All practice questions

Question 1601Question →

In a GMAT Data Sufficiency problem asking for the unique value of an integer $x$ , Statement (1) establishes that $x \in \{3, 7\}$ and Statement (2) establishes that $|x - 5| = 2$ . Evaluating both statements together provides sufficient information to determine a unique value for $x$ .

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. Combining both statements yields the intersection set {3, 7}, which still contains two possible values for x and therefore does not uniquely determine x.

The statement is false because solving Statement (2)'s absolute value equation

|x - 5| = 2

produces

x = 7

or

x = 3

, which is identical to the candidate set given by Statement (1). Combining two identical solution sets leaves the candidate set as

\{3, 7\}

, which does not yield a single unique value for

x

.

Step-by-Step Solution

1

Evaluate Statement (1) solution set

Statement (1) restricts

x

to the set

\{3, 7\}

.

Statement (1) explicitly provides two candidate values for

x

.

2

Evaluate Statement (2) solution set independently

Statement (2) yields

|x - 5| = 2 \implies x = 7

or

x = 3

. The solution set is

\{3, 7\}

.

Solving the absolute value equation yields the two roots 3 and 7 without using any information from Statement (1).

3

Combine Statement (1) and Statement (2)

The intersection of the two solution sets is

\{3, 7\} \cap \{3, 7\} = \{3, 7\}

.

When combining statements in Data Sufficiency, valid values must satisfy both statements simultaneously.

4

Determine sufficiency of the combined statements

Since

x

can still be either 3 or 7, a single unique value is not determined. The combined statements are insufficient.

A Value Data Sufficiency question requires a single, unique numerical value to be considered sufficient.

Key Concept

Statement Combination and Redundancy in Data Sufficiency

Question 1602Question →

A commercial real estate firm leased office space across two properties, Property X and Property Y. The rental rate per square foot for space in Property X was $20\%$ higher than the rental rate per square foot for space in Property Y. Was the total rental revenue generated from Property X greater than the total rental revenue generated from Property Y?

(1) Property X accounted for more than $45\%$ of the total square feet of office space leased across both properties.
(2) Property Y accounted for less than $54\%$ of the total square feet of office space leased across both properties.

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 to answer the question with a definitive 'Yes', but Statement (1) ALONE is not sufficient.

The correct response identifies that Statement (2) alone is sufficient because it establishes that Property X's area share relative to Property Y yields a ratio

\frac{S_X}{S_Y} > \frac{23}{27}

. Because

\frac{23}{27} > \frac{5}{6}

, the revenue of Property X is guaranteed to exceed that of Property Y, providing a definitive 'Yes'. Statement (1) alone is insufficient because it permits ratios below

\frac{5}{6}

.

Step-by-Step Solution

1

Rephrase the question stem in terms of algebraic variables.

Let

S_X

and

S_Y

be the square footage leased in Property X and Property Y, respectively, and let

r

be the rate per sq ft for Property Y. The rate for Property X is

1.20r

. Revenue from X is

1.20r S_X

and revenue from Y is

r S_Y

. The question asks whether

1.20r S_X > r S_Y

, which simplifies to asking whether

\frac{S_X}{S_Y} > \frac{1}{1.20} = \frac{5}{6}

.

Simplifying the target question into a ratio threshold

\frac{S_X}{S_Y} > \frac{5}{6} \approx 0.8333

streamlines the statement evaluation.

2

Evaluate Statement (1):

S_X > 0.45(S_X + S_Y)

.

0.55 S_X > 0.45 S_Y \implies \frac{S_X}{S_Y} > \frac{0.45}{0.55} = \frac{9}{11} \approx 0.8182

. Since

\frac{9}{11} < \frac{5}{6}

,

\frac{S_X}{S_Y}

could be

0.82

(giving a 'No' answer to the question) or

1.0

(giving a 'Yes' answer).

Statement (1) allows values both above and below the required threshold of

5/6

, making it insufficient.

3

Evaluate Statement (2):

S_Y < 0.54(S_X + S_Y)

.

0.46 S_Y < 0.54 S_X \implies \frac{S_X}{S_Y} > \frac{0.46}{0.54} = \frac{23}{27} \approx 0.8519

. Comparing

\frac{23}{27}

and

\frac{5}{6}

:

23 \times 6 = 138

and

27 \times 5 = 135

. Since

138 > 135

,

\frac{23}{27} > \frac{5}{6}

. Thus,

\frac{S_X}{S_Y}

must be strictly greater than

\frac{5}{6}

.

