All practice questions

Question 1701Question →

A municipal study observed that cities with a higher number of public parks also report higher average levels of physical activity among their residents. Based on this observation, a researcher concluded that constructing public parks directly causes residents to become more physically active. Match each statement below with the logical role it plays in evaluating the researcher's causal claim.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement 1 strengthens the direct causal claim; Statement 2 demonstrates reverse causality; Statement 3 identifies a confounding common cause.

The correct matches accurately distinguish between evidence supporting direct causation, evidence illustrating reverse causation, and evidence establishing a third-variable confounder.

Step-by-Step Solution

1

Analyze the researcher's conclusion

The researcher posits a direct causal link: Park construction (Cause)

\rightarrow

Resident activity (Effect).

Identifying the proposed direction of cause and effect is essential to evaluating logical roles.

2

Evaluate the first statement

The first statement establishes a chronological sequence where the park opening precedes the increase in activity, supporting direct causality.

Evidence showing that the cause precedes the effect strengthens a causal argument.

3

Evaluate the second statement

The second statement shows that active people move to cities with parks, implying activity level (Effect) drives the residency pattern near parks (Cause).

Reversing cause and effect undermines the researcher's claim of direct causality.

4

Evaluate the third statement

The third statement introduces municipal wealth as an alternate factor influencing both park availability and exercise programs.

A third factor causing both observed variables explains the correlation without direct causality.

Key Concept

Causal Reasoning and Logical Roles in Correlation Analysis

Question 1702Question →

A commercial airline manages its long-haul fleet using two aircraft configurations: Configuration P (Passenger-focused) and Configuration C (Cargo-focused).

On a standard transcontinental route:
- Operating $4$ Configuration P flights and $3$ Configuration C flights requires a total of $98,000$ gallons of fuel.
- Operating $2$ Configuration P flights and $5$ Configuration C flights requires a total of $112,000$ gallons of fuel.

Assuming fuel consumption per flight depends solely on the aircraft configuration, select the fuel consumption (in gallons) per flight for Configuration P and for Configuration C.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Configuration P fuel consumption per flight is 11,000 gallons; Configuration C fuel consumption per flight is 18,000 gallons.

Solving the linear system

4 f_P + 3 f_C = 98,000

and

2 f_P + 5 f_C = 112,000

gives

f_P = 11,000

gallons and

f_C = 18,000

gallons.

Step-by-Step Solution

1

Formulate a system of simultaneous linear equations based on the problem statement.

Let

f_P

be fuel per Configuration P flight and

f_C

be fuel per Configuration C flight. Equation 1:

4 f_P + 3 f_C = 98,000

. Equation 2:

2 f_P + 5 f_C = 112,000

.

Translates the two total fuel conditions into explicit linear equations.

2

Eliminate variable

f_P

by multiplying Equation 2 by 2.

Multiplying Equation 2 by 2 yields

4 f_P + 10 f_C = 224,000

.

Equalizes the coefficients of

f_P

across both equations to enable cancellation.

3

Subtract Equation 1 from the modified equation to solve for

f_C

.

(4 f_P + 10 f_C) - (4 f_P + 3 f_C) = 224,000 - 98,000 \implies 7 f_C = 126,000 \implies f_C = 18,000

.

Subtracting cancels

f_P

, yielding the fuel consumption per Configuration C flight.

4

Substitute

f_C = 18,000

back into Equation 1 to find

f_P

.

4 f_P + 3(18,000) = 98,000 \implies 4 f_P + 54,000 = 98,000 \implies 4 f_P = 44,000 \implies f_P = 11,000

.

Determines the fuel consumption per Configuration P flight.

Key Concept

Solving simultaneous linear equations with two unknowns in a Two-Part Analysis format.

Question 1703Question →

Machine A produces $120$ widgets in $4$ hours at a constant rate, and Machine B produces $150$ widgets in $3$ hours at a constant rate. If both machines work simultaneously at their respective constant rates, how many total widgets will they produce in $2$ hours?

Show answer & explanation

Answer: 160

Answer

The total number of widgets produced by both machines in 2 hours is 160.

Machine A produces

30

widgets per hour (

120 \div 4

), and Machine B produces

50

widgets per hour (

150 \div 3

). Together, their combined rate is

80

widgets per hour (

30 + 50

). Working together for

2

hours, they produce a total of

160

widgets (

80 \times 2

).

Step-by-Step Solution

1

Find the hourly rate of Machine A

Machine A produces

\frac{120}{4} = 30

widgets per hour.

Dividing total output by time gives the unit work rate per hour.

2

Find the hourly rate of Machine B

Machine B produces

\frac{150}{3} = 50

widgets per hour.

Dividing total output by time gives the unit work rate per hour.

3

Calculate the combined production rate per hour

The combined rate is

30 + 50 = 80

widgets per hour.

When working simultaneously, individual rates add together.

4

Multiply combined rate by the target time

In

2

hours, total production is

80 \times 2 = 160

widgets.

Total work equals rate multiplied by time.

Key Concept

Combined Work Rates

Estimated Time:45s

Question 1704Question →

If $u$ and $v$ are real numbers, what is the value of $u + 2v$ ?

(1) $3u + 6v = 15$
(2) $u^2 - 4v^2 = 0$

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.

Dividing Statement (1) by 3 directly gives

u + 2v = 5

, providing a unique numerical answer. Statement (2) permits multiple values for

u + 2v

because

(u - 2v)(u + 2v) = 0

only guarantees that at least one factor is zero, not necessarily

u + 2v = 0

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

Step-by-Step Solution

1

Analyze Statement (1) algebraically.

The equation is

3u + 6v = 15

. Factoring out 3 gives

3(u + 2v) = 15

. Dividing both sides by 3 yields

u + 2v = 5

.

