase the total volume of water remaining in the underground aquifer.

Identifying the explicit premise and conclusion isolates the author's underlying assumption.

2

Identify the unstated assumption

The argument assumes that water lost to evaporation is the only factor determining how much water reaches or stays in the aquifer, and that water not lost to evaporation was not already returning to the aquifer under flood irrigation.

Weakening questions require finding new information that shatters the link between the premise and conclusion.

3

Evaluate the impact of the correct answer choice

If unevaporated water under flood irrigation regularly seeped down to recharge the aquifer, then flood irrigation was actually replenishing the underground water storage. Drip irrigation eliminates this recharge mechanism, meaning less total water reaches the aquifer despite reduced evaporation.

This directly refutes the conclusion that aquifer levels will increase.

Key Concept

Weakening Causal and Plan-to-Goal Arguments via Countervailing Factors

Question 1396Question →

Every commercial flight route operating out of Hub H that utilizes wide-body aircraft is assigned a Tier-1 maintenance protocol. Any route at Hub H assigned a Tier-1 maintenance protocol is subjected to mandatory weekly safety audits unless that route serves exclusively international destinations. Last year, every route at Hub H subjected to mandatory weekly safety audits was operated by FlightCorp, and FlightCorp operated no routes at Hub H that served international destinations.

If the statements above are true, which of the following must also be true about Hub H last year?

Every route at Hub H operated by FlightCorp utilized wide-body aircraft.

FlightCorp operated more domestic routes out of Hub H than did any other airline.

Any route at Hub H that utilized wide-body aircraft but was not operated by FlightCorp served exclusively international destinations.

Any route at Hub H that served exclusively international destinations was assigned a Tier-1 maintenance protocol.

No route at Hub H serving exclusively international destinations was subjected to mandatory weekly safety audits.

Show answer & explanation

Answer: Any route at Hub H that utilized wide-body aircraft but was not operated by FlightCorp served exclusively international destinations.

Answer

Any route at Hub H that utilized wide-body aircraft but was not operated by FlightCorp served exclusively international destinations.

The statement regarding wide-body routes not operated by FlightCorp must be true based on the logical structure of the premises: Wide-body aircraft routes automatically receive Tier-1 maintenance. Tier-1 routes require weekly audits unless they are exclusively international. Because all audited routes were operated by FlightCorp, any non-FlightCorp route was not audited. For a Tier-1 route to avoid weekly audits, it must meet the exemption condition of serving exclusively international destinations.

Step-by-Step Solution

1

Represent the premises as conditional logic statements.

1. Wide-Body -> Tier-1 Maintenance.
2. Tier-1 Maintenance AND NOT Exclusively International -> Weekly Audits.
3. Weekly Audits -> Operated by FlightCorp.

Establishing clear conditional rules allows logical synthesis.

2

Take the contrapositive of Premise 3.

NOT Operated by FlightCorp -> NOT Weekly Audits.

If a route was not operated by FlightCorp, it could not have been subjected to mandatory weekly safety audits.

3

Combine the premises for a route that uses wide-body aircraft but is not operated by FlightCorp.

The route has Tier-1 Maintenance (from Premise 1) and does NOT undergo Weekly Audits (from contrapositive of Premise 3).

Linking the conditions isolates the exception clause in Premise 2.

4

Apply Premise 2 to the combined state.

Premise 2 states that Tier-1 routes undergo weekly audits UNLESS they serve exclusively international destinations. Since this route has Tier-1 maintenance but does NOT undergo weekly audits, it MUST fall under the exception and serve exclusively international destinations.

The absence of the audit requirement for a Tier-1 route strictly necessitates that the exemption condition (exclusively international) holds true.

Key Concept

Conditional Logic Deductions and Contrapositives

Estimated Time:2m 0s

Question 1397Question →

In 2024, 40 percent of Company X's total workforce were software engineers. In 2025, software engineers made up 50 percent of the total workforce. If the total number of employees at Company X decreased by 30 percent between 2024 and 2025, which of the following must be true?

The total number of software engineers employed at Company X was smaller in 2025 than in 2024.