Statement (2) forces

\frac{S_X}{S_Y}

to be strictly greater than

5/6

, yielding a definitive 'Yes' to the question stem.

Key Concept

Question Stem Rephrasing and Threshold Analysis in Data Sufficiency Ratio Problems

Estimated Time:2m 0s

Question 1603Question →

To cut long-distance cargo transit expenses, a regional freight company plans to replace its entire fleet of diesel transport trucks with electric trucks powered by newly developed solid-state batteries. Management reasons that because electric trucks incur 40 percent lower energy costs per mile than diesel trucks and require significantly fewer routine engine maintenance services, making this transition will substantially reduce the company's total annual operational expenses over the next five years.

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

The solid-state batteries required for these electric transport trucks degrade rapidly under continuous long-distance heavy usage and require full replacement every two years at a cost exceeding the total energy savings achieved during that period.

Regional diesel fuel prices are projected to rise significantly over the next five years, further widening the gap in fuel expenditure between diesel and electric vehicles.

The freight company's primary competitors have announced plans to invest in alternative hydrogen fuel cell technology for delivery vehicles scheduled to launch in seven years.

Several municipal transit authorities have successfully deployed short-range electric passenger buses in dense urban centers to reduce local tailpipe emissions.

The freight company will need to provide short training sessions for its existing fleet drivers to familiarize them with operating electric trucks.

Show answer & explanation

Answer: The solid-state batteries required for these electric transport trucks degrade rapidly under continuous long-distance heavy usage and require full replacement every two years at a cost exceeding the total energy savings achieved during that period.

Answer

The statement regarding rapid battery degradation and expensive replacement costs most seriously weakens the argument by demonstrating that total operational costs over five years will actually increase rather than decrease.

The conclusion relies on the assumption that lower energy costs and fewer routine maintenance services will lead to lower net operational expenses. The option pointing out that the batteries degrade rapidly and require replacement every two years at a cost exceeding the total energy savings directly refutes this assumption by introducing a major ongoing expense that makes the transition more costly overall.

Step-by-Step Solution

1

Deconstruct the argument into premise and conclusion

Premises: Electric trucks have 40% lower energy costs per mile and fewer routine engine maintenance needs. Conclusion: Transitioning the fleet will substantially reduce total annual operational expenses over five years.

Identifying the logic path allows us to uncover the author's unstated assumption.

2

Identify the unstated assumption

The author assumes that energy savings and lower engine maintenance will not be offset by other unexpected, mandatory operational costs unique to electric trucks over the five-year timeframe.

A weakening answer choice will target and undermine this unstated assumption.

3

Evaluate the impact of new information on the assumption

If solid-state batteries require replacement every two years at a cost greater than the total energy savings, overall expenses over five years will rise, directly invalidating the conclusion.

Pointing out a massive, recurrent operational expense directly disproves the claim of reduced total operational expenses.

Key Concept

Evaluating plan-to-goal feasibility by identifying hidden or offsetting operational costs

Question 1604Question →

In a corporate compliance framework, any employee who receives level-3 data access authorization must first complete an advanced cybersecurity certification and obtain written clearance from the chief security officer. Furthermore, no employee is granted written clearance from the chief security officer unless that employee has passed a background check within the preceding two years. Employee V did not pass a background check within the preceding two years.

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

Employee V does not possess level-3 data access authorization.

Employee V has completed the advanced cybersecurity certification but failed the chief security officer's review.

Passing a background check guarantees that an employee will receive written clearance from the chief security officer.

If Employee V completes the advanced cybersecurity certification, Employee V will become eligible for level-3 data access authorization.

Any employee who has obtained written clearance from the chief security officer has also completed the advanced cybersecurity certification.

Show answer & explanation

Answer: Employee V does not possess level-3 data access authorization.

Answer

Employee V does not possess level-3 data access authorization.

The correct option is derived via a valid contrapositive chain. The passage dictates that Level-3 Access requires CSO Clearance, which in turn requires a recent background check. Since Employee V lacks a recent background check, Employee V cannot have obtained CSO Clearance and consequently cannot hold Level-3 Access authorization.

Step-by-Step Solution

1

Identify the formal conditional relationships in the premises.

