Two-Part Analysis Practice Questions — GMAT

Question 1Question →

A financial research study across 60 regional credit unions examined the implementation of machine-learning credit risk algorithms and subsequent small-business loan default rates. The study observed that credit unions implementing machine-learning algorithms experienced a 40 percent lower default rate on small-business loans over a three-year period than credit unions relying strictly on traditional manual underwriting. Skeptical financial analysts contend that the algorithm itself did not cause the lower default rate. Instead, they argue that credit unions adopting the algorithm had systematically raised their minimum credit score requirements for all loan applicants immediately prior to software installation, thereby selecting an inherently lower-risk applicant pool.

Based on the information provided, select the statement that most strengthens the financial analysts' alternative explanation, and select the statement that most weakens the financial analysts' alternative explanation (thereby supporting a direct causal relationship between algorithm adoption and reduced defaults).

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Answer

The statement strengthening the analysts' argument is that credit unions raising credit score requirements without the algorithm achieved equal default reductions. The statement weakening the analysts' argument is that default reductions occurred even among borrowers with credit scores below the new threshold.

To strengthen the analysts' claim that credit score threshold increases (and not algorithm installation) caused the reduction in defaults, we look for evidence showing that raising thresholds alone produces the same result. The statement noting that unions raising score thresholds without algorithms achieved equal default reductions directly confirms this alternative cause. To weaken the analysts' claim, we look for evidence where default reductions occurred independently of the higher credit score threshold. The statement showing default reductions among waiver-program borrowers below the threshold proves the algorithm worked even when the proposed confounding factor was absent.

Step-by-Step Solution

1

Analyze the causal claim and the counter-argument

Study Claim: Algorithm adoption causes lower default rates. Analysts' Claim: Tightened minimum credit score requirements (confounding variable), not the algorithm, caused lower default rates.

To strengthen or weaken an alternative causal explanation, we must isolate the proposed confounding variable (credit score threshold) from the primary variable (algorithm adoption).

2

Evaluate candidate statements to strengthen the analysts' argument

The statement regarding credit unions that raised credit score requirements without installing the algorithm shows that credit score tightening alone yields an identical default reduction. This proves the confounder is sufficient to explain the outcome without the algorithm.

A control group demonstrating that the outcome occurs to the same degree without the treatment directly strengthens the alternative explanation.

3

Evaluate candidate statements to weaken the analysts' argument

The statement showing default reductions among borrowers below the new credit score threshold demonstrates that the algorithm reduced defaults in a population where the credit score change was absent.

Demonstrating the effect in a subgroup unaffected by the proposed confounding variable directly undermines the claim that the confounder is responsible for the overall effect.

Key Concept

Evaluating Confounding Variables and Alternative Causal Explanations

Estimated Time:2m 30s

Question 2Question →

An investor allocates a sum of money between two financial products, Account A and Account B. Account A yields an annual simple interest rate of $6\%$ , while Account B yields an annual simple interest rate of $10\%$ . After one year, the total interest earned from both accounts combined is $\$2,600$ . If the amount invested in Account B is exactly twice the amount invested in Account A, select the value that corresponds to the amount invested in Account A and the value that corresponds to the amount invested in Account B.

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Answer

The amount invested in Account A is

\$10,000

and the amount invested in Account B is

\$20,000

.

Solving the simultaneous system

0.06x + 0.10y = 2,600

and

y = 2x

yields

0.26x = 2,600

, resulting in

x = \$10,000

for Account A and

y = \$20,000

for Account B.

Step-by-Step Solution

1

Define variables and formulate the system of equations based on interest earned and relative investment ratio.

Let

x

be the amount in Account A and

y

be the amount in Account B. The problem statements give: (1)

0.06x + 0.10y = 2,600

and (2)

y = 2x

.

Translating word constraints into algebraic representations sets up a two-variable system.

2

Substitute equation (2) into equation (1) to solve for

x

.

0.06x + 0.10(2x) = 2,600 \implies 0.06x + 0.20x = 2,600 \implies 0.26x = 2,600 \implies x = 10,000

.

Substitution simplifies the simultaneous system into a single linear equation in terms of

x

.

3

Calculate

y

using the relationship

y = 2x

.

y = 2(10,000) = 20,000

.

Multiplying the value of

x

by 2 gives the value for Account B.

Key Concept

Simultaneous Linear Equations by Substitution

Question 3Question →

A logistics company packages cargo into two types of containers: Standard containers and Heavy-duty containers.

A shipment of $3$ Standard containers and $2$ Heavy-duty containers has a total mass of $1,400$ kilograms. A second shipment of $2$ Standard containers and $4$ Heavy-duty containers has a total mass of $2,000$ kilograms.

Based on this information, select the value in kilograms for the mass of a single Standard container and for the mass of a single Heavy-duty container so that the selections are consistent with the given information.

Click a left item, then click its matching right item

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Answer

The mass of a single Standard container is 200 kg, and the mass of a single Heavy-duty container is 400 kg.

Setting up the simultaneous linear equations

3s + 2h = 1400

and

2s + 4h = 2000

yields

s = 200

and

h = 400

. Thus, selecting 200 for the Standard container column and 400 for the Heavy-duty container column correctly matches the calculated values.

