All practice questions

Question 1361Question →

If $m$ and $n$ are non-zero real numbers, is $\frac{|m + n|}{m} > 1$ ?

(1) $m < -|n|$
(2) $mn > 0$ and $|m + n| = m + n$

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

m

to negative values, guaranteeing that the numerator is non-negative while the denominator is negative, so the ratio can never exceed 1 (yielding a definitive 'No'). Statement (2) forces both

m

and

n

to be strictly positive, which simplifies the ratio to

1 + \frac{n}{m} > 1

(yielding a definitive 'Yes'). Since each statement provides a definitive answer independently, each statement alone is sufficient.

Step-by-Step Solution

1

Analyze the question stem target

\frac{|m + n|}{m} > 1

.

Since absolute value

|m + n|

is always non-negative (

|m + n| \ge 0

), if

m < 0

, the ratio

\frac{|m + n|}{m} \le 0

, which can never be greater than 1. Thus, if

m < 0

, the answer is a definitive 'No'. If

m > 0

, the expression simplifies to

|m + n| > m

.

Establishing the behavior of the expression based on the sign of

m

simplifies statement evaluation.

2

Evaluate Statement (1):

m < -|n|

.

Since

n \neq 0

,

|n| > 0

, which implies

-|n| < 0

. Therefore,

m < 0

. Because

m < 0

and

|m + n| \ge 0

, the fraction

\frac{|m + n|}{m}

is non-positive (

\le 0

). Thus,

\frac{|m + n|}{m}

cannot be greater than 1, yielding a definitive 'No'. Statement (1) ALONE is sufficient.

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

3

Evaluate Statement (2):

mn > 0

and

|m + n| = m + n

.

From

mn > 0

,

m

and

n

must have the same sign (both positive or both negative). The condition

|m + n| = m + n

requires

m + n \ge 0

. If both

m

and

n

were negative,

m + n

would be negative, contradicting

|m + n| \ge 0

. Hence, both

m

and

n

must be positive (

m > 0

and

n > 0

). Substituting into the expression:

\frac{|m + n|}{m} = \frac{m + n}{m} = 1 + \frac{n}{m}

. Since

n > 0

and

m > 0

,

\frac{n}{m} > 0

, so

1 + \frac{n}{m} > 1

. This yields a definitive 'Yes'. Statement (2) ALONE is sufficient.

Determining that

m

and

n

must both be positive allows exact evaluation of the inequality.

Key Concept

Data Sufficiency logic for Yes/No questions involving absolute value properties and variable sign analysis.

Question 1362Question →

Complete the passage logically by filling in the blank with the phrase that best concludes the argument.

Fill in the blanks below

To combat the growing hazard of orbital debris in Low Earth Orbit, space safety regulators have proposed requiring all commercial satellite operators to install heavy, automated de-orbit propulsion modules that force satellites into the atmosphere at the end of their operational life. However, environmental analysts point out that manufacturing and launching these heavy modules significantly increases rocket fuel consumption and atmospheric pollutant emissions during launch. Given that existing lightweight maneuvering thrusters already enable operational satellites to prevent over 98 percent of potential debris collisions during their active lifespan, mandating the inclusion of dedicated de-orbit modules will likely fail to achieve its net environmental risk reduction goal, because .

Show answer & explanation

Answer

the atmospheric pollution generated during launch exceeds the marginal reduction in orbital risk provided after decommissioning

The correct completion logically synthesizes the two conflicting factors presented in the stimulus: the high environmental penalty of launching heavy de-orbit modules and the minimal marginal benefit gained over existing lightweight thrusters. Since active thrusters already eliminate over 98% of collision risks, the added environmental harm from extra launch emissions outweighs the tiny remaining collision risk mitigated after decommissioning.

Step-by-Step Solution

1

Analyze the premises and identify the central tension in the argument.

The regulation aims to lower environmental/orbital risk. However, heavy de-orbit modules cause high environmental costs (launch emissions), while providing only a small marginal benefit because existing thrusters already handle 98% of collision risks.

To complete the passage logically, the conclusion must connect the premises to show why the overall environmental goal is undermined.

2

Synthesize the cost-benefit trade-off into a logical conclusion.

Since the environmental cost (increased emissions) is large and the remaining risk being addressed (under 2%) is small, the net impact of the policy will be negative.

The word 'because' requires an explanation directly supported by the relative magnitude of the environmental costs versus benefits stated in the passage.

Key Concept

Completing the Passage Logically

Estimated Time:1m 30s

Question 1363Question →

If $x$ and $y$ are real numbers such that $x \neq y$ and $x + y \neq 0$ , is $\frac{x^3 - y^3}{x^2 - y^2} > x + y$ ?

(1) $x > y > 0$

(2) $|x + y| < |x - y|$

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.

Factoring the numerator and denominator of the target expression transforms the question 'Is

\frac{x^3 - y^3}{x^2 - y^2} > x + y

?' into the simplified target 'Is

\frac{xy}{x + y} < 0

?'. Under Statement (1), both

x

and

y

are positive, so

xy > 0

and

x + y > 0

, making

\frac{xy}{x + y} > 0

. This conclusively answers the target question with a definitive 'No', proving Statement (1) is sufficient alone. Statement (2) simplifies to

xy < 0

, which allows

x + y

to be positive or negative, resulting in both 'Yes' and 'No' possibilities, rendering Statement (2) insufficient.

Step-by-Step Solution

1

Rephrase the question target algebraically before evaluating the statements.

Simplifying

\frac{x^3 - y^3}{x^2 - y^2}

by factoring numerator and denominator yields

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

. The inequality

\frac{x^2 + xy + y^2}{x + y} > x + y

simplifies to

\frac{x^2 + xy + y^2 - (x + y)^2}{x + y} > 0

, which reduces to

\frac{-xy}{x + y} > 0

, or equivalently

\frac{xy}{x + y} < 0

.