Premise 1: Level-3 Access → Advanced Certification AND CSO Clearance. Premise 2: CSO Clearance → Background Check (within 2 years).

Mapping conditional statements allows chaining requirements together.

2

Chain the conditional statements to establish necessary conditions for Level-3 Access.

Level-3 Access → CSO Clearance → Background Check (within 2 years). Therefore, Level-3 Access → Background Check (within 2 years).

If A requires B, and B requires C, then A cannot exist without C.

3

Apply the contrapositive rule using the factual premise about Employee V.

Fact: Employee V has NOT passed a background check within 2 years. Contrapositive: NO Background Check → NO CSO Clearance → NO Level-3 Access.

Negating the necessary condition forces the negation of all preceding sufficient conditions.

Key Concept

Conditional Logic & Contrapositive Deduction

Question 1605Question →

The table below shows logistics performance data for six regional warehouses during the third quarter:

Warehouse	Region	Total Shipments	On-Time Delivery Rate	Avg. Processing Time (Hours)
Alpha	East	12,000	94%	14.5
Beta	West	8,500	96%	12.0
Gamma	East	15,200	91%	16.0
Delta	South	9,100	98%	10.5
Epsilon	West	11,400	95%	13.0
Zeta	South	14,000	93%	15.0

Match each statement on the left with its correct evaluation outcome on the right based on the table.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement I matches with True (West region average is 12.5 hours); Statement II matches with True (Gamma has highest shipments and lowest delivery rate); Statement III matches with False (3 out of 6 is exactly half, not more than half).

Each statement is evaluated against the data in the table: Statement I evaluates to True because the average for West warehouses (12.0 and 13.0) is 12.5 hours. Statement II evaluates to True because Gamma holds both the maximum shipment volume (15,200) and minimum delivery rate (91%). Statement III evaluates to False because exactly 3 out of 6 warehouses (50%) have delivery rates above 94%, which does not exceed half.

Step-by-Step Solution

1

Evaluate Statement I by filtering by Region = West.

Beta (12.0 hrs) and Epsilon (13.0 hrs) are in the West. Average = (12.0 + 13.0) / 2 = 12.5 hours. 12.5 < 13.0 is True.

Calculate the mean value of processing time for the specified subset.

2

Evaluate Statement II by identifying the maximum shipment count and minimum delivery rate.

Maximum shipments = 15,200 (Gamma). Minimum delivery rate = 91% (Gamma). The condition holds True.

Determine if both extreme statistical properties apply to the same entity.

3

Evaluate Statement III by filtering for delivery rates > 94%.

Beta (96%), Delta (98%), and Epsilon (95%) qualify (3 warehouses). 3 out of 6 equals 50%, which is not > 50%. The statement is False.

Compare the count of matching rows against the threshold 'more than half' (strictly greater than 50%).

Key Concept

Multi-Statement Boolean Evaluation on Tabular Data

Question 1606Question →

If $u$ and $v$ are non-zero real numbers, what is the value of $\frac{u - 2v}{u + v}$ ?

(1) $3u^2 - 5uv - 2v^2 = 0$
(2) $u > v > 0$

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

Answer

Both statements together are sufficient, but neither statement alone is sufficient.

The correct answer identifies that neither statement alone provides a unique value for the expression, but combining them eliminates the negative root case, leaving a unique value of 0 for the target expression.

Step-by-Step Solution

1

Rephrase the target expression

Dividing numerator and denominator by

v

, the target expression is

\frac{\frac{u}{v} - 2}{\frac{u}{v} + 1}

. Finding a unique value for

\frac{u}{v}

determines the target expression.

Simplifying the question target clarifies what information is necessary to achieve sufficiency.

2

Evaluate Statement (1) independently

Factor

3u^2 - 5uv - 2v^2 = 0

as

(3u + v)(u - 2v) = 0

. This gives

3u + v = 0 \implies u = -\frac{v}{3}

or

u - 2v = 0 \implies u = 2v

. If

u = 2v

, then

\frac{u - 2v}{u + v} = \frac{0}{3v} = 0

. If

u = -\frac{v}{3}

, then

\frac{u - 2v}{u + v} = \frac{-\frac{v}{3} - 2v}{-\frac{v}{3} + v} = \frac{-\frac{7}{3}v}{\frac{2}{3}v} = -\frac{7}{2}

. Two different values are possible.