Step-by-Step Solution

1

Define variables and set up the system of equations from the problem stem.

Let

s

be the mass of a Standard container in kg and

h

be the mass of a Heavy-duty container in kg. The given shipments yield:
Equation 1:

3s + 2h = 1400

Equation 2:

2s + 4h = 2000

Translate word problem conditions into algebraic equations.

2

Simplify Equation 2 by dividing all terms by 2.

s + 2h = 1000 \implies s = 1000 - 2h

Isolate variable

s

to use the substitution method.

3

Substitute

s = 1000 - 2h

into Equation 1 and solve for

h

.

3(1000 - 2h) + 2h = 1400 \implies 3000 - 6h + 2h = 1400 \implies 3000 - 4h = 1400 \implies 4h = 1600 \implies h = 400

Determine the value for the mass of a Heavy-duty container.

4

Substitute

h = 400

back into

s = 1000 - 2h

to solve for

s

.

s = 1000 - 2(400) = 1000 - 800 = 200

Determine the value for the mass of a Standard container.

Key Concept

Solving two-variable linear systems using substitution or elimination in a Two-Part Analysis format

Question 4Question →

An agricultural research team conducted a five-year study across 30 coffee-growing districts to investigate the relationship between shade-tree canopy coverage and outbreaks of coffee leaf rust, a devastating fungal disease. The researchers observed that farms maintaining a dense shade canopy (>50% coverage) experienced a 60% lower incidence of fungal rust compared to full-sun farms (<10% coverage). Based on these observational findings, the head researcher hypothesized that the dense canopy directly creates a microclimate that inhibits the germination of fungal rust spores. From the options provided, select the statement that most strongly strengthens the head researcher's causal hypothesis for Column 1, and select the statement that most strongly weakens the causal hypothesis by providing an alternative explanation for Column 2.

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Answer

For Column 1 (Strengthens), the correct choice is the statement confirming controlled laboratory evidence that shade microclimates directly prevent fungal spore germination. For Column 2 (Weakens), the correct choice is the statement revealing that shade-canopy farmers applied double the frequency of fungicides, providing a confounding alternative cause for the reduced infection rate.

The causal hypothesis asserts that dense shade canopy microclimates directly inhibit fungal rust spore germination. The statement providing controlled laboratory evidence that shade microclimates prevent germination directly verifies the proposed physiological mechanism, strongly strengthening Column 1. Conversely, the statement revealing that shade-canopy farmers applied twice as much fungicide provides a plausible alternative explanation for the lower rust rates, effectively weakening the causal claim for Column 2.

Step-by-Step Solution

1

Analyze the core argument and hypothesis in the stem.

Premise: High canopy farms have 60% lower rust incidence than full-sun farms. Hypothesis: Dense canopy shade directly creates a microclimate that inhibits fungal spore germination.

Understanding the precise causal link (shade microclimate -> reduced spore germination) is essential to evaluate strengthening and weakening statements.

2

Evaluate candidate statements for Column 1 (Strengthens).

The statement regarding controlled laboratory trials proves that the light and temperature conditions under shade directly stop spore germination, ruling out coincidental correlation and confirming the causal mechanism.

Direct experimental confirmation of the proposed mechanism strengthens a causal hypothesis.

3

Evaluate candidate statements for Column 2 (Weakens via alternative explanation).

The statement noting that shade-canopy farmers used twice as much fungicide introduces a confounding variable (fungicide treatment), which explains the lower rust levels without requiring shade microclimate to be the cause.

An alternative cause that accounts for the observed effect severely weakens the claim that shade microclimate was the driving factor.

Key Concept

Logical Arguments and Causal Relationships

Estimated Time:2m 0s

Question 5Question →

A fintech company implemented an automated peer-to-peer appreciation platform allowing employees to award micro-bonuses and commendations to colleagues in other departments. Over the following six months, cross-departmental dispute escalations submitted to executive management decreased by 35%. The HR analytics committee concluded that the appreciation platform directly caused the reduction in escalations by fostering cross-team goodwill.

Which of the following findings, if true, represent valid logical evaluations of the HR analytics committee's causal conclusion? Select TWO options: one statement that strongly STRENGTHENS the causal claim and one statement that provides a valid ALTERNATIVE CAUSAL EXPLANATION that weakens the claim.

Select all that apply

Departments with the highest platform adoption rates experienced the largest percentage decreases in dispute escalations, whereas departments with negligible platform activity saw no change in escalation rates.

Simultaneously with the platform's launch, executive management instituted a strict policy that penalized department heads whose teams failed to resolve disputes internally before escalating them.

Employees who received fewer escalations from other departments subsequently awarded significantly higher numbers of micro-bonuses back to those teams.

The monetary value of all micro-bonuses distributed across the entire six-month period accounted for less than 0.5% of the company's total payroll expenditure.

Over the same six-month trial period, overall employee job satisfaction scores across the financial services sector increased by an average of 2%.

Show answer & explanation

Answer: Departments with the highest platform adoption rates experienced the largest percentage decreases in dispute escalations, whereas departments with negligible platform activity saw no change in escalation rates.; Simultaneously with the platform's launch, executive management instituted a strict policy that penalized department heads whose teams failed to resolve disputes internally before escalating them.