Company X employed more software engineers in total in 2025 than it did in 2024.

The productivity per software engineer at Company X increased significantly following the restructuring.

Software engineers represented a smaller proportion of Company X's total workforce in 2025 than in 2024.

Company X laid off more non-engineering employees than software engineers due to budget constraints.

Show answer & explanation

Answer: The total number of software engineers employed at Company X was smaller in 2025 than in 2024.

Answer

The total number of software engineers employed at Company X was smaller in 2025 than in 2024.

The correct answer is logically necessitated by combining the percentage of software engineers with the overall workforce reduction. An increase in proportion from 40 percent to 50 percent applied to a base that dropped by 30 percent results in fewer total software engineers.

Step-by-Step Solution

1

Calculate the initial number of software engineers using a hypothetical base workforce

Assuming a total workforce of 100 employees in 2024, 40 percent corresponds to 40 software engineers.

Establishing a base number allows straightforward calculation of relative change.

2

Calculate the updated total workforce and number of software engineers in 2025

A 30 percent reduction reduces the workforce to 70 employees. In 2025, 50 percent of 70 equals 35 software engineers.

Applying the given percentage parameters to the reduced base size yields the new count.

3

Compare the total count of software engineers between the two years

The absolute count of engineers fell from 40 to 35.

Comparing absolute counts verifies which deduction logically must follow.

Key Concept

Numerical, Proportion, and Statistical Inferences

Question 1398Question →

For all real numbers $a$ and $b$ with $a \neq b$ , the Data Sufficiency Yes/No target question "Is $\frac{a^2 - b^2}{(a - b)^2} > 1$ ?" is algebraically equivalent to the simplified target question "Is $a > b$ ?"

True

False

Show answer & explanation

Answer: False

Answer

The statement is False because rephrasing the target inequality yields

\frac{2b}{a-b} > 0

, which requires analyzing the signs of both

b

and

a-b

, rather than evaluating whether

a > b

alone.

The statement is False. Correct simplification of

\frac{a^2 - b^2}{(a - b)^2} > 1

leads to

\frac{2b}{a-b} > 0

. This inequality requires

2b

and

a-b

to have identical signs, which holds either when

b > 0

and

a > b

or when

b < 0

and

a < b

. Because

a > b

can be true while

b < 0

(making the original inequality false), the proposed rephrasing is invalid.

Step-by-Step Solution

1

Factor the algebraic expression in the numerator of the target question.

The numerator

a^2 - b^2

factors as

(a-b)(a+b)

, yielding

\frac{(a-b)(a+b)}{(a-b)^2} > 1

.

Factoring allows simplification of common terms between the numerator and denominator.

2

Simplify the fraction by canceling common non-zero terms.

Since

a \neq b

,

a - b \neq 0

, so

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

.

Canceling

(a-b)

is valid as long as

a \neq b

.

3

Compare the fraction to zero by subtracting 1 from both sides.

\frac{a+b}{a-b} - 1 > 0 \implies \frac{(a+b) - (a-b)}{a-b} > 0 \implies \frac{2b}{a-b} > 0.

Subtracting 1 avoids multiplying by a variable expression

(a-b)

whose sign is unknown.

4

Determine the conditions under which

\frac{2b}{a-b} > 0

.

The quotient is positive when

2b

and

a-b

have the same sign: Case 1 (

b > 0

and

a > b

) OR Case 2 (

b < 0

and

a < b

).

A quotient is strictly positive if and only if its numerator and denominator share the same sign.

5

Test whether "Is

a > b

?" is equivalent to the derived condition using a counterexample.

If

a = 2

and

b = -1

, then

a > b

is true (

2 > -1

). However,

\frac{2(-1)}{2 - (-1)} = -\frac{2}{3} \ngtr 0

.

Finding a scenario where

a > b

is true but the original inequality fails proves the two target questions are not algebraically equivalent.

Key Concept

Question Stem Simplification and Target Rephrasing

Question 1399Question →

If $x$ and $y$ are non-zero real numbers, is $\frac{|x|}{y} < 1$ ?