Since Statement (1) produces two distinct numerical outcomes, it is not sufficient alone.

3

Evaluate Statement (2) independently

Statement (2) states

u > v > 0

. This indicates that both

u

and

v

are positive, but gives no fixed algebraic equality for

\frac{u}{v}

.

Infinitely many positive pairs

(u, v)

satisfy

u > v > 0

while yielding different values for the expression. Statement (2) is not sufficient alone.

4

Evaluate Statements (1) and (2) combined

From Statement (2),

u > 0

and

v > 0

, so

3u + v > 0

. Therefore, the factor

3u + v = 0

is impossible. This leaves

u - 2v = 0

as the only valid relation, so

u = 2v

. Substituting

u = 2v

yields

\frac{2v - 2v}{2v + v} = 0

.

Combining the inequality constraint with the quadratic factorization uniquely determines the value of the target expression.

Key Concept

Algebraic Equations and Systems in Data Sufficiency

Estimated Time:2m 0s

Question 1607Question →

Consider the following multi-source information regarding VeloCity's urban e-scooter deployment program:

Tab 1: Executive Proposal (Transportation Board)
To reduce downtown carbon emissions, VeloCity proposes subsidizing a 500-unit shared e-scooter fleet. The proposal asserts that replacing short-distance commuter car trips with zero-emission e-scooter rides will reduce overall transportation-related carbon emissions in the downtown core by at least $15\%$ within twelve months.

Tab 2: Municipal Traffic & Environmental Audit
A recent survey of downtown commuters revealed that $72\%$ of micro-mobility trips (including e-scooters) replace walking, cycling, or public transit journeys rather than personal motor vehicle trips. Furthermore, tabular data on total lifecycle emissions for the proposed e-scooter model is presented below:

Stage / Impact Factor	Grams $CO_2$ Equivalent per Passenger-Mile
Manufacturing & Raw Materials	$45$
Daily Fleet Collection & Charging (Diesel Vans)	$65$
Operational Electricity	$10$
Total Lifecycle Impact	$120$

*Note: Walking and cycling generate $0$ g $CO_2$ /mile; downtown public transit averages $50$ g $CO_2$ /mile; average inner-city passenger car generates $110$ g $CO_2$ /mile.*

Statement to Evaluate:
Evaluating the data across both tabs demonstrates that the introduction of the e-scooter fleet, as currently operated, is more likely to increase total downtown transportation carbon emissions than to achieve the proposed $15\%$ reduction.

True

False

Show answer & explanation

Answer: True

Answer

True. The cross-tab evidence demonstrates that the e-scooter lifecycle emissions (120 g CO2/mile) exceed those of cars (110 g CO2/mile) and public transit (50 g CO2/mile), and that most trips replace zero- or low-emission transport modes.

The evaluation statement is true because synthesizing Tab 1's core claim with Tab 2's empirical data shows that e-scooters emit 120 g CO2/mile (higher than inner-city cars at 110 g CO2/mile) and mostly replace walking, cycling, or public transit (0–50 g CO2/mile).

Step-by-Step Solution

1

Analyze the claim in Tab 1.

The executive proposal claims that deploying e-scooters will lower downtown carbon emissions by replacing car trips.

Establishing the core premise requires identifying the assumed mechanism of emission reduction.

2

Integrate lifecycle emission data from Tab 2.

Total e-scooter emissions equal

45 + 65 + 10 = 120

g

CO_2

/mile, which exceeds average inner-city car emissions (

110

g

CO_2

/mile).

A comprehensive evaluation must account for manufacturing, re-charging transport, and maintenance emissions rather than operational electricity alone.

3

Integrate commuter displacement survey data from Tab 2.

Only

28\%

of e-scooter trips replace car trips, while

72\%

replace walking (

0

g), cycling (

0

g), or transit (

50

g).

Determining net emissions impact requires comparing the new mode's emissions against the actual modes being displaced.

4

Synthesize cross-tab evidence to evaluate the statement.

Shifting trips from walking/transit (

0

-

50

g

CO_2

/mile) or cars (

110

g

CO_2

/mile) to e-scooters (

120

g

CO_2

/mile) increases overall net carbon emissions.

Since net emissions per passenger-mile rise across displaced modes, the program will increase emissions rather than achieve a

15\%

reduction.