Target rephrasing reveals that the question is asking whether

xy

and

x + y

have opposite signs.

2

Evaluate Statement (1):

x > y > 0

.

Since

x > 0

and

y > 0

,

xy > 0

and

x + y > 0

. Consequently,

\frac{xy}{x + y} > 0

. This yields a definitive 'No' to the rephrased question 'Is

\frac{xy}{x + y} < 0

?'. A definitive 'No' is sufficient.

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

3

Evaluate Statement (2):

|x + y| < |x - y|

.

Squaring both sides gives

(x + y)^2 < (x - y)^2 \implies x^2 + 2xy + y^2 < x^2 - 2xy + y^2 \implies 4xy < 0 \implies xy < 0

. However, knowing

xy < 0

leaves the sign of

x + y

undetermined. For example, if

x = 3, y = -1

, then

x + y = 2 > 0

and

\frac{xy}{x+y} = -1.5 < 0

(Yes). If

x = 1, y = -3

, then

x + y = -2 < 0

and

\frac{xy}{x+y} = 1.5 > 0

(No).

Since the outcome can be either 'Yes' or 'No', Statement (2) alone is not sufficient.

Key Concept

Data Sufficiency Target Simplification and Yes/No Decision Logic

Question 1364Question →

If $x$ is a real number, is $|2x - 3| \le 5$ ?

(1) $|x - 1| \le 2$
(2) $x^2 - 3x - 4 \le 0$

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 target inequality

|2x - 3| \le 5

gives

-1 \le x \le 4

. Statement (1) yields

-1 \le x \le 3

, which is completely contained within

[-1, 4]

and therefore guarantees a definitive 'Yes'. Statement (2) yields

-1 \le x \le 4

, which matches the condition directly and also gives a definitive 'Yes'. Hence, each statement alone is sufficient.

Step-by-Step Solution

1

Rephrase the question stem target inequality algebraically.

-5 \le 2x - 3 \le 5 \implies -2 \le 2x \le 8 \implies -1 \le x \le 4

. Target Question: Is

-1 \le x \le 4

?

Simplifying the question stem converts an absolute value inequality into a clear number range for

x

.

2

Evaluate Statement (1):

|x - 1| \le 2

.

-2 \le x - 1 \le 2 \implies -1 \le x \le 3

. Since every value in

[-1, 3]

is also in

[-1, 4]

, the answer to 'Is

-1 \le x \le 4

?' is a definitive YES.

If a statement's allowed range is a subset of the target range, it guarantees a definitive 'Yes' answer.

3

Evaluate Statement (2):

x^2 - 3x - 4 \le 0

.

Factor the quadratic:

(x - 4)(x + 1) \le 0 \implies -1 \le x \le 4

. This matches the target range exactly, yielding a definitive YES.

Matching the target inequality range provides a definitive 'Yes' answer.

Key Concept

Data Sufficiency Yes/No decision logic for absolute value range constraints and subset range implications.

Estimated Time:1m 30s

Question 1365Question →

To cut heating costs, the management of a high-rise office complex replaced all single-pane windows with double-pane low-emissivity glass. Although weather conditions over the following winter were identical to those of the previous winter, the building's overall energy consumption for heating increased by 8 percent. The management concluded that the new windows were defective and failed to provide the promised thermal insulation.

Which of the following, if true, most strengthens the conclusion drawn by the building management?

The average internal thermostat settings across all office suites were raised by 3 degrees Celsius during the second winter to accommodate tenant complaints.

Single-pane windows installed in nearby residential apartments required lower maintenance costs over the same period than did the newly installed low-emissivity glass.

A building-wide policy implemented prior to the second winter reduced evening office hours, which under typical operating conditions lowers overall heating energy demand by at least 10 percent.

The manufacturer of the double-pane windows recently introduced a revised installation guide for commercial residential buildings.

The initial purchase cost of the double-pane low-emissivity windows was higher than the management had budgeted for the facility upgrade project.

Show answer & explanation

Answer: A building-wide policy implemented prior to the second winter reduced evening office hours, which under typical operating conditions lowers overall heating energy demand by at least 10 percent.

Answer

The argument is most strengthened by the statement indicating that a building-wide policy reduced evening office hours, which normally lowers heating energy demand by at least 10 percent.

The conclusion asserts that defective window insulation caused an unexpected 8% increase in heating energy consumption despite identical weather conditions. The option stating that evening operating hours were reduced—a change that normally cuts heating demand by 10%—strongly supports the conclusion. If heating demand dropped, energy consumption should have decreased; the fact that it rose by 8% demonstrates an even severe failure in thermal efficiency than the raw figures initially suggested.

Step-by-Step Solution

1

Deconstruct the argument into premises and conclusion

Premises: Single-pane windows were replaced with double-pane low-emissivity glass; weather conditions were identical across both winters; heating energy consumption increased by 8%. Conclusion: The new windows were defective and failed to insulate properly.

Identifying the core causal claim (defective windows caused increased energy consumption) isolates the logical gap that needs support.

2

Determine the required strengthening mechanism

To strengthen the conclusion, we must rule out alternative explanations for the energy increase or show that energy consumption should have dropped even further under normal operations.

Demonstrating that operational factors pushed heating demand down makes the actual 8% energy increase even more anomalous and directly attributable to defective window insulation.

3

Evaluate the impact of reduced operating hours

If reduced operating hours should have lowered heating demand by 10%, an actual increase of 8% represents an 18% net deficit in thermal performance, strongly confirming window defectiveness.

Eliminating operational workload as a driver of energy consumption rules out confounders and confirms the insulating failure.