Answer

The two correct findings are: (1) the statement establishing that departments with higher adoption rates experienced larger decreases in escalations while inactive departments saw no change (Strengthener), and (2) the statement noting that executive management simultaneously instituted penalties for escalating disputes internally (Alternative Explanation / Weakener).

The causal argument claims that the peer appreciation platform caused a 35% drop in escalated disputes. The finding regarding adoption rates by department strengthens the argument by demonstrating a clear dose-response relationship between platform use and dispute reduction. The finding regarding executive penalties for escalated disputes weakend the argument by introducing a simultaneous, independent policy change that plausibly accounts for the decrease in escalations without requiring the platform's intervention.

Step-by-Step Solution

1

Identify the core causal argument in the prompt stem.

Premise: Peer recognition platform launched; dispute escalations dropped 35% six months later.
Conclusion: The platform directly caused the drop in escalations by fostering cross-team goodwill.

Evaluating a causal claim requires separating the observed event (correlation) from the inferred causal mechanism.

2

Evaluate candidate findings for a logical strengthener.

The statement showing a direct dose-response relationship (higher platform usage correlates with greater escalation drops across departments) eliminates key background noise and reinforces that the platform itself drives the effect.

Concomitant variation across controlled sub-groups provides strong empirical support for a causal relationship.

3

Evaluate candidate findings for a logical weakener / alternative explanation.

The statement detailing a simultaneous management policy penalty provides an alternate reason why escalations dropped (managers suppressed escalations to avoid penalties), undermining the claim that goodwill was the driver.

An unaddressed external factor introduced at the same time offers a competing explanation for the exact same outcome.

Key Concept

Causal Reasoning in Two-Part Analysis (Strengthening vs. Alternative Explanations)

Question 6Question →

An environmental study across 40 agricultural counties observed that farms adopting rotational grazing techniques experienced a 30 percent decrease in soil erosion compared to farms using traditional continuous grazing. Based on this correlation, agricultural consultants concluded that adopting rotational grazing directly causes a reduction in soil erosion. However, critics point out that farms adopting rotational grazing also tended to be located in areas with significantly higher baseline soil organic matter, which independently stabilizes soil structure. Which of the following pairs of statements best identifies: (1) a statement that, if true, would most STRENGTHEN the consultants' causal claim by addressing the critics' concern, and (2) a statement that, if true, would REVERSE the directional causality of the observed correlation?

(1) Strengthener: Farms with low baseline soil organic matter experienced an identical 30 percent decrease in soil erosion after switching to rotational grazing; (2) Reversal: Decreased soil erosion creates favorable ground conditions that prompt farmers to adopt rotational grazing techniques.

(1) Strengthener: Decreased soil erosion creates favorable ground conditions that prompt farmers to adopt rotational grazing techniques; (2) Reversal: Farms with low baseline soil organic matter experienced no reduction in soil erosion when adopting rotational grazing.

(1) Strengthener: Traditional continuous grazing requires higher upfront capital expenditure for livestock fencing; (2) Reversal: Rotational grazing requires more labor hours per week to manage than traditional continuous grazing.

(1) Strengthener: Soil erosion rates were measured using standardized satellite topography metrics across all counties; (2) Reversal: Rotational grazing equipment was subsidized by local government environmental grants during the study period.

(1) Strengthener: Farms with high baseline soil organic matter adopted rotational grazing at twice the rate of other farms; (2) Reversal: High soil organic matter reduces the rate of erosion regardless of the grazing technique used.

Show answer & explanation

Answer: (1) Strengthener: Farms with low baseline soil organic matter experienced an identical 30 percent decrease in soil erosion after switching to rotational grazing; (2) Reversal: Decreased soil erosion creates favorable ground conditions that prompt farmers to adopt rotational grazing techniques.

Answer

(1) Strengthener: Farms with low baseline soil organic matter experienced an identical 30 percent decrease in soil erosion after switching to rotational grazing; (2) Reversal: Decreased soil erosion creates favorable ground conditions that prompt farmers to adopt rotational grazing techniques.

The correct choice accurately satisfies both conditions. First, showing that the 30 percent erosion reduction occurs even on farms with low baseline soil organic matter eliminates the critics' alternative explanation, thereby strengthening the consultants' claim. Second, stating that decreased erosion causes farmers to adopt rotational grazing flips the cause and effect, fulfilling the requirement for a causal direction reversal.

Step-by-Step Solution

1

Analyze the causal claim and the critics' counterargument

The consultants argue that Rotational Grazing (Cause) leads to Reduced Soil Erosion (Effect). Critics argue that Baseline Soil Organic Matter is a confounding variable driving both or causing the erosion reduction independently.

To strengthen the claim, a statement must eliminate or control for the confounding variable (soil organic matter).

2

Evaluate candidate statements for the Strengthener role

Showing that farms with LOW baseline soil organic matter still experience the 30% reduction when adopting rotational grazing isolates rotational grazing as the cause, effectively ruling out organic matter as the sole driver.

Demonstrating the effect persists when the potential confounding factor is absent isolates the primary cause.

3

Evaluate candidate statements for the Causal Reversal role

Showing that reduced soil erosion comes first and causes farmers to adopt rotational grazing reverses the directional relationship (Effect -> Cause instead of Cause -> Effect).