Key Concept

Evaluating Argument Support and Weakening Across Tabs

Question 1608Question →

Passage: A commercial shipping logistics firm retrofitted half of its cargo fleet with synthetic polymer lubricants, while the remaining half continued using traditional petroleum lubricants. Over a two-year observation period, vessels using synthetic polymer lubricants reported 40% fewer engine overheating incidents. The operations director concluded that synthetic polymer lubricants directly reduce the frequency of engine overheating.

Statement: The fact that vessels using synthetic polymer lubricants were assigned exclusively to cold-water northern trade routes, where lower sea surface temperatures naturally assist engine cooling, functions as a confounding variable that weakens the operations director's causal conclusion.

True

False

Show answer & explanation

Answer: True

Answer

True. The exclusive assignment of synthetic-lubricant vessels to cold-water routes introduces a confounding variable (ambient sea temperature) that offers an alternative explanation for the decreased engine overheating, thereby weakening the director's causal claim.

The statement accurately identifies a classic confounding variable. In causal arguments, when the test group differs from the control group in a systematic background condition (route temperature) that independently influences the measured outcome (engine overheating), the argument commits a causal flaw by overlooking an alternative explanation.

Step-by-Step Solution

1

Analyze the causal claim in the passage.

Premise: Ships with synthetic polymer lubricants had 40% fewer overheating incidents than ships with petroleum lubricants. Conclusion: Synthetic polymer lubricant directly causes the reduction in engine overheating.

Deconstructing the argument isolates the observed correlation and the author's causal inference.

2

Evaluate the statement's potential as a confounding variable.

The statement reveals that the synthetic-lubricant group was systematically exposed to lower ambient temperatures (cold northern routes), which independently cool engines.

A confounding variable is an extrinsic factor correlated with both the cause and outcome that offers a competing explanation for the observed effect.

3

Determine the effect on the causal conclusion.

Because cold water independently prevents overheating, one cannot determine whether the reduced overheating was caused by the lubricant or the route climate. Therefore, the factor in the statement serves as a valid confounder that weakens the argument.

Establishing that an alternative cause accounts for the outcome confirms that the statement accurately identifies a causal flaw.

Key Concept

Third-variable confounding in causal reasoning

Estimated Time:1m 30s

Question 1609Question →

An investment portfolio consists of three funds: Fund Alpha, Fund Beta, and Fund Gamma. The table below presents the capital committed (in millions of dollars) and the annual yield percentage for each fund during the past fiscal year:

Fund	Capital Committed ($ millions)	Annual Yield (%)
Fund Alpha	40	8%
Fund Beta	60	12%
Fund Gamma	$c$	$y\%$

What was the overall annual yield percentage for the combined portfolio of all three funds?

(1) The capital committed to Fund Gamma, $c$ , was equal to the total capital committed to Fund Alpha and Fund Beta combined.
(2) The annual yield percentage for Fund Gamma, $y\%$ , was equal to the weighted average annual yield percentage of Fund Alpha and Fund Beta combined.

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 to answer the question, but statement (1) alone is not sufficient.

The option stating that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient is correct. Fund Alpha and Fund Beta combined have a weighted average yield of

\frac{40(8\%) + 60(12\%)}{100} = 10.4\%

. Statement (2) tells us that Fund Gamma's yield is also

10.4\%

. Combining any two groups with identical average yields results in an overall average yield equal to

10.4\%

, regardless of the amount of capital

c

in Fund Gamma. Statement (1) provides only the capital amount

c = 100

, leaving the yield

y

unknown and thus insufficient.

Step-by-Step Solution

1

Formulate the algebraic expression for the overall portfolio yield.

Overall Portfolio Yield =

\frac{40(8\%) + 60(12\%) + c(y\%)}{40 + 60 + c} = \frac{3.2 + 7.2 + \frac{cy}{100}}{100 + c} = \frac{10.4 + \frac{cy}{100}}{100 + c}

The total annual return is the sum of returns from each fund, divided by total capital committed.

2

Calculate the combined weighted average yield of Fund Alpha and Fund Beta.

Sub-portfolio yield =

\frac{40(8) + 60(12)}{40 + 60} = \frac{320 + 720}{100} = 10.4\%

Determining the performance of the known portion of the portfolio simplifies statement evaluation.

3

Evaluate Statement (1) independently:

c = 40 + 60 = 100

.