Key Concept

Strengthening Causal Arguments by Ruling Out Alternative Causes and Establishing Baseline Expectations

Question 1366Question →

If $x$ is a positive integer, is $x^2 - 5x + 6 > 0$ ?

(1) $(x - 2)(x - 3) \le 0$
(2) $x < 5$

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 sufficient is correct. Statement (1) restricts the positive integer

x

to

\{2, 3\}

, for both of which

x^2 - 5x + 6 = 0

. This yields a definitive 'No' to the question of whether the expression is strictly greater than 0, making Statement (1) sufficient. Statement (2) permits values such as

x = 1

(which yields 'Yes') and

x = 2

(which yields 'No'), making it insufficient.

Step-by-Step Solution

1

Rephrase the question stem target algebraically.

The target expression

x^2 - 5x + 6

factors into

(x - 2)(x - 3)

. The question asks: 'Is

(x - 2)(x - 3) > 0

?'

Factoring simplifies evaluating the sign of the expression for specific values of

x

.

2

Evaluate Statement (1) independently.

Statement (1) gives

(x - 2)(x - 3) \le 0

. Since

x

is a positive integer, the integer solutions to this inequality are

x = 2

and

x = 3

. For

x = 2

,

(2-2)(2-3) = 0

. For

x = 3

,

(3-2)(3-3) = 0

. In both cases,

x^2 - 5x + 6 = 0

, which is NOT

> 0

. Thus, the answer to the stem question is a definitive 'NO'.

In a Yes/No Data Sufficiency question, any statement that yields a definitive 'No' for all possible values of the variable is SUFFICIENT.

3

Evaluate Statement (2) independently.

Statement (2) gives

x < 5

. Since

x

is a positive integer,

x

can be 1, 2, 3, or 4. If

x = 1

,

1^2 - 5(1) + 6 = 2 > 0

(Answer: YES). If

x = 2

,

2^2 - 5(2) + 6 = 0

, which is not

> 0

(Answer: NO). Since Statement (2) allows both 'YES' and 'NO' outcomes, it is NOT SUFFICIENT.

A statement that leads to conflicting answers ('Maybe') is insufficient.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic

Question 1367Question →

A shipping port recently installed automated inspection cranes at two of its primary terminals, resulting in a significant reduction in customs clearance delays at those locations. Based on this success, the port authority concludes that installing automated inspection cranes across all remaining terminals will eliminate customs processing backlogs port-wide. Which of the following, if true, most seriously weakens the port authority's conclusion?

The remaining terminals exclusively process non-standard cargo that requires manual physical inspection regardless of crane automation.

Crane operators at the initial terminals reported a thirty percent increase in hourly container throughput after the automated equipment was installed.

Competing ports in neighboring regions recently upgraded their customs software to accelerate clearance times.

The initial acquisition cost of the automated cranes exceeded the port authority's original budget.

Customs clearance delays contribute more to total container transit times than weather-related shipping delays do.

Show answer & explanation

Answer: The remaining terminals exclusively process non-standard cargo that requires manual physical inspection regardless of crane automation.

Answer

The argument is most seriously weakened by the fact that the remaining terminals process non-standard cargo requiring manual inspection regardless of crane automation.

The author concludes that expanding automated crane installation to remaining terminals will eliminate backlogs, assuming those terminals will experience the same benefits as the first two. The correct option reveals that the remaining terminals handle cargo requiring manual physical inspection regardless of crane automation. Because automated cranes cannot bypass manual inspection requirements, installing them will not eliminate backlogs at those terminals, directly undermining the conclusion.

Step-by-Step Solution

1

Identify the author's premise and conclusion

Premise: Automated cranes reduced delays at two primary terminals. Conclusion: Installing automated cranes at all remaining terminals will eliminate port-wide backlogs.

Understanding the logic gap between the sample terminals and the remaining terminals is essential for weakening the argument.

2

Identify the central assumption

The author assumes that the conditions at the remaining terminals are sufficiently similar to those at the test terminals so that automated cranes will yield the same results.

Weakening questions target unstated assumptions that bridge evidence to conclusions.

3

Select the option that undermines this assumption

Finding that remaining terminals handle cargo requiring manual inspections demonstrates that automated cranes will not resolve backlogs at those locations.

Showing a key difference between the test group and remaining group negates the feasibility of the plan.

Key Concept

Weakening a generalization by demonstrating unrepresentative sample conditions

Question 1368Question →

To reduce fuel costs, a regional cargo airline operating primarily in high-altitude mountainous terrain plans to retrofit its turboprop fleet with newly engineered lightweight winglets. Flight tests conducted at sea level demonstrated that these winglets reduced fuel consumption by 8 percent by minimizing aerodynamic drag. Based on these sea-level test results, executives conclude that retrofitting the fleet with these winglets will significantly decrease the carrier's overall fuel expenditure on its mountain routes.

Which of the following, if true, provides the strongest support for the executives' conclusion?

The initial capital expense of acquiring and retrofitting the winglets exceeds the estimated fuel cost savings during the fleet's first year of operation.

Competing cargo carriers operating exclusively on flat coastal routes reported high overall reliability after installing similar winglet modifications.

At high altitudes, lower air density reduces engine efficiency, causing aircraft to burn more fuel per flight hour regardless of winglet installation.

Aerodynamic drag accounts for a greater proportion of total engine workload during flight maneuvers in high-altitude mountain conditions than during sea-level flight.

The price per gallon of aviation fuel in mountain regions is projected to fluctuate at the same rate as the price of fuel in coastal areas.

Show answer & explanation

Answer: Aerodynamic drag accounts for a greater proportion of total engine workload during flight maneuvers in high-altitude mountain conditions than during sea-level flight.

Answer

The argument is most strongly supported by the statement indicating that aerodynamic drag accounts for a greater proportion of total engine workload during flight maneuvers in high-altitude mountain conditions than during sea-level flight.