A reversal of causality demonstrates that the presumed outcome is actually the independent variable driving the action.

Key Concept

Causal Argument Analysis: Confounding Variables and Directional Causality

Question 7Question →

An agricultural research team evaluated the impact of a new organic bio-fertilizer, BioCrop, on wheat yield across 60 regional farms. The study observed that farms utilizing BioCrop produced an average wheat yield 25% higher than farms using traditional synthetic fertilizers. Consequently, the lead researcher concluded that applying BioCrop directly causes an increase in wheat yield.

Which of the following statements, if true, would weaken the lead researcher's causal conclusion by presenting an alternative explanation or confounding variable? Select TWO correct statements.

Select all that apply

Farms that used BioCrop were also equipped with modern drip-irrigation systems that optimized water delivery during critical growth stages.

Farmers selected for the BioCrop group applied the product primarily to fields with higher baseline soil nutrient levels recorded prior to the study.

Higher wheat yields cause farmers to invest more revenue into purchasing premium fertilizers like BioCrop for future planting seasons.

Traditional synthetic fertilizers are significantly less expensive to purchase per acre than BioCrop.

BioCrop contains higher concentrations of nitrogen compounds than standard organic composts.

Show answer & explanation

Answer: Farms that used BioCrop were also equipped with modern drip-irrigation systems that optimized water delivery during critical growth stages.; Farmers selected for the BioCrop group applied the product primarily to fields with higher baseline soil nutrient levels recorded prior to the study.

Answer

The two statements that weaken the conclusion are the statement regarding modern drip-irrigation systems and the statement regarding higher baseline soil nutrient levels.

The correct selections both introduce plausible alternative explanations for the observed higher yield. If farms using BioCrop also used drip-irrigation systems or already possessed superior soil fertility, the yield increase cannot be definitively attributed to BioCrop itself.

Step-by-Step Solution

1

Identify the causal argument structure

Premise: Farms using BioCrop had 25% higher yields than farms using traditional fertilizer. Conclusion: BioCrop directly causes the yield increase.

To weaken a causal claim (

X \nrightarrow Y

), one must demonstrate alternative causes (

Z \nrightarrow Y

), reverse causality, or flawed experimental control.

2

Evaluate alternative explanations and confounding factors

The option noting drip-irrigation introduces an unobserved factor (

Z

) that improves yield. The option noting higher baseline soil nutrient levels indicates that the treatment group was inherently more fertile prior to BioCrop application.

Both factors provide plausible alternative reasons for the 25% higher yield that do not depend on BioCrop's effectiveness.

3

Eliminate invalid options

The options addressing purchasing cost, chemical comparison with compost, and future investment patterns fail to weaken the specific observational study's conclusion.

Irrational or irrelevant factors do not address the logical validity of the causal inference.

Key Concept

Evaluating Alternative Causes and Confounding Variables in Causal Arguments

Estimated Time:2m 0s

Question 8Question →

A logistics company uses two types of automated cargo drones, Drone X and Drone Y, to complete long-distance freight deliveries.

- Drone X travels at a constant speed of $40\text{ km/h}$ and consumes energy at a constant rate of $15\text{ kWh/h}$ .
- Drone Y travels at a constant speed of $60\text{ km/h}$ and consumes energy at a constant rate of $25\text{ kWh/h}$ .

On a completed joint mission, the two drones traveled a combined total distance of $480\text{ km}$ and consumed a combined total energy of $190\text{ kWh}$ .

In the table below, select the number of hours that Drone X operated and the number of hours that Drone Y operated during this mission.

Drone X Operating Time	Drone Y Operating Time	Hours
[ ]	[ ]	3
[ ]	[ ]	4
[ ]	[ ]	5
[ ]	[ ]	6
[ ]	[ ]	8

Which of the following correctly identifies the operating time, in hours, for Drone X and Drone Y, respectively?

Drone X: 4 hours; Drone Y: 6 hours

Drone X: 6 hours; Drone Y: 4 hours

Drone X: 5 hours; Drone Y: 5 hours

Drone X: 3 hours; Drone Y: 6 hours

Drone X: 8 hours; Drone Y: 3 hours

Show answer & explanation

Answer: Drone X: 6 hours; Drone Y: 4 hours

Answer

Drone X operated for 6 hours and Drone Y operated for 4 hours.

The system of equations

40 t_X + 60 t_Y = 480

and

15 t_X + 25 t_Y = 190

uniquely yields

t_X = 6

and

t_Y = 4

. Substituting Drone X = 6 hours and Drone Y = 4 hours gives a total distance of

40(6) + 60(4) = 480\text{ km}

and a total energy consumption of

15(6) + 25(4) = 190\text{ kWh}

, perfectly matching both given conditions.

Step-by-Step Solution

1

Set up a system of two linear equations representing total distance and total energy consumption.

Let

t_X

be the operating time of Drone X in hours, and

t_Y

be the operating time of Drone Y in hours.
Distance equation:

40 t_X + 60 t_Y = 480

Energy equation:

15 t_X + 25 t_Y = 190

Distance is calculated as

\text{speed} \times \text{time}

and energy as

\text{rate} \times \text{time}

.

2

Simplify both linear equations by dividing by their greatest common divisors.