Overall Yield =

\frac{10.4 + y}{200} \times 100\% = \frac{10.4 + y}{2}\%

. Since

y

is unknown, this value is not unique.

Without knowing Fund Gamma's yield rate

y\%

, the capital amount alone does not provide a definitive overall yield.

4

Evaluate Statement (2) independently:

y\% = 10.4\%

.

Overall Yield =

\frac{100(10.4\%) + c(10.4\%)}{100 + c} = \frac{10.4\%(100 + c)}{100 + c} = 10.4\%

.

When a new component is added to a group with a value equal to the group's current average, the overall average remains unchanged regardless of the size (

c

) of the new component.

Key Concept

Weighted Average Invariance in Data Sufficiency

Question 1610Question →

The table below displays performance metrics for six regional branch offices of a retail company.

Branch	Region	Customer Satisfaction Score (1–10)	Q3 Revenue ($ thousands)	Q4 Revenue ($ thousands)
North	East	8.2	450	510
South	West	9.1	380	420
Metro	East	8.2	520	490
Summit	North	7.5	610	580
Valley	West	8.8	490	530
Harbor	North	9.1	410	460

If the table is sorted in descending order by Customer Satisfaction Score, and any ties are broken by sorting in descending order by Q3 Revenue ($ thousands), which branch office will be listed third from the top?

Harbor

South

Valley

Metro

Summit

Show answer & explanation

Answer: Valley

Answer

Valley is listed third from the top after performing the specified primary and secondary sorts.

Sorting the branches by Customer Satisfaction Score in descending order groups Harbor and South at the top with scores of 9.1. Ordering them by Q3 Revenue places Harbor first (

410 thousand) and South second (

380 thousand). The next highest satisfaction score is 8.8, held by Valley, placing Valley third from the top.

Step-by-Step Solution

1

Identify the primary sort criterion and group branches by Customer Satisfaction Score in descending order.

Highest scores (9.1): Harbor, South. Next highest (8.8): Valley. Next highest (8.2): North, Metro. Lowest score (7.5): Summit.

The primary sort requires ordering by Customer Satisfaction Score from highest to lowest.

2

Apply the tie-breaker criterion (Q3 Revenue in descending order) to branches tied at a score of 9.1.

Harbor (

410 thousand) comes before South (

380 thousand). Rank 1: Harbor, Rank 2: South.

Ties in Customer Satisfaction Score must be broken by sorting Q3 Revenue in descending order.

3

Determine the branch in the 3rd position.

Valley has the next highest score of 8.8, placing it in Rank 3.

Since only two branches have a score of 9.1, the branch with the next highest score (8.8) occupies the 3rd row.

Key Concept

Multi-column sorting requires applying the primary sort column first, followed by secondary tie-breaking logic on secondary columns without reading positions from default unsorted rows.

Question 1611Question →

### Tab 1: Policy Terms & Exclusions
- Base Coverage Limits: Standard Tier-A cyber liability insurance covers incident losses up to $1,000,000 per breach event. - **Deductible**: A base deductible of$ 100,000 applies to all Tier-A claims.
- SLA Penalties: If containment time exceeds 24 hours, the gross claim payout (before deductible) is reduced by 20%.
- Exclusion Exception (Section 4.1): If a breach involves fewer than 10,000 records AND root-cause analysis verifies an unpatched zero-day vulnerability, the 20% SLA penalty is waived, but the base deductible increases to $150,000.

### Tab 2: Incident Response Audit (Q2 Event #408)
- Affected Records: 8,500 customer identity records compromised.
- Time to Containment: 28 hours (exceeding 24-hour baseline SLA).
- Audit Findings: Breach originated via an unpatched zero-day exploit in the primary firewall firmware.
- Total Assessed Direct Loss: $600,000.

### Tab 3: Claims Calculation Log
- Formula: Net Payable = Gross Loss $\times$ (1 - SLA Penalty Rate) - Applicable Deductible.

Statement: Based on the three sources, the net insurance payout payable to the insured organization for Incident #408 is $380,000.

True

False

Show answer & explanation

Answer: False

Answer

False

The correct response is False because under Tab 1 (Section 4.1), the breach meets both criteria for an exclusion exception: fewer than 10,000 affected records (8,500) and a verified zero-day vulnerability. This waives the 20% SLA containment penalty but increases the deductible to

150,000. Subtracting the

150,000 deductible from the

600,000 gross loss yields a net payout of

450,000, not $380,000.