This determines a unique, definitive numerical value for the target expression

u + 2v

. Therefore, Statement (1) alone is sufficient.

2

Analyze Statement (2) independently.

The equation

u^2 - 4v^2 = 0

factors as

(u - 2v)(u + 2v) = 0

.

This statement implies that either

u + 2v = 0

or

u - 2v = 0

. If

u = 4

and

v = 2

, then

u - 2v = 0

and

u + 2v = 8

. If

u = 0

and

v = 0

, then

u + 2v = 0

. Since

u + 2v

can take multiple values, Statement (2) alone is not sufficient.

Key Concept

Algebraic Expression Simplification and Unique Determination in Data Sufficiency

Question 1705Question →

A municipal water authority plans to install automated acoustic leak detectors along its primary underground distribution pipeline network. City officials calculate that detecting subterranean micro-leaks early will save millions of gallons of treated water annually, thereby reducing overall water purification and pumping costs by significantly more than the installation and maintenance expense of the sensors. Therefore, city officials conclude that implementing this sensor network will increase the municipal water utility's net annual operating budget surplus.

Which of the following would it be most useful to establish in order to evaluate the validity of the argument?

Whether neighboring municipal water authorities plan to adopt similar automated acoustic leak-detection technologies within the next decade.

Whether residential customers in the municipality consume significantly less water per capita than industrial and commercial entities do.

Whether subterranean vibrations from surface vehicle traffic frequently trigger false alarm signals in the sensors that require manual on-site inspection by technicians.

Whether the total revenue generated from residential water tariffs increased over the preceding fiscal year.

Whether the current water purification facilities operated by the municipality are performing at full capacity during peak summer months.

Show answer & explanation

Answer: Whether subterranean vibrations from surface vehicle traffic frequently trigger false alarm signals in the sensors that require manual on-site inspection by technicians.

Answer

Determining whether ambient traffic vibrations trigger frequent false alarms that require costly manual inspections by utility technicians is the most useful factor for evaluating the argument's validity.

The correct answer provides a critical unknown operational variable. If subterranean traffic vibrations cause frequent false positives, utility technicians must be dispatched to manually verify non-existent leaks, introducing substantial unanticipated labor and inspection costs. If these secondary costs exceed the net purification and pumping savings, the net operating budget surplus will decrease rather than increase. Conversely, if false alarms rarely occur, the projected financial surplus remains intact. Because opposite answers to this question produce opposite impacts on the viability of the plan, it is the most decisive factor for evaluating the argument's validity.

Step-by-Step Solution

1

Deconstruct the argument structure into premises and conclusion

Premise: Acoustic sensors save water, cutting purification/pumping costs by an amount greater than sensor purchase/maintenance cost. Conclusion: Implementing the sensor network will increase the utility's net annual operating budget surplus.

Evaluating validity requires identifying the logical gap between the stated cost savings and the final net budget outcome.

2

Identify the unstated assumption in the financial projection

The argument assumes that sensor purchase and routine maintenance are the only significant new costs introduced by the program.

If hidden or auxiliary operational costs arise from operating the system, total costs might exceed savings.

3

Apply the Test of Variance to evaluate potential evaluation questions

Testing extreme outcomes for false alarm inspection costs: If YES (false alarms are frequent and expensive to inspect), total costs rise and net surplus drops (weakens argument). If NO (false alarms are rare/inexpensive), net surplus increases as projected (strengthens argument).

A valid evaluation criteria must produce opposite impacts on the argument's conclusion when answered at opposite extreme ends of the spectrum.

Key Concept

Evaluating Argument Validity & Test of Variance

Estimated Time:1m 40s

Question 1706Question →

An investment firm allocates a total of $\$60,000$ between two funds, Fund X and Fund Y, in the ratio of $3:2$ , respectively. Fund X yields an annual return of $10\%$ , while Fund Y yields an annual return of $15\%$ .

Which of the following correctly pairs the amount invested in Fund X with the total dollar return generated from both funds combined after one year?

\ halt{\$36,000}

invested in Fund X, and

\$7,200

total return

\$24,000

invested in Fund X, and

\$7,200

total return

\$36,000

invested in Fund X, and

\$6,000

total return

\$40,000

invested in Fund X, and

\$8,000

total return

\$36,000

invested in Fund X, and

\$9,000

total return

Show answer & explanation

Answer: $\ halt{\$36,000}$ invested in Fund X, and $\$7,200$ total return

Answer

The investment in Fund X is

\$36,000

, and the total dollar return from both funds combined is

\$7,200

.

The option stating '

\$36,000

invested in Fund X, and

\$7,200

total return' is correct because Fund X receives

3/5

of the

\$60,000

total (

\$36,000

), generating

\$3,600

at

10\%

. Fund Y receives

2/5

of the total (

\$24,000

), generating

\$3,600

at

15\%

. The combined return is

\$3,600 + \$3,600 = \$7,200

.

Step-by-Step Solution

1

Determine the dollar amount allocated to each fund using the given ratio.

Fund X allocation:

\frac{3}{3+2} \times \$60,000 = \frac{3}{5} \times \$60,000 = \$36,000

. Fund Y allocation:

\frac{2}{5} \times \$60,000 = \$24,000

.

The total ratio parts equal

3 + 2 = 5

parts.

2

Calculate the annual return for Fund X.

Fund X return:

10\% \text{ of } \$36,000 = 0.10 \times \$36,000 = \$3,600

.

Fund X yields a

10\%

return on its invested capital.

3

Calculate the annual return for Fund Y.

Fund Y return:

15\% \text{ of } \$24,000 = 0.15 \times \$24,000 = \$3,600

.

Fund Y yields a

15\%

return on its invested capital.

4

Sum the returns from both funds to find the total return.