Dividing the distance equation by 20 gives:

2 t_X + 3 t_Y = 24

.
Dividing the energy equation by 5 gives:

3 t_X + 5 t_Y = 38

.

Simplifying coefficients reduces computational complexity during elimination.

3

Solve the system using elimination.

Multiply

2 t_X + 3 t_Y = 24

by 3:

6 t_X + 9 t_Y = 72

.
Multiply

3 t_X + 5 t_Y = 38

by 2:

6 t_X + 10 t_Y = 76

.
Subtract the first multiplied equation from the second:

(6 t_X + 10 t_Y) - (6 t_X + 9 t_Y) = 76 - 72 \implies t_Y = 4\text{ hours}

.

Eliminating

t_X

allows direct solving for

t_Y

.

4

Substitute

t_Y = 4

back into

2 t_X + 3 t_Y = 24

to solve for

t_X

.

2 t_X + 3(4) = 24 \implies 2 t_X + 12 = 24 \implies 2 t_X = 12 \implies t_X = 6\text{ hours}

.

Determines the exact value for Drone X's operating duration.

Key Concept

Simultaneous Linear Equations with Work and Rate Constraints

Estimated Time:2m 30s

Question 9Question →

An automated data processing pipeline evaluates five sequential stages ( $k = 1, 2, 3, 4, 5$ ) to process machine learning workloads. At the start ( $k = 0$ ), the system state is defined by Storage $S_0 = 10\text{ GB}$ and System Load $L_0 = 20\%$ . At each subsequent stage $k$ , the state vector $(S_k, L_k)$ updates according to the following rules:

- Stage 1 (Data Scrubbing): $S_1 = S_0 + 15$ , $L_1 = L_0 + 10$
- Stage 2 (Feature Extraction): $S_2 = 2 \times S_1$ , $L_2 = L_1 + 15$
- Stage 3 (Model Training): $S_3 = S_2 - 10$ , $L_3 = L_2 + 25$
- Stage 4 (Batch Validation): $S_4 = S_3 + 20$ , $L_4 = L_3 - 30$
- Stage 5 (System Deployment): $S_5 = S_4 - 25$ , $L_5 = L_4 + 50$

The pipeline performance metric at any stage is defined as $M_k = S_k + L_k$ .

Arrange the five stages in increasing order of their pipeline performance metric $M_k$ (from smallest value to largest value).

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct increasing order of the stages by metric

M_k

is Data Scrubbing (

M_1 = 55

), Feature Extraction (

M_2 = 95

), Batch Validation (

M_4 = 100

), Model Training (

M_3 = 110

), and System Deployment (

M_5 = 125

).

Tracking each state sequentially yields

M_1 = 55

,

M_2 = 95

,

M_3 = 110

,

M_4 = 100

, and

M_5 = 125

. Arranging these from smallest to largest places Batch Validation (

M_4 = 100

) before Model Training (

M_3 = 110

).

Step-by-Step Solution

1

Calculate state vector and metric for Stage 1

S_1 = 10 + 15 = 25

,

L_1 = 20 + 10 = 30 \implies M_1 = 25 + 30 = 55

Apply state transformation rules for Stage 1 starting from initial condition

(S_0=10, L_0=20)

.

2

Calculate state vector and metric for Stage 2

S_2 = 2 \times 25 = 50

,

L_2 = 30 + 15 = 45 \implies M_2 = 50 + 45 = 95

Apply state transformation rules using values from Stage 1.

3

Calculate state vector and metric for Stage 3

S_3 = 50 - 10 = 40

,

L_3 = 45 + 25 = 70 \implies M_3 = 40 + 70 = 110

Apply state transformation rules using values from Stage 2.

4

Calculate state vector and metric for Stage 4

S_4 = 40 + 20 = 60

,

L_4 = 70 - 30 = 40 \implies M_4 = 60 + 40 = 100

Apply state transformation rules using values from Stage 3.

5

Calculate state vector and metric for Stage 5

S_5 = 60 - 25 = 35

,

L_5 = 40 + 50 = 90 \implies M_5 = 35 + 90 = 125

Apply state transformation rules using values from Stage 4.

6

Sort the computed metric values in ascending order

M_1 (55) < M_2 (95) < M_4 (100) < M_3 (110) < M_5 (125)

Ordering the values yields Data Scrubbing, Feature Extraction, Batch Validation, Model Training, and System Deployment.

Key Concept

Sequential state tracking requires evaluating recursive function rules step-by-step before applying ordering logic.

Question 10Question →

A regional health authority conducted a study across corporate workplaces to evaluate the impact of mandatory 15-minute guided mindfulness breaks introduced twice daily. Over a six-month trial, participating companies reported a 25% decrease in formal employee sick leave requests. Based on this outcome, the health authority concluded that the mindfulness breaks directly improved employee physical health and reduced illness incidence. Analysts and independent researchers provided four statements regarding these results.

Match each analytical statement with the precise logical role it plays in evaluating the health authority's causal argument.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Each analytical statement correctly matches its respective logical role in causal argument evaluation: baseline exercise differences represent Selection Bias / Pre-existing Confounder; the new remote-work policy represents an Alternative Causal Explanation; concentrated stress-reduction with control validation represents Strengthening Evidence; and fear of losing bonuses represents a Measurement Artifact / Reporting Incentive Shift.