The correct answer directly connects the premise (sea-level drag reduction) with the target scenario (high-altitude mountain flights). By establishing that aerodynamic drag represents a larger share of engine workload in mountain conditions, it confirms that reducing drag will yield significant fuel savings in the specific environment where the fleet operates.

Step-by-Step Solution

1

Identify the argument's premises and conclusion.

Premise: Winglets reduced fuel consumption by 8% during tests at sea level by cutting aerodynamic drag. Conclusion: Installing the winglets will significantly cut overall fuel expenditure on high-altitude mountain routes.

Deconstructing the argument reveals the logical gap between sea-level test results and real-world high-altitude performance.

2

Identify the unstated assumption required for the argument to hold.

The argument assumes that aerodynamic drag reduction observed at sea level remains significant and effective under high-altitude mountain flight conditions.

If high-altitude conditions alter aerodynamic workload, sea-level results might not guarantee expected savings.

3

Evaluate the answer choices to find the statement that confirms or enhances this core connection.

Showing that aerodynamic drag plays an even larger role in engine workload at high altitudes validates and strengthens the assumption that drag-reducing winglets will generate substantial fuel savings on mountain routes.

Direct evidence confirming the relevance of drag reduction in the target operating environment directly strengthens the conclusion.

Key Concept

Strengthening Arguments by Confirming Key Assumptions across Environments

Question 1369Question →

To combat severe peak-hour traffic congestion on the city's central highway, municipal planners plan to convert one of the four existing traffic lanes in each direction into a dedicated lane for high-speed express commuter buses. Planners estimate that the increased speed and reliability of these express buses will convince 20 percent of current private automobile commuters to switch to public transit, thereby significantly reducing overall highway traffic congestion during peak commuting hours.

Which of the following, if true, most seriously weakens the municipal planners' argument?

Recent municipal surveys indicate that over 30 percent of current automobile commuters would willingly switch to public transit if express travel times were guaranteed.

Converting one of the four traffic lanes in each direction into a dedicated bus lane reduces the highway capacity for remaining private vehicles by 25 percent, exacerbating bottleneck delays for those vehicles.

The new high-speed express buses will produce slightly higher per-vehicle carbon emissions than the standard buses currently operating on city streets.

The operational maintenance costs for the express bus fleet will require an increase in municipal transit fares after the first year of service.

A portion of the ridership on the new express buses will consist of commuters who previously traveled during off-peak hours.

Show answer & explanation

Answer: Converting one of the four traffic lanes in each direction into a dedicated bus lane reduces the highway capacity for remaining private vehicles by 25 percent, exacerbating bottleneck delays for those vehicles.

Answer

The argument is most seriously weakened by the evidence that converting an existing lane reduces highway vehicle capacity for private automobiles by 25 percent, which exceeds the 20 percent reduction in vehicle volume and thus increases overall bottleneck delays.

The correct answer identifies a fatal flaw in the plan's mathematical trade-off. Converting 1 out of 4 lanes reduces capacity for general traffic by 25 percent (

1/4

). Even if 20 percent of automobile drivers switch to buses, the remaining 80 percent of traffic must fit into 75 percent of the original road capacity. As a result, congestion per available lane actually increases, directly refuting the claim that overall traffic congestion will decrease.

Step-by-Step Solution

1

Identify the conclusion and underlying premises of the argument.

Premise: Converting 1 of 4 existing lanes to a dedicated bus lane will attract 20% of automobile commuters to express buses. Conclusion: Overall highway traffic congestion during peak hours will decrease significantly.

Understanding the precise link between premise (volume reduction) and conclusion (congestion reduction) reveals key unstated assumptions about highway capacity.

2

Identify the core unstated assumption.

The argument assumes that removing 20% of vehicle drivers will decrease congestion despite taking away 1 out of 4 general lanes (a 25% drop in general capacity).

A plan to reduce congestion by taking away existing road capacity fails if the reduction in road capacity exceeds the reduction in vehicle volume.

3

Evaluate the answer choices to find the statement that undermines this assumption.

The option pointing out that dedicated lane conversion cuts general traffic capacity by 25% demonstrates that remaining traffic will experience worse bottlenecking, directly counteracting the 20% volume drop.

Showing that net throughput capacity falls faster than demand volume invalidates the claim that traffic congestion will decrease.

Key Concept

Plan-to-Goal Feasibility & Capacity Offsets

Question 1370Question →

Consider the following principles established by a marine bioarchaeology research consortium:

1. Every wooden artifact recovered from an anaerobic silt deposit that displays under $5\%$ cellulose degradation is classified as a Type-A Preserved artifact.
2. No artifact classified as Type-A Preserved is ever treated with polymer sealant X, because polymer sealant X is applied exclusively to timber that has sustained structural cell-wall collapse.
3. Any wooden artifact displaying under $5\%$ cellulose degradation that was submerged for over $400$ years has sustained structural cell-wall collapse unless it was deposited in anaerobic silt prior to $1500$ CE.

Statement: Based strictly on the principles above, a wooden artifact submerged for $600$ years that displays under $5\%$ cellulose degradation and has been treated with polymer sealant X was not recovered from an anaerobic silt deposit in which it was placed prior to $1500$ CE.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True because the artifact's treatment with polymer sealant X logically guarantees that it was not recovered from an anaerobic silt deposit.

The statement is logically valid and must be true based on the provided premises. Principle 2 establishes that no Type-A Preserved artifact is treated with polymer sealant X. Consequently, any artifact treated with polymer sealant X cannot be a Type-A Preserved artifact. Principle 1 specifies that a Type-A Preserved artifact is any artifact that both comes from an anaerobic silt deposit and displays under 5% cellulose degradation. Because the artifact in question displays under 5% cellulose degradation yet is not a Type-A Preserved artifact, it must fail the location condition—meaning it was not recovered from an anaerobic silt deposit. If it was not recovered from an anaerobic silt deposit, it logically must not have been recovered from an anaerobic silt deposit in which it was placed prior to 1500 CE.