Total combined return: \$3,600 + \$3,600 = \$7,200.

The total return is the sum of returns from Fund X and Fund Y.

Key Concept

Ratio Allocation and Weighted Percentage Rates

Question 1707Question →

A corporate health study observed a strong positive correlation between weekly consumption of energy drinks and reported workplace stress levels among software engineers. The researchers hypothesized that the high caffeine content in energy drinks directly causes increased workplace stress.

Which of the following statements, if true, provide either valid evidence supporting the researchers' causal hypothesis or a valid alternative causal explanation for the observed correlation? Select all that apply.

Select all that apply

Engineers who participated in a four-week trial eliminating energy drinks reported a statistically significant decrease in their workplace stress levels.

Engineers experiencing severe workplace stress often consume energy drinks as a coping mechanism to sustain focus during long hours.

Higher workplace stress levels cause engineers to develop metabolic changes that reduce the physiological impact of caffeine.

Energy drinks are generally more expensive than other caffeinated beverages such as coffee or tea.

Software engineers who report low stress levels tend to prefer working during morning hours rather than late nights.

Show answer & explanation

Answer: Engineers who participated in a four-week trial eliminating energy drinks reported a statistically significant decrease in their workplace stress levels.; Engineers experiencing severe workplace stress often consume energy drinks as a coping mechanism to sustain focus during long hours.

Answer

The correct selections are the statement demonstrating that eliminating energy drinks reduces stress levels, and the statement explaining that workplace stress leads engineers to consume energy drinks.

The correct options are the statement showing that removing energy drinks lowers stress levels (which directly supports the causal hypothesis) and the statement revealing that high stress leads to energy drink consumption (which presents a valid reverse-causality alternative explanation for the observed correlation).

Step-by-Step Solution

1

Identify the core causal hypothesis in the stem.

Hypothesis: Energy drink consumption (Cause) leads to increased workplace stress (Effect).

Establishing the directional claim made by researchers is necessary to evaluate supporting or alternative evidence.

2

Evaluate statements for direct empirical support.

The trial showing reduced stress after eliminating energy drinks supports the causal claim by showing that removing the cause reduces the effect.

Demonstrating cause-and-effect control in a trial strengthens a causal hypothesis.

3

Evaluate statements for alternative causal explanations.

The statement that stressed engineers consume energy drinks as a coping mechanism provides a reverse causality explanation.

Reverse causality explains the correlation while challenging the original directional claim.

Key Concept

Evaluating Causal Arguments and Alternative Explanations

Question 1708Question →

A metropolitan transportation authority implemented a peak-hour congestion pricing toll for private vehicles entering District X. Over the following 18 months, private vehicle traffic entering District X decreased by $22\%$ , while retail foot traffic in District X increased by $14\%$ . The transit board concluded that the congestion toll directly caused the increase in retail foot traffic by eliminating traffic congestion and encouraging suburban shoppers to visit downtown via public transit.

Match each logical argument role below with the statement that best exemplifies that role when evaluating the transit board's causal claim.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The statement describing retail merchant lobbying matches the reverse causal relationship role; the statement concerning the launch of a zero-fare light rail line matches the confounding variable role; and the statement regarding transit lines operating at 99% capacity matches the invalidation of a necessary assumption role.

Each argument role correctly aligns with its corresponding logical effect: the merchant lobbying statement reverses the temporal and causal sequence; the zero-fare light rail statement introduces a concurrent external factor driving both observed trends; and the 99% transit capacity statement demonstrates a physical bottleneck that breaks a required link in the board's proposed mechanism.

Step-by-Step Solution

1

Analyze the board's core causal hypothesis.

Cause = Congestion pricing toll → Effect = Reduced car traffic & increased retail foot traffic via public transit conversion.

Establishing the explicit mechanism (toll → less car congestion → suburban shoppers take transit → higher foot traffic) is necessary to evaluate logical flaws.

2

Evaluate the statement concerning merchant lobbying.

This statement indicates that higher pedestrian traffic came first and caused the political demand for the toll.

This directly reverses the direction of causality (

Y \rightarrow X

instead of

X \rightarrow Y

), matching the reverse causal relationship role.

3

Evaluate the statement concerning the zero-fare light rail extension.

The light rail extension introduces an external event occurring at the same time that independently drives both observed trends.

A third factor (

Z

) that causes both decreased vehicle traffic and increased foot traffic constitutes a classic confounding variable alternative explanation.

4

Evaluate the statement concerning transit capacity operating at 99%.

Because transit was already saturated and received no upgrades, it physically could not carry new shoppers into District X.

The board's conclusion hinges on the unstated premise that transit could accommodate modal shift; proving capacity was zero invalidates this necessary assumption.

Key Concept

Evaluating Causal Arguments in Two-Part Analysis

Question 1709Question →

If $p$ and $q$ are real numbers, what is the value of $p^2 + 4q^2$ ?

(1) $p + 2q = 8$
(2) $pq = 6$

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 (1) and (2) 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 (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Answer

BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

The target expression

p^2 + 4q^2

can be related to the binomial square

(p + 2q)^2 = p^2 + 4pq + 4q^2

. Rearranging gives

p^2 + 4q^2 = (p + 2q)^2 - 4pq

. Neither statement alone provides both

p + 2q

and

pq

. However, combining Statement (1) (

p + 2q = 8

) and Statement (2) (

pq = 6

) allows direct substitution:

p^2 + 4q^2 = 8^2 - 4(6) = 40

. Because this yields a single unique value, both statements together are sufficient.

Step-by-Step Solution

1

Evaluate Statement (1) independently

Statement (1) states

p + 2q = 8

. Squaring both sides yields

(p + 2q)^2 = p^2 + 4pq + 4q^2 = 64

, so

p^2 + 4q^2 = 64 - 4pq

. Without the value of

pq

, a unique numerical value for

p^2 + 4q^2

cannot be determined.