The correct pairings accurately classify each statement according to standard critical reasoning principles: pre-existing habit differences indicate selection bias; concurrent operational changes represent alternative explanations; controlled subgroup variance provides strengthening support; and metric distortion due to incentive perception represents a measurement artifact.

Step-by-Step Solution

1

Analyze the central causal claim made by the health authority.

The authority claims: Guided mindfulness breaks (Cause) directly led to improved physical health and reduced illness, measured via sick leave requests (Effect).

Evaluating logical arguments requires isolating the proposed cause, effect, and metric of measurement.

2

Evaluate the first statement regarding voluntary personal exercise.

It highlights pre-existing health habits in the participant pool, which points to selection bias rather than the intervention's efficacy.

When study subjects possess inherent baseline advantages, outcome differences cannot be attributed solely to the tested variable.

3

Evaluate the second statement regarding the simultaneous remote-work policy.

It presents an alternative cause for decreased formal sick leave filings (working from home while sick).

A confounding variable introduced concurrently with the treatment offers a competing explanation for the outcome.

4

Evaluate the third statement regarding stress-group concentration and control stability.

It confirms that the outcome occurred where expected (high-stress groups) and did not occur without the treatment (control groups).

Differentiating results between treatment and control groups while showing expected subgroup responsiveness strengthens a causal connection.

5

Evaluate the fourth statement regarding bonus forfeiture concerns.

It reveals that actual sickness may not have dropped, but rather employee willingness to officially report sick leave changed.

An incentive that discourages reporting alters the metric itself without changing the underlying health state being measured.

Key Concept

Causal Fallacies, Confounding Variables, and Argument Evaluation in Observational Data

Estimated Time:2m 0s

Question 11Question →

A telecommunications provider observed a 25% drop in subscriber churn in service areas where it concurrently upgraded its cell tower network to 5G and introduced a free device-protection plan for long-term contract holders. Company executives concluded that the speed improvements from the 5G upgrades were directly responsible for the reduction in subscriber churn. Which of the following statements, if true, provide valid logical evaluations that weaken the executives' causal conclusion? (Select all that apply.)

Select all that apply

In service areas where the 5G tower upgrades were completed but the free device-protection plan was not offered, subscriber churn rates remained unchanged.

Subscribers in control markets who received the free device-protection plan without any 5G network upgrades experienced a comparable 25% drop in churn.

The 25% drop in subscriber churn rate directly prompted company executives to initiate the 5G cell tower upgrades across all service areas.

Company executives evaluated only the single 25% churn metric without cross-referencing customer satisfaction survey metrics from other internal reporting sources.

While 5G tower upgrades and device-protection plans each independently increase customer retention, implementing both simultaneously exceeds departmental budget limits.

Show answer & explanation

Answer: In service areas where the 5G tower upgrades were completed but the free device-protection plan was not offered, subscriber churn rates remained unchanged.; Subscribers in control markets who received the free device-protection plan without any 5G network upgrades experienced a comparable 25% drop in churn.

Answer

The two statements that weaken the executives' conclusion are the one showing that 5G upgrades alone caused no change in churn in areas without device protection, and the one showing that device protection alone produced an identical 25% drop in churn without 5G upgrades.

To weaken a causal claim derived from two simultaneous interventions, a valid response must isolate the variables. The statement establishing that churn remained unchanged when 5G upgrades were implemented without device protection proves that 5G speed improvements alone were not sufficient to reduce churn. Similarly, the statement demonstrating an identical 25% churn drop in markets receiving only device protection provides a strong alternative explanation for the outcome. Together, these two statements logically dismantle the executives' conclusion that 5G upgrades were the cause.

Step-by-Step Solution

1

Identify the causal argument and premise structure in the stem.

Premise: Two simultaneous changes occurred (5G upgrades and free device protection) alongside a 25% drop in churn. Conclusion: 5G upgrades directly caused the drop.

Evaluating a causal claim requires identifying whether conflated variables or alternative explanations exist.

2

Evaluate statements that test for confounding variables or variable isolation.

The statement showing no churn change in 5G-only areas isolates 5G and shows it is insufficient on its own. The statement showing a 25% churn drop in protection-only areas presents a viable alternative cause.

Showing that the supposed cause fails to produce the effect when isolated, or that the effect occurs without the supposed cause, invalidates a claim of exclusive causality.

3

Filter out irrelevant statements or logical fallacies.

Statements reversing causal direction, mentioning single-source tunnel vision, or discussing budget constraints do not logically weaken the causal relationship.

Only empirical or logical counter-evidence regarding the stated variables can effectively weaken a causal conclusion.

Key Concept

Evaluating Causal Arguments and Confounding Variables in Two-Part Scenarios

Question 12Question →

A chemical processing plant prepares a batch of solution by mixing two stock liquid compounds, Solution A and Solution B, to form an initial mixture with a total mass of $480\text{ kg}$ . Solution A contains $25\%$ active compound by mass, and Solution B contains $5\%$ active compound by mass. Solution A and Solution B are combined in a mass ratio of $3:1$ , respectively.

To satisfy export specifications, technicians must raise the active compound concentration of the entire mixture to $25\%$ by mass by adding a quantity of pure active compound. How many kilograms of pure active compound must be added to the $480\text{ kg}$ mixture?