Step-by-Step Solution

1

Analyze the relationship between polymer sealant X and the Type-A Preserved classification.

By Principle 2, no Type-A Preserved artifact is treated with polymer sealant X. Therefore, an artifact treated with polymer sealant X is NOT a Type-A Preserved artifact.

Direct modus tollens application on Principle 2.

2

Evaluate the criteria for Type-A Preserved classification using Principle 1.

Type-A Preserved requires two conditions: (A) Recovery from an anaerobic silt deposit, and (B) Displaying under 5% cellulose degradation. Since the artifact displays under 5% degradation but is NOT Type-A Preserved, it must fail condition A.

If (A and B) implies C, and we have B and NOT C, then NOT A must be true.

3

Synthesize the deduction regarding recovery location and historical timing.

Since the artifact was not recovered from an anaerobic silt deposit at all, it cannot have been recovered from an anaerobic silt deposit in which it was placed prior to 1500 CE.

Logical set containment: failing the general condition automatically falsifies any specific subset of that condition.

Key Concept

Deductive Conditional Logic and Contrapositive Chains

Question 1371Question →

Mayor: To revitalize our city's commercial district, we should eliminate municipal parking fees. When our neighboring city, Oakhaven, abolished its parking fees three years ago, retail revenue in its downtown sector increased by 20 percent over the subsequent two years.

City Analyst: However, during that same two-year period, Oakhaven completed a major light-rail line connecting its suburban residential areas directly to downtown, while our city has made no transit improvements. Therefore, eliminating parking fees alone will not produce the outcome you predict.

Which of the following best describes the method of reasoning used by the City Analyst in responding to the Mayor?

Mistaking an intermediate conclusion about municipal infrastructure for the primary premise of the opposing argument.

Rejecting an analogical argument on the grounds that the two situations share surface-level infrastructural features.

Pointing out an unaddressed confounding factor in a cited precedent to challenge a causal inference.

Dismissing a proposed policy by showing that its implementation will generate counterproductive side effects.

Refuting a general principle by offering a counterexample that directly contradicts the initial premise.

Show answer & explanation

Answer: Pointing out an unaddressed confounding factor in a cited precedent to challenge a causal inference.

Answer

The argument proceeds by pointing out an unaddressed confounding factor in a cited precedent to challenge a causal inference.

The Mayor infers a direct causal link between abolishing parking fees and increasing downtown retail revenue based on Oakhaven's experience. The City Analyst counters by revealing that Oakhaven simultaneously implemented a major transit project (light-rail), which serves as a confounding variable. Pointing out this alternate cause undermines the Mayor's claim that parking fee removal alone was responsible for Oakhaven's success or that it will work locally.

Step-by-Step Solution

1

Analyze the Mayor's argument structure

The Mayor argues that eliminating parking fees caused Oakhaven's 20% revenue growth, inferring that doing the same locally will produce a similar result.

Identifying the author's premise, conclusion, and underlying logic is necessary before assessing the response.

2

Analyze the City Analyst's response strategy

The Analyst introduces a second major event in Oakhaven occurring during the exact same timeframe—the light-rail line completion.

This alternative factor provides an plausible alternate cause for Oakhaven's revenue growth.

3

Match the strategy to abstract structural language

By introducing the light-rail system, the Analyst demonstrates that Oakhaven's success cannot be definitively attributed solely to parking fee elimination, thus exposing a confounding factor in the Mayor's comparative argument.

This abstract description accurately encapsulates challenging a causal claim via a confounding variable in empirical evidence.

Key Concept

Identifying Argumentative Strategies and Methods of Reasoning

Question 1372Question →

Consider the following argument:

A five-year municipal study compared thirty industrial cities that enacted regulations requiring commercial buildings to install vegetation-covered green roofs against thirty comparable cities without such mandates. The cities with mandated green roofs recorded a 25 percent reduction in emergency room admissions for heat-stroke and heat-stress illnesses during summer heatwaves. Researchers concluded that the microclimate cooling produced by green-roof vegetation was directly responsible for mitigating extreme urban heat and reducing heat-related hospitalizations.

Evaluate the following statement:
In the argument above, the fact that all thirty green-roof cities simultaneously modernized their municipal power grids—preventing summer blackouts and allowing residential air conditioning units to operate without interruption—functions as a confounding variable that weakens the researchers' causal conclusion.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. The concurrent electrical grid modernization introduces an alternative explanation for the reduced hospitalizations, thereby functioning as a confounding variable that undermines the causal attribution to green roofs.

The evaluated statement accurately identifies a classic confounding variable. In causal evaluation, when an extraneous event coincides perfectly with the proposed cause and provides an alternative pathway to the observed effect, the argument commits a causal flaw by failing to rule out alternative explanations.

Step-by-Step Solution

1

Deconstruct the core argument in the passage.

Premise: Green-roof cities experienced a 25% drop in heat-stress admissions relative to non-green-roof cities. Conclusion: Green-roof vegetation directly caused the reduction in heat-stress admissions.

Isolating the explicit causal link (Cause: Green roofs -> Effect: Reduced admissions) is required before evaluating potential flaws.

2

Analyze the impact of the additional factor described in the statement.

Power grid modernization prevented outages, ensuring continuous operation of residential air conditioning during extreme heat.

Air conditioning directly protects individuals from environmental heat stress, providing an independent mechanism for lowering hospital admissions.

3

Determine if this factor constitutes a confounding variable.