Statement (1) alone leaves one degree of freedom (the product

pq

is unknown).

2

Evaluate Statement (2) independently

Statement (2) states

pq = 6

. Knowing only the product of

p

and

q

allows infinitely many pairs

(p, q)

, resulting in infinitely many values for

p^2 + 4q^2

.

Statement (2) alone does not constrain the linear sum

p + 2q

.

3

Combine Statements (1) and (2)

From Statement (1),

p^2 + 4q^2 = 64 - 4pq

. Substituting

pq = 6

from Statement (2) yields

p^2 + 4q^2 = 64 - 4(6) = 40

. This provides a unique, definitive numerical answer.

Combining both statements eliminates all unknown parameters from the target expression

p^2 + 4q^2

.

Key Concept

Algebraic Identity Expansion and System Combination in Data Sufficiency

Estimated Time:1m 30s

Question 1710Question →

A corporate study evaluated the relationship between flexible remote work policies and employee turnover in technology firms. Researchers observed that firms introducing remote work experienced a 20% drop in voluntary departures, leading them to conclude that remote work directly reduces employee burnout and thereby improves retention.

Match each statement below with the logical role it plays in evaluating this causal argument.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The statement regarding employee self-selection reverses the direction of causality. The statement regarding concurrent salary increases introduces a confounding variable. The statement regarding commute stress elaborates on the causal mechanism.

Each statement directly matches its precise logical role in causal analysis: reversing cause and effect exposes selection bias; introducing concurrent pay raises presents an alternative explanation; and detailing commute reduction establishes the causal mechanism.

Step-by-Step Solution

1

Analyze the core causal argument

Cause: Remote work policy -> Intermediary Effect: Reduced burnout -> Final Effect: Reduced voluntary turnover.

Establishing the precise structure of the argument is essential to determine how new statements alter its validity.

2

Evaluate the statement on employee self-selection

Shows that low burnout precedes placement in remote work positions.

When the presumed effect (low burnout) is the condition that leads to the presumed cause (remote work), the causal direction is reversed.

3

Evaluate the statement on salary increases

Identifies an unaddressed parallel factor capable of reducing turnover.

An independent, concurrent change offers an alternative causal explanation for the outcome, serving as a confounding variable.

4

Evaluate the statement on commute strain

Provides the step-by-step physical explanation connecting remote work to burnout reduction.

Detailing the intermediate pathway strengthens a causal claim by demonstrating how the cause produces the effect.

Key Concept

Causal Arguments: Reverse Causality, Confounding Variables, and Underlying Mechanisms

Question 1711Question →

Council Member: The proposed city ordinance requiring developers to allocate 15 percent of new residential land to municipal green space will inevitably improve overall community public health. We can be certain that dedicated urban parkland enhances resident health because any residential development that incorporates designated green spaces inherently produces superior public health outcomes.

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

It supports its conclusion about public health benefits by offering a premise that merely restates that conclusion in different terms.

It mistakes an intermediate statement regarding land allocation for the argument's main conclusion.

It draws an unwarranted extrapolation about future health trends from a small, unrepresentative sample of developers.

It presumes without justification that a correlation between green space and resident exercise proves a direct causal relationship.

It treats a condition that is necessary for improving community health as though it were sufficient to guarantee that outcome.

Show answer & explanation

Answer: It supports its conclusion about public health benefits by offering a premise that merely restates that conclusion in different terms.

Answer

The argument commits the flaw of circular reasoning because its premise offers no independent evidence, simply rephrasing the main conclusion.

The correct answer accurately describes the flaw of begging the question (circular reasoning). The council member attempts to justify the claim that green space allocation will improve public health by stating as a premise that green space development inherently produces superior public health outcomes. Because the premise is merely a rephrasing of the conclusion, the argument offers no independent evidence.

Step-by-Step Solution

1

Identify the main conclusion of the argument.

Main Conclusion: The proposed ordinance requiring 15% green space will improve community public health.

Understanding the ultimate claim being made is necessary before evaluating its support.

2

Identify the evidence (premise) offered in support of the main conclusion.

Premise: Dedicated urban parkland enhances resident health because residential green spaces inherently produce superior public health outcomes.

Evaluating the support mechanism reveals how the speaker attempts to prove the claim.

3

Analyze the relationship between the premise and the conclusion.

The premise does not provide external evidence, data, or logical explanation; it assumes that green spaces inherently improve health, which is the exact claim requiring proof.

This logical structure is the classic definition of begging the question or circular reasoning.

Key Concept

Circular Reasoning and Begging the Question

Estimated Time:1m 45s

Question 1712Question →

Tab 1: Security Strategy Proposal
CyberTech Corp proposes replacing traditional password authentication with biometric facial recognition across all corporate departments. The proposal claims that this transition will reduce total IT security incident resolution costs by $40\%$ , arguing that biometric credentials eliminate costs associated with phished, forgotten, or shared passwords.

Tab 2: Helpdesk Cost Breakdown
A breakdown of the company's IT security incident resolution costs over the past fiscal year shows:
- Biometric enrollment lockouts and sensor failures: $65\%$
- Password resets and forgotten credential tickets: $15\%$
- Phishing-related account compromise investigations: $10\%$
- Other security incidents: $10\%$

Statement: The cost breakdown in Tab 2 weakens the claim in Tab 1 that transitioning to biometric authentication will reduce total IT security incident resolution costs by $40\%$ .

True

False

Show answer & explanation

Answer: True

Answer

The statement is True.

The statement is correct because Tab 2 demonstrates that password-related security incidents account for only

25\%

of total resolution costs (

15\% + 10\% = 25\%

). Therefore, eliminating password issues cannot logically produce the

40\%

cost reduction claimed in Tab 1, thereby weakening the argument.