Show answer & explanation

Answer: 32

Answer

32 kg of pure active compound must be added to reach a final concentration of 25% active compound by mass.

The initial mixture consists of 360 kg of Solution A and 120 kg of Solution B. This contains a total of 96 kg of active compound (90 kg from A and 6 kg from B). Adding 32 kg of pure active compound brings the total active compound to 128 kg and total mixture mass to 512 kg, yielding an exact concentration of 128 / 512 = 25%.

Step-by-Step Solution

1

Calculate the mass of Solution A and Solution B in the initial mixture

Solution A = 360 kg, Solution B = 120 kg

The total mass of 480 kg is divided according to the 3:1 ratio (3/4 and 1/4).

2

Calculate the mass of pure active compound in the initial mixture

Initial active compound = 96 kg

Solution A provides 25% of 360 kg (90 kg) and Solution B provides 5% of 120 kg (6 kg).

3

Set up an equation for the final concentration after adding x kg of active compound

(96 + x) / (480 + x) = 1/4

Adding pure active compound increases both the mass of the active compound and the total mass of the mixture by x kg.

4

Solve for x

x = 32 kg

Cross-multiplying gives 4(96 + x) = 480 + x, which simplifies to 3x = 96.

Key Concept

Weighted average mixtures and algebraic optimization of concentration ratios

Question 13Question →

An automated logistics drone starts an operation at Cycle $k = 0$ with an initial battery charge of $C_0 = 100\%$ and a payload mass of $P_0 = 40\text{ kg}$ . At the end of each subsequent cycle $k$ (where $k = 1, 2, 3, 4$ ), the payload mass decreases by $8\text{ kg}$ according to $P_k = P_{k-1} - 8$ , and the remaining battery charge updates according to the state transition rule $C_k = C_{k-1} - (5 + 0.2 P_{k-1})\%$ . Match each operational cycle on the left with its exact state $(C_k, P_k)$ at the end of that cycle on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

End of Cycle 1 matches with C_1 = 87.0%, P_1 = 32 kg; End of Cycle 2 matches with C_2 = 75.6%, P_2 = 24 kg; End of Cycle 3 matches with C_3 = 65.8%, P_3 = 16 kg; End of Cycle 4 matches with C_4 = 57.6%, P_4 = 8 kg.

Each cycle follows the recursive state equations P_k = P_{k-1} - 8 and C_k = C_{k-1} - (5 + 0.2 P_{k-1}). Evaluating step by step yields the exact matching pairs for all four cycles.

Step-by-Step Solution

1

Calculate state values at the end of Cycle 1 (k = 1)

P_1 = 40 - 8 = 32 kg; C_1 = 100 - (5 + 0.2 * 40) = 100 - 13 = 87.0%

Use the state transition formula using initial values P_0 = 40 and C_0 = 100.

2

Calculate state values at the end of Cycle 2 (k = 2)

P_2 = 32 - 8 = 24 kg; C_2 = 87.0 - (5 + 0.2 * 32) = 87.0 - 11.4 = 75.6%

Apply the recursive transition rules to the state obtained at k = 1.

3

Calculate state values at the end of Cycle 3 (k = 3)

P_3 = 24 - 8 = 16 kg; C_3 = 75.6 - (5 + 0.2 * 24) = 75.6 - 9.8 = 65.8%

Apply the recursive transition rules to the state obtained at k = 2.

4

Calculate state values at the end of Cycle 4 (k = 4)

P_4 = 16 - 8 = 8 kg; C_4 = 65.8 - (5 + 0.2 * 16) = 65.8 - 8.2 = 57.6%

Apply the recursive transition rules to the state obtained at k = 3.

Key Concept

Sequential Process and Recursive State Transition Tracking

Estimated Time:2m 0s

Question 14Question →

A corporate governance study monitored 60 multinational technology firms over a three-year period to evaluate the impact of introducing automated AI hiring software for mid-level managerial positions. The study observed that firms adopting the AI software experienced a 25 percent increase in annual manager turnover. Based on this observation, the lead researcher concluded that automated AI screening causes increased manager attrition because candidates selected by AI lack interpersonal compatibility with existing teams. Which of the following statements, if true, weaken the lead researcher's causal conclusion? Select all that apply.

Select all that apply

Firms experiencing elevated manager turnover prior to the study were significantly more likely to adopt the automated AI hiring software to streamline recruitment.

The increased manager attrition rates prompted affected firms to substantially expand their internal human resources departments.

Simultaneously with adopting the AI software, participating firms introduced stricter quarterly performance targets that resulted in higher rates of performance-based terminations.

Non-managerial staff turnover remained entirely stable across all 60 multinational technology firms throughout the three-year monitoring period.

The automated AI hiring software reduced the average time required to fill vacant managerial positions from 45 days to 12 days.

Show answer & explanation

Answer: Firms experiencing elevated manager turnover prior to the study were significantly more likely to adopt the automated AI hiring software to streamline recruitment.; Simultaneously with adopting the AI software, participating firms introduced stricter quarterly performance targets that resulted in higher rates of performance-based terminations.

Answer

The statements establishing selection bias in pre-existing high turnover firms and introducing an alternative explanation through stricter performance targets both weaken the causal conclusion.