Because grid modernization occurred exclusively and uniformly alongside the green-roof mandates in the observed cities, the study cannot separate the cooling effect of vegetation from the cooling effect of air conditioning.

When a third variable systematically co-occurs with the tested cause and provides an alternative explanation for the effect, it acts as a confounding variable that invalidates the causal claim.

Key Concept

Causal Flaws and Confounding Variables

Question 1373Question →

A survey conducted at an exclusive luxury health resort found that 85 percent of guests exercise for at least six hours every week. Based on these survey results, a researcher concluded that most adults in the general population maintain a highly active lifestyle involving at least six hours of weekly exercise. Which of the following best expresses the flaw in the researcher's reasoning?

The argument draws a conclusion about the general adult population based on a sample of individuals who are unlikely to be representative of that population.

The argument assumes that exercising six hours per week is a necessary requirement for maintaining long-term physical health.

The argument fails to specify whether the surveyed resort guests spent their exercise hours indoors or outdoors.

The argument assumes that an increase in weekly exercise hours directly reduces overall medical expenditures.

The argument relies on a detailed comparison between guests at luxury resorts and members of municipal community centers.

Show answer & explanation

Answer: The argument draws a conclusion about the general adult population based on a sample of individuals who are unlikely to be representative of that population.

Answer

The argument draws a conclusion about the general adult population based on a sample of individuals who are unlikely to be representative of that population.

The correct answer identifies that guests at a luxury health resort are self-selected fitness enthusiasts who cannot be assumed to reflect the habits of the general adult population. Inferring a characteristic about a broad population from a non-representative subgroup is a classic sampling flaw.

Step-by-Step Solution

1

Identify the conclusion and the supporting evidence

Evidence: 85% of luxury resort guests exercise 6+ hours weekly. Conclusion: Most adults in the general population exercise 6+ hours weekly.

Understanding the gap between premise and conclusion is essential for identifying reasoning flaws.

2

Evaluate the relationship between the sample and the target population

Luxury resort guests choose to attend a health resort and have the resources to do so, making them far more likely to prioritize exercise than an average member of the general population.

A valid inductive generalization requires a sample that fairly represents the target group.

3

Select the choice that pinpoints the sampling bias

The statement highlighting that the sample is unlikely to represent the broader population accurately describes the flaw.

Generalizing from a skewed, non-random sample constitutes a classic sampling flaw.

Key Concept

Sampling and Generalization Flaws

Question 1374Question →

A corporate logistics firm plans to reduce carbon emissions by replacing its fleet of diesel trucks with electric vehicles. Management argues that because the local electricity grid is powered primarily by zero-emission hydroelectric dams, this fleet transition will eliminate the company's net greenhouse gas emissions from freight transportation. Evaluate whether the following claim is a necessary unstated assumption of the management's argument: The total lifecycle emissions generated during the manufacturing and disposal of the electric vehicle fleet will not exceed the operational emissions produced by the existing diesel fleet over the same period.

True

False

Show answer & explanation

Answer: True

Answer

True. The claim represents a necessary unstated assumption required for the argument's conclusion to hold.

The author concludes that replacing diesel trucks with electric vehicles will eliminate net greenhouse gas emissions from freight transportation, relying solely on the premise that the electricity used during operation comes from zero-emission hydroelectric dams. For the total net emissions to be eliminated, non-operational sources of emissions associated with the new fleet—specifically manufacturing and disposal—must not outweigh the operational emissions saved by abandoning diesel. Negating the statement establishes that manufacturing and disposal emissions would exceed diesel operational emissions, which directly contradicts the claim that net emissions will be eliminated. Therefore, the argument depends on this unstated assumption.

Step-by-Step Solution

1

Deconstruct the argument into premise and conclusion.

Premise: The electricity grid powering the new electric vehicles relies on zero-emission hydroelectric energy. Conclusion: Replacing diesel trucks with electric vehicles will eliminate net greenhouse gas emissions from freight transportation.

Isolating the core argument components allows identification of structural gaps between the premise and conclusion.

2

Apply the Negation Test to the proposed assumption.

Negated claim: The total lifecycle emissions generated during manufacturing and disposal of the electric vehicle fleet WILL exceed the operational emissions of the diesel fleet over the same period.

If the logically negated form of a statement logically destroys the conclusion, that statement is a necessary assumption.

3

Evaluate the impact of the negated statement on the author's conclusion.

If producing and disposing of electric vehicles creates more emissions than operating diesel trucks saves, net emissions from freight transportation will increase rather than reach zero.

The claim of total net emission elimination fails entirely if unmeasured non-operational stages produce a net surge in emissions.

Key Concept

Identifying Unstated Assumptions via the Negation Test

Question 1375Question →

If $a$ and $b$ are non-zero real numbers, is $|a - b| > |a + b|$ ?

(1) $|a + 2b| < |a - 2b|$
(2) $|a - 1| < |b - 1|$

Which of the following choices correctly 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 option stating that Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient is correct. Squaring both sides of the question stem inequality

|a - b| > |a + b|

yields

a^2 - 2ab + b^2 > a^2 + 2ab + b^2

, which simplifies directly to

ab < 0

. Statement (1) states

|a + 2b| < |a - 2b|

. Squaring both sides yields

a^2 + 4ab + 4b^2 < a^2 - 4ab + 4b^2

, which simplifies to

8ab < 0

, or

ab < 0

. This gives a definitive YES to the question, so Statement (1) is sufficient. Statement (2) compares the distances of

a

and

b

from 1 on the number line. Choosing

a = 0.5

and

b = -2

satisfies

|0.5 - 1| < |-2 - 1|

and gives

ab = -1 < 0

(YES), whereas choosing

a = 0.5

and

b = 3

satisfies

|0.5 - 1| < |3 - 1|

and gives

ab = 1.5 > 0

(NO). Thus, Statement (2) is insufficient.