Step-by-Step Solution

1

Identify the central claim and premise in Tab 1

Tab 1 claims a

40\%

reduction in total IT security incident resolution costs by eliminating password-related credential issues.

Understanding what evidence would support or weaken the claim requires defining the exact scope and source of the projected savings.

2

Calculate total password-related costs using Tab 2

Password resets (

15\%

) + Phishing investigations (

10\%

) =

25\%

of total incident resolution costs.

Cross-tab quantitative analysis determines the maximum possible impact of eliminating password issues.

3

Compare empirical data to the projected claim

Because password-related costs total only

25\%

, eliminating them entirely cannot achieve the claimed

40\%

reduction in total costs, which weakens the argument in Tab 1.

Demonstrating that the mathematical ceiling of savings is strictly less than the projected savings directly undermines the claim's validity.

Key Concept

Evaluating Argument Weakening Using Cross-Tab Quantitative Evidence

Question 1713Question →

Read the argument below regarding subglacial Antarctic lake exploration, then match each statement from the text to its corresponding logical role within the argument.

Argument:
Recent drillings into subglacial Antarctic lakes revealed microbial communities surviving in complete darkness. Astrobiologists frequently argue that discovering such extremophiles proves life could easily thrive in the subsurface oceans of icy moons like Europa. However, terrestrial subglacial lakes benefit from geothermal heat sources and chemical influxes from surrounding bedrock that are likely absent on icy celestial bodies. Thus, terrestrial extremophile survival cannot be treated as an exact model for extraterrestrial habitability. Consequently, researchers must establish direct spectroscopic criteria for extraterrestrial life rather than relying on terrestrial analogs.

Which statement matches which logical role?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The statement detailing geothermal heat and chemical influxes functions as a factual premise countering the opposing view. The assertion that extremophiles prove life on Europa represents the opposing position. The claim that terrestrial survival cannot be an exact model is an intermediate sub-conclusion. The final recommendation that researchers must establish direct spectroscopic criteria is the main conclusion of the argument.

The argument builds toward a final actionable recommendation introduced by 'Consequently': researchers must establish direct spectroscopic criteria. The factual statement about geothermal heat serves as a premise leading to the intermediate conclusion ('Thus, terrestrial extremophile survival cannot be treated as an exact model'), which directly supports the ultimate recommendation.

Step-by-Step Solution

1

Identify the structural pivot and main recommendation in the passage.

The indicator 'Consequently' signals the author's ultimate claim: researchers must establish direct spectroscopic criteria for extraterrestrial life rather than relying on terrestrial analogs.

The main conclusion is the final claim supported by all preceding evidence and sub-conclusions in the argument.

2

Analyze the role of intermediate inferences and opposing claims.

'Thus' signals an intermediate sub-conclusion ('terrestrial extremophile survival cannot be treated as an exact model'), which bridges the premise about heat sources and bedrock influxes to the final recommendation.

Distinguishing between intermediate conclusions and final claims prevents confusing subsidiary steps with the author's ultimate point.

3

Map each statement to its structural role.

Pair the opposing claim, supporting premise, intermediate conclusion, and main conclusion to their respective statements.

Ensures complete alignment across all components of the logical argument structure.

Key Concept

Identifying Main Conclusions and Intermediate Arguments in Critical Reasoning

Question 1714Question →

In 2022, organic crop protection treatments accounted for exactly 25 percent of all crop protection treatments applied in Region Z. By 2025, organic treatments accounted for 40 percent of all crop protection treatments in the region. During the same 2022–2025 period, the total number of non-organic crop protection treatments applied in Region Z decreased by 20 percent. If the statements above are true, which of the following must also be true regarding crop protection treatments in Region Z?

The total number of crop protection treatments applied in Region Z was the same in 2025 as it was in 2022.

The total volume of synthetic chemicals used in non-organic treatments decreased by more than 20 percent between 2022 and 2025.

The total number of organic crop protection treatments applied in Region Z was lower in 2025 than in 2022.

Farmer satisfaction with organic crop protection treatments increased significantly in Region Z between 2022 and 2025.

The percentage increase in organic treatments from 2022 to 2025 was equal to the percentage decrease in non-organic treatments.

Show answer & explanation

Answer: The total number of crop protection treatments applied in Region Z was the same in 2025 as it was in 2022.

Answer

The total number of crop protection treatments applied in Region Z was the same in 2025 as it was in 2022.

The option stating that total crop protection treatments remained the same in 2025 as in 2022 is logically inescapable. In 2022, non-organic treatments accounted for

75\%

of total applications. A

20\%

decrease in non-organic treatments leaves

0.75 \times 0.80 = 60\%

of the original 2022 total volume. Since non-organic treatments represent

60\%

of the 2025 total volume (as organic is

40\%

),

60\%

of the 2025 total equals

60\%

of the 2022 total. Thus, the total overall volume did not change.

Step-by-Step Solution

1

Define total treatments in 2022 as

T_{2022}

and express 2022 non-organic treatments.

Non-organic treatments in 2022 equaled

75\%

of

T_{2022}

, or

0.75 \cdot T_{2022}

.

Since organic treatments were

25\%

, non-organic treatments comprised the remaining

75\%

.

2

Calculate the absolute number of non-organic treatments in 2025.

Non-organic treatments in 2025 equaled

0.75 \cdot T_{2022} \cdot (1 - 0.20) = 0.60 \cdot T_{2022}

.

The stimulus states that non-organic treatments decreased by

20\%

from 2022 to 2025.

3

Relate the 2025 non-organic treatment count to the total 2025 treatments (

T_{2025}

).