The causal claim is that AI hiring software causes increased manager turnover due to team incompatibility. The option noting that high-turnover firms selectively adopted the AI software demonstrates reverse causality and selection bias, showing that turnover predated software adoption. The option noting that firms concurrently instituted stricter performance targets introduces a confounding variable that provides an alternative explanation for the increased terminations. Both statements undermine the researcher's conclusion.

Step-by-Step Solution

1

Identify the causal claim and proposed mechanism in the stem

The researcher claims that automated AI hiring software causes increased manager attrition due to poor interpersonal compatibility of AI-selected candidates.

Understanding the precise cause and effect is necessary to evaluate weakening conditions.

2

Evaluate statements for alternative causal directions or confounding variables

Showing that high turnover existed prior to adoption (reverse causality) or that stricter performance targets caused higher termination rates (confounding variable) invalidates the direct causal link.

Causal conclusions are weakened when reverse causality or confounding third variables explain the observed correlation.

Key Concept

Evaluating Causal Arguments and Weakening Causal Claims

Question 15Question →

A theater sold a total of $100$ tickets for a performance, consisting of standard tickets ( $s$ ) at $\$25$ each and VIP tickets ( $v$ ) at $\$50$ each. The total revenue from ticket sales was $\$3,500$ . Match each ticket category to the correct number of tickets sold.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Standard Tickets matches to 60; VIP Tickets matches to 40.

The correct matches are Standard Tickets to 60 and VIP Tickets to 40 because solving the system

s + v = 100

and

25s + 50v = 3500

gives

s = 60

and

v = 40

.

Step-by-Step Solution

1

Set up the simultaneous linear equations from the text.

s + v = 100

and

25s + 50v = 3500

The total count equation represents total tickets, and the price equation represents total revenue.

2

Divide the revenue equation by 25 to simplify terms.

s + 2v = 140

Simplifying the coefficients reduces calculation complexity.

3

Subtract the first equation (

s + v = 100

) from the simplified second equation (

s + 2v = 140

).

v = 40

Subtracting eliminates the variable

s

directly.

4

Substitute

v = 40

back into

s + v = 100

.

s = 60

Yields the value for the remaining variable

s

.

Key Concept

Solving simultaneous linear equations in two variables.

Question 16Question →

A chemist mixes $x$ liters of a $20\%$ acid solution with $y$ liters of a $50\%$ acid solution to produce $30$ liters of a $40\%$ acid solution. How many liters of the $20\%$ acid solution were used in the mixture?

Show answer & explanation

Answer: 10

Answer

10 liters of the 20% acid solution were used.

Solving the system of simultaneous linear equations

x + y = 30

and

0.20x + 0.50y = 12

yields

x = 10

liters.

Step-by-Step Solution

1

Formulate the linear system of equations representing total volume and total pure acid content.

x + y = 30

and

0.20x + 0.50y = 12

.

The sum of component volumes equals total volume, and the sum of pure acid contents equals total pure acid.

2

Substitute

y = 30 - x

into the pure acid equation.

0.20x + 0.50(30 - x) = 12

Reduces the two-variable system to a single linear equation in terms of

x

.

3

Expand and solve for

x

.

15 - 0.30x = 12 \implies -0.30x = -3 \implies x = 10

Isolates the target variable

x

representing the volume of the 20% acid solution.

Key Concept

Simultaneous Linear Equations in Mixture Problems

Estimated Time:1m 0s

Question 17Question →

A manufacturing plant produces two types of solar panels: Model X and Model Y. Each Model X panel requires $2$ hours of assembly and $1$ hour of quality testing. Each Model Y panel requires $3$ hours of assembly and $2$ hours of quality testing. During a single week, the assembly line logged a total of $140$ hours and the quality testing line logged $80$ hours, with both departments operating at full capacity. How many Model X solar panels were produced during the week?

20

30

40

50

60

Show answer & explanation

Answer: $40$

Answer

40

Model X solar panels were produced during the week.

Setting up the simultaneous linear equations for assembly time (

2x + 3y = 140

) and testing time (

x + 2y = 80

) and solving for

x

gives

x = 40

, which accurately satisfies both constraints.

Step-by-Step Solution

1

Define variables and set up the system of linear equations based on resource constraints.

Let

x

be the number of Model X panels and

y

be the number of Model Y panels.
Assembly constraint:

2x + 3y = 140

Quality testing constraint:

x + 2y = 80

Each department's total logged hours must equal the sum of hours required by both panel types.

2

Express

x

in terms of

y

using the testing constraint equation.

x = 80 - 2y

Isolating

x

allows substitution into the assembly equation.

3

Substitute

x = 80 - 2y

into the assembly equation and solve for

y

.

2(80 - 2y) + 3y = 140 160 - 4y + 3y = 140 160 - y = 140 y = 20

Solving a single-variable equation determines the quantity of Model Y panels.

4

Substitute

y = 20

back to find

x

.

x = 80 - 2(20) = 40

Evaluating

x

determines the quantity of Model X panels requested in the question stem.

Key Concept

Solving simultaneous linear equations by substitution or elimination

Question 18Question →

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

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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 19Question →

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.

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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 20Question →

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

Two-Part Analysis

Answer

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