Step-by-Step Solution

1

Rephrase the question stem target using absolute value properties.

Since both sides of

|a - b| > |a + b|

are non-negative, square both sides:

(a - b)^2 > (a + b)^2 \implies a^2 - 2ab + b^2 > a^2 + 2ab + b^2 \implies -2ab > 2ab \implies 4ab < 0 \implies ab < 0

. Thus, the question asks: 'Is

ab < 0

?' (Do

a

and

b

have opposite signs?)

Simplifying the target inequality converts an absolute value relationship into a clear sign constraint on the product

ab

.

2

Evaluate Statement (1):

|a + 2b| < |a - 2b|

.

Square both sides:

(a + 2b)^2 < (a - 2b)^2 \implies a^2 + 4ab + 4b^2 < a^2 - 4ab + 4b^2 \implies 4ab < -4ab \implies 8ab < 0 \implies ab < 0

. This provides a definitive YES to the question 'Is

ab < 0

?'

Statement (1) uniquely guarantees that

a

and

b

have opposite signs, making Statement (1) ALONE sufficient.

3

Evaluate Statement (2):

|a - 1| < |b - 1|

.

Test numbers: Case 1: If

a = 0.5

and

b = -2

, then

|0.5 - 1| = 0.5

and

|-2 - 1| = 3

. Since

0.5 < 3

, Statement (2) holds, and

ab = (0.5)(-2) = -1 < 0

(YES). Case 2: If

a = 0.5

and

b = 3

, then

|0.5 - 1| = 0.5

and

|3 - 1| = 2

. Since

0.5 < 2

, Statement (2) holds, and

ab = (0.5)(3) = 1.5 > 0

(NO).

Because Statement (2) permits both

ab < 0

and

ab > 0

, it cannot determine whether

ab < 0

. Statement (2) ALONE is insufficient.

Key Concept

Properties of Absolute Value Inequalities and Rephrased Data Sufficiency Targets

Estimated Time:2m 0s

Question 1376Question →

If $x$ is a real number, what is the value of $(x + 3)^2$ ?

(1) $x^2 + 6x = 7$
(2) $x = 1$

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.

Expanding the target expression

(x + 3)^2

gives

x^2 + 6x + 9

. Statement (1) provides

x^2 + 6x = 7

, which can be directly substituted into the expanded expression to get

7 + 9 = 16

, yielding a unique value. Statement (2) explicitly provides

x = 1

, which gives

(1 + 3)^2 = 16

. Because each statement independently provides enough information to determine a single value for the expression, the option stating that each statement alone is sufficient is correct.

Step-by-Step Solution

1

Rephrase the target expression using algebraic expansion.

(x + 3)^2 = x^2 + 6x + 9

Expanding the binomial allows direct comparison with given algebraic statements.

2

Evaluate Statement (1) using the expanded target expression.

Since

x^2 + 6x = 7

, substituting this into

x^2 + 6x + 9

gives

7 + 9 = 16

. Alternatively, solving

x^2 + 6x - 7 = 0

yields

x = 1

or

x = -7

. If

x = 1

,

(1 + 3)^2 = 16

. If

x = -7

,

(-7 + 3)^2 = (-4)^2 = 16

. Both roots yield the exact same value of

16

.

Statement (1) alone uniquely determines the target value.

3

Evaluate Statement (2) independently.

Given

x = 1

, substituting directly into the target expression gives

(1 + 3)^2 = 4^2 = 16

.

Statement (2) alone uniquely determines the target value.

4

Conclude sufficiency based on independent evaluations.

Both Statement (1) alone and Statement (2) alone are sufficient.

Since each statement independently determines a single value of 16, EACH statement ALONE is sufficient.

Key Concept

Algebraic Expression Expansion and Target Rephrasing in Data Sufficiency

Estimated Time:1m 0s

Question 1377Question →

A rare manuscript preservation protocol at a archival library dictates that every document crafted prior to the 15th century that has undergone chemical ink stabilization must be stored in a vacuum-sealed chamber. Furthermore, no document stored in a vacuum-sealed chamber is ever exposed to ambient fluorescent lighting. During a recent audit, conservators confirmed that several 14th-century codices in the library's collection have undergone chemical ink stabilization.

Statement: Based strictly on the facts provided, at least one document in the library's collection is not exposed to ambient fluorescent lighting.

True

False

Show answer & explanation

Answer: True

Answer

True. The statement logically must be true based on the transitive combination of the conditional premises.

The statement is logically valid and guaranteed 100% by the premises. Connecting the conditional statements demonstrates that the stabilized 14th-century codices meet all conditions required to be in a vacuum-sealed chamber, which in turn guarantees they are not exposed to ambient fluorescent lighting.

Step-by-Step Solution

1

Identify the temporal and conditional scope of Premise 1.

Documents crafted prior to the 15th century AND chemically stabilized

\rightarrow

Vacuum-sealed chamber.

Establishing the precise criteria for mandatory vacuum-sealed storage.

2

Identify the scope of Premise 2.

Vacuum-sealed chamber

\rightarrow

NOT exposed to ambient fluorescent lighting.

Connecting vacuum-sealed storage to lighting conditions.

3

Apply existential premises (the factual evidence confirmed by conservators).

14th-century codices are prior to the 15th century, and several have undergone chemical ink stabilization.

Confirming that existing items in the collection satisfy the antecedent of the conditional rule.

4

Synthesize the chain to deduce the necessary conclusion.

Stabilized 14th-century codices

\rightarrow

Vacuum-sealed chamber

\rightarrow

NOT exposed to ambient fluorescent lighting. Hence, at least one document in the collection is not exposed to ambient fluorescent lighting.

Combining the existential premise with the transitive conditional chain yields a valid must-be-true statement.