In 2025, non-organic treatments were

60\%

of

T_{2025}

, so

0.60 \cdot T_{2025} = 0.60 \cdot T_{2022}

, which simplifies to

T_{2025} = T_{2022}

.

Because organic treatments were

40\%

of

T_{2025}

, non-organic treatments accounted for

60\%

of

T_{2025}

.

Key Concept

Calculating absolute values from relative percentages and percentage changes

Estimated Time:2m 0s

Question 1715Question →

The table below presents subscriber numbers and annual operating revenue data for five regional divisions of a telecommunications provider in fiscal year 2025.

Region	Total Broadband Subscribers (thousands)	Fiber-Optic Subscribers (thousands)	Total Operating Revenue ($ millions)
North	250	150	45.0
South	400	200	64.0
East	180	90	27.0
West	320	224	57.6
Central	500	350	80.0

Across the two regional divisions with the highest total operating revenue combined, fiber-optic subscribers represent what percentage of total broadband subscribers? Express your answer to the nearest tenth of a percent.

Show answer & explanation

Answer: 61.1

Answer

61.1%

To find the proportion of fiber-optic subscribers across the top two revenue-generating divisions, first rank the divisions by Total Operating Revenue: Central (

80.0M) and South (

64.0M) are the highest. Combine their subscriber counts to find the appropriate base: Central has 500 thousand total broadband subscribers and South has 400 thousand, giving a total base of

500 + 400 = 900

thousand. Next, combine their fiber-optic subscribers: Central has 350 thousand and South has 200 thousand, giving

350 + 200 = 550

thousand fiber-optic subscribers. The combined percentage is

\frac{550}{900} \times 100\% \approx 61.111\%

, which rounds to

61.1\%

.

Step-by-Step Solution

1

Identify the top two divisions by operating revenue

Central (

80.0M) and South (

64.0M)

The question specifically restricts the calculation to the two divisions with the highest operating revenue.

2

Sum total broadband subscribers for Central and South

500 + 400 = 900 thousand subscribers

This establishes the correct aggregate base value for the percentage calculation.

3

Sum fiber-optic subscribers for Central and South

350 + 200 = 550 thousand subscribers

This gives the total combined numerator value for the fiber-optic subgroup.

4

Calculate percentage and round to the nearest tenth

(550 / 900) * 100% = 61.111...% -> 61.1%

Dividing the target subgroup total by the base total yields the requested proportion.

Key Concept

Ratio, Proportion, and Percent Calculations across Filtered Aggregate Groups

Estimated Time:1m 30s

Question 1716Question →

If $x$ and $y$ are real numbers, what is the value of $x - y$ ?

(1) $(x - y)^2 = 16$
(2) $x^2 - y^2 = 24$

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

Answer

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

The option stating that statements (1) and (2) together are not sufficient is correct because combining both equations results in two valid candidate solution sets for

(x, y)

, specifically

(5, 1)

and

(-5, -1)

. These produce two different values for the target expression

x - y

(

4

and

-4

), preventing a single unique determination.

Step-by-Step Solution

1

Evaluate Statement (1) independently.

(x - y)^2 = 16 \implies x - y = 4

or

x - y = -4

.

Taking the square root of both sides yields two possible values for

x - y

, so Statement (1) alone is not sufficient.

2

Evaluate Statement (2) independently.

x^2 - y^2 = (x - y)(x + y) = 24

.

Without knowing

x + y

, the expression

x - y

can take infinitely many numerical values, so Statement (2) alone is not sufficient.

3

Evaluate Statements (1) and (2) together.

Case 1: If

x - y = 4

, then

4(x + y) = 24 \implies x + y = 6

, giving

(x, y) = (5, 1)

where

x - y = 4

. Case 2: If

x - y = -4

, then

-4(x + y) = 24 \implies x + y = -6

, giving

(x, y) = (-5, -1)

where

x - y = -4

.

Both coordinate pairs

(5, 1)

and

(-5, -1)

satisfy both given statements, but yield two distinct values (

4

and

-4

) for

x - y

. Therefore, both statements combined remain insufficient.

Key Concept

Degree Ambiguity in Systems of Non-Linear Algebraic Equations

Question 1717Question →

A cloud infrastructure provider operates two categories of servers: High-Memory servers and High-CPU servers. Last month, High-Memory servers accounted for $40\%$ of the total server-hours logged by the provider, and High-CPU servers accounted for the remaining $60\%$ . What was the average operational cost per server-hour across all servers operated by the provider last month?

(1) The operational cost per server-hour for a High-Memory server was $\$3.00$ greater than the operational cost per server-hour for a High-CPU server.

(2) The total operational cost for a combination of $200$ server-hours of High-Memory servers and $300$ server-hours of High-CPU servers was $\$1,400$ .

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 response is that statement (2) alone is sufficient while statement (1) alone is not. Rephrasing the question stem shows that the overall average cost per hour is

0.40m + 0.60c

, where

m

and

c

represent the hourly rates of High-Memory and High-CPU servers, respectively. Statement (1) gives only the difference

m - c = 3

, which leaves the overall average dependent on an unknown base rate. Statement (2) provides the equation

200m + 300c = 1,400

. Dividing this equation by

500

yields

0.40m + 0.60c = 2.80

, directly matching the target expression without requiring individual values for

m

or

c

.

Step-by-Step Solution

1

Rephrase the question stem algebraically.

Let

m

be the hourly cost of High-Memory servers and

c

be the hourly cost of High-CPU servers. The target average cost per server-hour is

A = 0.40m + 0.60c

.

Rephrasing identifies the exact linear combination of variables required to solve the question.

2

Evaluate Statement (1) independently.

Statement (1) states

m = c + 3

. Substituting into the target gives

A = 0.40(c + 3) + 0.60c = c + 1.20

.