(1) $x^2 < y^2$
(2) $x + y < 0$

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.

EITHER 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.

Statement (1) gives

x^2 < y^2

, which means

|x| < |y|

. If

y > 0

,

|y| = y

, so

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

. If

y < 0

,

|x| > 0

implies

\frac{|x|}{y} < 0 < 1

. Thus, Statement (1) alone yields a definitive 'Yes' and is sufficient. Statement (2) allows

x = -3, y = 1

(yielding a ratio of 3, which is not less than 1) and

x = -1, y = -2

(yielding a ratio of -0.5, which is less than 1), so Statement (2) alone is insufficient.

Step-by-Step Solution

1

Rephrase the target question

The target question asks whether

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

for non-zero real numbers

x

and

y

.

Since

|x| > 0

for any non-zero real number

x

, if

y < 0

, the ratio

\frac{|x|}{y}

is strictly negative, which is always less than 1. If

y > 0

,

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

is equivalent to

|x| < y

.

2

Evaluate Statement (1):

x^2 < y^2

Taking the principal square root of both sides gives

|x| < |y|

.

If

y > 0

,

|y| = y

, so

|x| < y

, which implies

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

(YES). If

y < 0

, then

y

is negative and

|x|

is positive, so

\frac{|x|}{y} < 0 < 1

(YES). Since Statement (1) yields a definitive YES in all cases, Statement (1) ALONE is sufficient.

3

Evaluate Statement (2):

x + y < 0

Test suitable numbers.

Case A: Let

x = -3

and

y = 1

. Then

x + y = -2 < 0

, but

\frac{|-3|}{1} = 3 \not< 1

(NO). Case B: Let

x = -1

and

y = -2

. Then

x + y = -3 < 0

, and

\frac{|-1|}{-2} = -0.5 < 1

(YES). Because Statement (2) can yield both YES and NO, Statement (2) ALONE is not sufficient.

Key Concept

Data Sufficiency evaluation of absolute values and algebraic inequalities with unknown signs

Estimated Time:2m 0s

Question 1400Question →

If $m$ is a real number, is $m > 0$ ?

(1) $|m + 4| = -3m$
(2) $m^2 + 3m + 2 = 0$

Which of the following correctly 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.

The choice stating that EACH statement ALONE is sufficient is correct. Statement (1) restricts

m

uniquely to

m = -1

due to the absolute value non-negativity constraint, yielding a definitive 'No' to the question

m > 0

. Statement (2) yields

m = -1

or

m = -2

; since both values are negative, Statement (2) also conclusively answers 'No'. Therefore, both statements independently provide sufficient information.

Step-by-Step Solution

1

Analyze the question stem

The target is a Yes/No question asking whether

m > 0

. A statement is sufficient if it conclusively proves

m > 0

(Yes) or conclusively proves

m \le 0

(No).

Understanding Yes/No Data Sufficiency logic is essential: a definitive 'No' is just as sufficient as a definitive 'Yes'.

2

Evaluate Statement (1):

|m + 4| = -3m

Since an absolute value cannot be negative,

-3m \ge 0 \implies m \le 0

. Solving

m + 4 = -3m

gives

4m = -4 \implies m = -1

. Solving

-(m + 4) = -3m

gives

2m = 4 \implies m = 2

(extraneous because

m \le 0

). Thus,

m = -1

uniquely.

Testing

m = -1

in the target question gives: Is

-1 > 0

? No. Because Statement (1) provides a single unique value that yields a definitive 'No', Statement (1) alone is sufficient.

3

Evaluate Statement (2):

m^2 + 3m + 2 = 0

Factoring gives

(m + 1)(m + 2) = 0

, so

m = -1

or

m = -2

.

If

m = -1

, is

m > 0

? No. If

m = -2

, is

m > 0

? No. Because all possible values for

m

consistently lead to a definitive 'No', Statement (2) alone is sufficient.

4

Combine evaluations to select the correct choice

Since Statement (1) alone is sufficient and Statement (2) alone is sufficient, the correct response is that each statement alone is sufficient.

Matches standard GMAT Data Sufficiency Option D.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic

Answer

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