Key Concept

Transitive Conditional Logic & Categorical Deduction

Question 1378Question →

For all distinct non-zero real numbers $x$ and $y$ , the Data Sufficiency Yes/No target question "Is $\frac{x|y| - y|x|}{x - y} > 0$ ?" is algebraically equivalent to the simplified target question "Is $xy < 0$ ?"

True

False

Show answer & explanation

Answer: True

Answer

The statement is true. Simplifying the target question by considering the relative signs of

x

and

y

proves that the expression is strictly positive if and only if

x

and

y

have opposite signs (

xy < 0

).

Rephrasing a Data Sufficiency target question requires finding a simpler, logically equivalent condition. Testing the two distinct operational domains (

xy > 0

vs.

xy < 0

) demonstrates that the given algebraic fraction yields a positive result if and only if

x

and

y

carry opposite signs (

xy < 0

). Therefore, the proposed rephrasing is completely accurate and equivalent.

Step-by-Step Solution

1

Analyze the expression when

x

and

y

have the same sign (

xy > 0

).

If

x > 0, y > 0

, then

|x| = x

and

|y| = y

, so

x|y| - y|x| = xy - yx = 0

. If

x < 0, y < 0

, then

|x| = -x

and

|y| = -y

, so

x|y| - y|x| = x(-y) - y(-x) = -xy + xy = 0

. Thus, when

xy > 0

,

\frac{x|y| - y|x|}{x - y} = 0

, yielding a 'No' to the question 'Is the expression

> 0

?'.

Determining the behavior of absolute value expressions under identical signs simplifies the numerator to zero.

2

Analyze the expression when

x

and

y

have opposite signs (

xy < 0

).

Case A: If

x > 0

and

y < 0

, then

|x| = x

and

|y| = -y

. The numerator is

x(-y) - y(x) = -2xy > 0

. The denominator is

x - y > 0

. The quotient is

\frac{\text{positive}}{\text{positive}} > 0

.
Case B: If

x < 0

and

y > 0

, then

|x| = -x

and

|y| = y

. The numerator is

x(y) - y(-x) = 2xy < 0

. The denominator is

x - y < 0

. The quotient is

\frac{\text{negative}}{\text{negative}} > 0

.

Evaluating absolute values under opposite signs demonstrates that the numerator and denominator always have matching signs.

3

Compare the conditions for a 'Yes' answer.

The target expression is strictly positive if and only if

x

and

y

have opposite signs, which is defined by the inequality

xy < 0

.

Establishing biconditional equivalence confirms that rephrasing the target stem to 'Is

xy < 0

?' preserves all logical outcomes.

Key Concept

Data Sufficiency target rephrasing using piecewise definition of absolute value and sign analysis.

Question 1379Question →

Read the argument below and match each statement to its logical role within the argument.

Argument: A pharmaceutical company recently introduced a new drug designed to treat migraines. Although early clinical trials indicated high efficacy, several recent independent studies revealed significant side effects in long-term users. Therefore, health authorities ought to suspend approval of this medication until comprehensive safety trials are completed.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The statement regarding suspending approval matches 'Main Conclusion / Final Claim', the statement regarding side effects matches 'Premise / Supporting Evidence', and the statement regarding early clinical trial efficacy matches 'Concession / Counterargument Context'.

The claim advocating that health authorities suspend drug approval is the ultimate takeaway of the passage, directly supported by evidence of long-term side effects and signaled by 'Therefore'. The statement about side effects provides the necessary empirical reason for this action, and the statement regarding early efficacy is an acknowledged concession.

Step-by-Step Solution

1

Locate structural signal words in the argument

Identified 'Although' introducing a concession, and 'Therefore' introducing the main claim.

Transition words signal logical relationships between premises and conclusions.

2

Identify the author's central recommendation

The final sentence ('Health authorities ought to suspend approval...') is supported by the rest of the text and makes a normative policy recommendation.

The main conclusion is the ultimate claim the author is advocating for.

3

Classify remaining supporting statements

The report of side effects provides evidence for the conclusion, while the initial high efficacy finding represents opposing evidence acknowledged by the author.

Distinguishing evidence from concessions clarifies the argument's support structure.

Key Concept

Identifying Main Conclusions and Final Claims

Question 1380Question →

If $r$ and $s$ are positive integers, is the sum $r + s$ an odd integer?

(1) $r \cdot s$ is an odd integer.
(2) $r$ is an even integer.

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.

Statement (1) gives enough information to determine that

r + s

must be even, resulting in a definitive 'No' answer to the question. In Data Sufficiency, a definitive 'No' indicates sufficiency. Statement (2) does not fix the parity of

s

, so

r + s

could be either even or odd, making it insufficient.

Step-by-Step Solution

1

Analyze the question stem

We are given that

r

and

s

are positive integers and need to answer the Yes/No question: Is

r + s

odd?

Establishing the target question and constraints is essential before evaluating the statements.

2

Evaluate Statement (1):

r \cdot s

is an odd integer

The product of two integers is odd if and only if both integers are odd. Therefore,

r

is odd and

s

is odd. The sum of two odd integers is always an even integer (odd + odd = even). Thus,

r + s

is definitely not odd.

A definitive 'No' answer to a Yes/No Data Sufficiency question means the statement is SUFFICIENT.

3

Evaluate Statement (2):

r

is an even integer

If

r = 2

and

s = 1

, then

r + s = 3

(odd, answer is Yes). If

r = 2

and

s = 2

, then

r + s = 4

(even, answer is No). Because both Yes and No are possible, Statement (2) is INSUFFICIENT.

Since Statement (2) allows multiple outcomes for the target question, it does not provide sufficient information.

Key Concept

Parity rules for addition and multiplication of integers in Data Sufficiency Yes/No decision logic.

Answer

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