Since the value of

c

remains unknown, a single numerical value for

A

cannot be determined. Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) independently.

Statement (2) gives

200m + 300c = 1,400

. Dividing the entire equation by

500

yields

\frac{200}{500}m + \frac{300}{500}c = \frac{1,400}{500}

, which simplifies to

0.40m + 0.60c = 2.80

.

The coefficients of the given equation match the target proportion (

40\%

and

60\%

), directly providing the exact value

A = \$2.80

. Statement (2) alone IS sufficient.

Key Concept

Weighted Averages and Expression Rephrasing in Data Sufficiency

Estimated Time:2m 0s

Question 1718Question →

A municipal environmental agency conducted a study across 50 comparable mid-sized cities over a four-year period. The study observed that cities that introduced a mandatory pay-as-you-throw (PAYT) unit-pricing system—charging households per bag of municipal solid waste disposed—experienced a 35 percent decrease in landfilled waste and a 20 percent increase in curbside recycling rates. The environmental director concluded that the financial burden of the PAYT fees directly caused households to adopt waste-minimization habits and actively divert recyclable materials from the waste stream.

Which two of the following statements, if true, most strongly support the environmental director's causal conclusion?

Select all that apply

In the cities implementing PAYT, the reduction in landfilled waste began immediately following the introduction of per-bag fees rather than during prior years when public awareness campaigns were active.

Similar mid-sized cities in the same geographic region that did not implement a PAYT system experienced no significant change in landfilled waste volumes or recycling rates over the four-year study period.

Cities with residents who already exhibited above-average baseline recycling rates and high environmental consciousness were significantly more likely to adopt the PAYT pricing system.

Concurrently with the introduction of PAYT, the participating cities enacted strict municipal bans on single-use commercial plastic packaging.

Municipalities that increased municipal trash collection frequency saw a temporary 10 percent rise in total waste volume handled by private waste management contractors.

Show answer & explanation

Answer: In the cities implementing PAYT, the reduction in landfilled waste began immediately following the introduction of per-bag fees rather than during prior years when public awareness campaigns were active.; Similar mid-sized cities in the same geographic region that did not implement a PAYT system experienced no significant change in landfilled waste volumes or recycling rates over the four-year study period.

Answer

The two statements that most strongly support the causal conclusion are: (1) the statement indicating that waste reduction began immediately after per-bag fees were introduced rather than during prior awareness campaigns, and (2) the statement showing that control cities without PAYT experienced no significant changes in waste or recycling levels.

To strengthen a causal claim of the form 'X caused Y', an argument must demonstrate that Y occurred specifically following X (temporal precedence) and that Y does not occur in the absence of X (control comparison), while eliminating alternative explanations. The statement noting that waste reduction began immediately after per-bag fees were introduced establishes clear temporal precedence, ruling out earlier public awareness campaigns as the cause. The statement confirming that control cities without PAYT saw no changes in waste or recycling rules out broader regional macro-trends.

Step-by-Step Solution

1

Identify the director's core causal claim

The core claim is that mandatory per-bag PAYT fees directly caused households to decrease landfilled waste and increase recycling.

Evaluating causal arguments requires isolating the proposed cause (unit-pricing fees) and effect (waste reduction/recycling increase).

2

Evaluate potential strengtheners for temporal precedence and control group validity

The statement showing that waste reduction immediately followed fee implementation demonstrates temporal precedence over alternative factors like public awareness campaigns. The statement establishing that non-PAYT cities saw no changes provides a control group ruling out regional trends.

Showing that the effect occurs specifically when and where the cause is present (and not when/where it is absent) reinforces the causal link.

3

Identify and eliminate weakeners and irrelevant statements

The option describing pre-existing high recycling rates suggests selection bias (reverse/alternative causation). The option mentioning single-use plastic bans introduces a confounding variable. The option regarding collection frequency is irrelevant.

Alternative explanations and confounding variables undermine the claim that PAYT fees were the primary driver of the observed outcome.

Key Concept

Causal Argument Evaluation: Establishing Control Groups and Temporal Precedence

Question 1719Question →

A marine biology study observed that coral reefs with higher populations of herbivorous parrotfish experienced significantly lower levels of algae overgrowth over a five-year monitoring period. Based on these results, the lead researchers concluded that the presence of parrotfish prevents algae overgrowth on coral reefs.

Which of the following correctly pairs the proposed independent cause and the dependent effect in the researchers' conclusion?

Cause: Presence of herbivorous parrotfish | Effect: Lower levels of algae overgrowth

Cause: Lower levels of algae overgrowth | Effect: Presence of herbivorous parrotfish

Cause: Five-year monitoring period | Effect: Presence of herbivorous parrotfish

Cause: Overall coral reef growth | Effect: Increased algae overgrowth

Cause: Lower levels of algae overgrowth | Effect: Five-year monitoring period

Show answer & explanation

Answer: Cause: Presence of herbivorous parrotfish | Effect: Lower levels of algae overgrowth

Answer

Cause: Presence of herbivorous parrotfish | Effect: Lower levels of algae overgrowth

The conclusion asserts that the presence of parrotfish prevents algae overgrowth. Therefore, the presence of parrotfish is the independent cause, and the lower level of algae overgrowth is the dependent effect.

Step-by-Step Solution

1

Analyze the causal claim in the conclusion.

The claim states that 'the presence of parrotfish prevents algae overgrowth on coral reefs.'

Identifying the explicit conclusion isolates the variables being evaluated.

2

Determine which variable acts as the independent cause.

The presence of herbivorous parrotfish is the action/agent producing the change.

In causal reasoning, the cause is the independent variable introduced or observed first that influences the outcome.

3

Determine which variable acts as the dependent effect.

Lower levels of algae overgrowth is the outcome resulting from the action.

The effect is the measured response or dependent variable produced by the cause.

Key Concept

Distinguishing Cause and Effect in Causal Arguments

Estimated Time:45s

Question 1720Question →

### Tab 1: Urban Low-Emission Zone (LEZ) Permit Policy
Commercial delivery vehicles entering the municipal Low-Emission Zone (LEZ) are subject to entry regulations and fees based on engine emission class and Gross Vehicle Weight Rating (GVWR):
- Class 1 (Zero-Emission / Electric): Permitted $24/7$ . Exempt from all daily entry fees.
- Class 2 (Euro VI Hybrid / CNG): Permitted entry between $06:00$ and $20:00$ . Standard daily entry fee is $\$25$ .
- Class 3 (Standard Diesel / Gasoline): Permitted entry between $06:00$ and $20:00$ . Standard daily entry fee is $\$75$ .
- Overnight Operational Surcharge: Class $2$ vehicles operating outside standard hours ( $20:01$ to $05:59$ ) incur a $50\%$ surcharge added to their standard daily fee, provided they possess a Special Exemption Clearance. Operating overnight without clearance results in an unauthorized entry fine of $\$200$ instead of the daily fee and surcharge.

### Tab 2: Fleet Discount & Compliance Rules
- Fleet Volume Discount: Logistics providers registering a fleet of $\ge 10$ Class $2$ or Class $3$ vehicles receive a $20\%$ volume discount on all cumulative daily entry fees. Surcharges, fines, and penalties are excluded from this discount.
- Special Exemption Clearance: Automatically granted to any Class $2$ vehicle transporting temperature-controlled medical supplies.
- Overload Non-Compliance Penalty: If a vehicle's measured gross mass upon entry exceeds its registered GVWR by more than $10\%$ , the $20\%$ volume discount is revoked for that specific vehicle's daily entry fee, and a flat $\$150$ overload penalty is assessed.

### Tab 3: Apex Delivery Services Activity Log (July 15, 2026)
Apex Delivery Services operates a registered fleet of $12$ Class $2$ vehicles. All Apex fleet vehicles exclusively transport temperature-controlled medical supplies.

Vehicle ID	Registered GVWR	Measured Mass (July 15)	Entry Time	Cargo Type
V-101	$4,000\text{ kg}$	$4,300\text{ kg}$	$22:30$	Temp-Controlled Medical
V-102	$5,000\text{ kg}$	$5,600\text{ kg}$	$14:00$	Temp-Controlled Medical
V-103	$3,500\text{ kg}$	$3,700\text{ kg}$	$08:15$	Temp-Controlled Medical

Statement to Evaluate:
Based on the information provided in the three tabs, on July 15, 2026, the total net fees (including daily entry fees, surcharges, and overload penalties) assessed to Apex Delivery Services for Vehicle V-101 and Vehicle V-102 combined equal exactly $\$222.50$ .

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. The combined total net fees assessed for Vehicle V-101 and Vehicle V-102 on July 15, 2026, equal

\$207.50

, not

\$222.50

.

Evaluating the statement requires integrating data across all three tabs. Vehicle V-101 incurs a discounted base fee of

\$20.00

plus an undiscounted

50\%

overnight surcharge of

\$12.50

(enabled by its medical clearance), totaling

\$32.50

. Vehicle V-102 exceeds its weight rating by

12\%

, which revokes its base fee discount (full

\$25.00

) and adds a

\$150.00

overload penalty, totaling

\$175.00

. Combining

\$32.50

and

\$175.00

yields

\$207.50

. Because the statement asserts the total is

\$222.50

, the statement is False.

Step-by-Step Solution

1

Determine fleet discount qualification and medical exemption status.

Apex operates

12

Class

2

vehicles (

\ge 10

), qualifying for the

20\%

Fleet Volume Discount. Because all vehicles carry temperature-controlled medical supplies, every vehicle holds Special Exemption Clearance.

Tab 2 states that fleets of

\ge 10

Class

2

vehicles receive a

20\%

volume discount on base daily entry fees and medical supply vehicles automatically receive Special Exemption Clearance.

2

Calculate net fees for Vehicle V-101.

V-101 Net Fee =

\$32.50

.

V-101's mass excess is

\frac{4,300 - 4,000}{4,000} = \frac{300}{4,000} = 7.5\%

. Since

7.5\% \le 10\%

, no overload penalty applies and the fleet discount remains valid. Base entry fee after

20\%

discount =

\$25 \times (1 - 0.20) = \$20.00

. V-101 entered at

22:30

(overnight); with Special Exemption Clearance, it incurs a

50\%

surcharge on the standard fee (

\$25 \times 0.50 = \$12.50

). Note that Tab 2 excludes surcharges from volume discounts. Total for V-101 =

\$20.00 + \$12.50 = \$32.50

.

3

Calculate net fees for Vehicle V-102.

V-102 Net Fee =

\$175.00

.

V-102's mass excess is

\frac{5,600 - 5,000}{5,000} = \frac{600}{5,000} = 12\%

. Since

12\% > 10\%

, V-102 violates the weight policy. Per Tab 2, its

20\%

fee discount is revoked (base entry fee = full

\$25.00

), and a flat

\$150.00

overload penalty is added. Entry time is

14:00

(daytime), so no surcharge applies. Total for V-102 =

\$25.00 + \$150.00 = \$175.00

.

4

Sum the net fees for V-101 and V-102 and evaluate the statement.

Combined total =

\$32.50 + \$175.00 = \$207.50

.

The statement claims the combined fee equals

\$222.50

, which is incorrect. Therefore, the statement is False.

Key Concept

Multi-Tab Quantitative Reconciliation with Conditional Exception Policies

Estimated Time:2m 30s

Answer

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