Step-by-Step Solution

1

Evaluate containment SLA conditions from Tab 1 and Tab 2

Containment took 28 hours, which exceeds the 24-hour limit, normally triggering a 20% penalty.

Identify if SLA penalties apply under standard policy terms.

2

Check Exclusion Exception rules in Tab 1 against audit facts in Tab 2

Section 4.1 exception applies because records affected (8,500) < 10,000 and the cause was a verified zero-day exploit.

Determine if policy exceptions override standard SLA penalty rules.

3

Adjust calculation parameters based on Section 4.1

SLA Penalty = 0%; Deductible increases from

100,000 to

150,000.

Apply the modified financial terms dictated by the exception.

4

Calculate the net payout

Net Payable =

600,000 -

150,000 = $450,000.

Reconcile the final payout using the Tab 3 payout formula.

Key Concept

Reconciling policy rules and conditional exceptions across multiple sources to evaluate financial outcomes.

Question 1612Question →

A logistics company recorded data for all cargo shipments dispatched from Depot Alpha during 2025. In that year, every shipment containing perishable food items was transported in a refrigerated truck, and every shipment transported in a refrigerated truck arrived at its destination on schedule. Exactly 30 percent of all cargo shipments dispatched from Depot Alpha in 2025 contained perishable food items.

Which of the following statements can be properly inferred from the passage above?

Every cargo shipment containing perishable food items dispatched from Depot Alpha in 2025 arrived at its destination on schedule.

Refrigerated trucks were used exclusively for transporting perishable cargo shipments from Depot Alpha in 2025.

Depot Alpha achieved a higher overall on-schedule delivery rate in 2025 than it did in 2024.

Any cargo shipment dispatched from Depot Alpha in 2025 that arrived on schedule must have contained perishable food items.

At least 70 percent of all cargo shipments dispatched from Depot Alpha in 2025 failed to arrive at their destinations on schedule.

Show answer & explanation

Answer: Every cargo shipment containing perishable food items dispatched from Depot Alpha in 2025 arrived at its destination on schedule.

Answer

Every cargo shipment containing perishable food items dispatched from Depot Alpha in 2025 arrived at its destination on schedule.

The stimulus establishes two universal rules: every perishable shipment was transported in a refrigerated truck, and every shipment in a refrigerated truck arrived on schedule. Linking these premises directly proves that every perishable shipment dispatched from Depot Alpha in 2025 arrived at its destination on schedule.

Step-by-Step Solution

1

Extract the explicit factual premises from the stimulus

Premise 1: Perishable shipment -> Refrigerated truck. Premise 2: Refrigerated truck -> Arrived on schedule. Premise 3: 30 percent of shipments were perishable.

Inference questions require relying solely on given premises without introducing unstated assumptions.

2

Apply transitive conditional logic to Premises 1 and 2

If a shipment is perishable, it was in a refrigerated truck; if it was in a refrigerated truck, it arrived on schedule. Therefore, Perishable shipment -> Arrived on schedule.

Combining two universal statements creates a valid deductive chain.

3

Evaluate the options against the deduced chain

The statement asserting that all perishable shipments arrived on schedule must strictly be true.

A valid GMAT inference must be 100 percent guaranteed by the stimulus.

Key Concept

Distinguishing Inferences from Assumptions and Speculations

Question 1613Question →

The table below provides financial performance metrics for five corporate divisions of Vertex Global:

Division	Revenue ($M)	Operating Cost ($M)	Profit Margin (%)	Employees
Alpha	120	90	25.0%	450
Beta	200	170	15.0%	800
Gamma	80	50	37.5%	250
Delta	150	105	30.0%	500
Epsilon	300	270	10.0%	1,200

Evaluate the following statement as True or False based on the provided table:

Statement: For more than half of the divisions listed, the Revenue per employee strictly exceeds $250,000.

True

False

Show answer & explanation

Answer: True

Answer

True. Exactly 3 out of the 5 divisions (Alpha, Gamma, and Delta) have a Revenue per employee greater than $250,000, which satisfies the condition of being more than half.

The correct evaluation is True because calculating the ratio of Revenue to Employees for each of the five divisions shows that Alpha (

266,667), Gamma (

320,000), and Delta (

300,000) all have a Revenue per employee above

250,000. Three out of five divisions represents 60% of the divisions, which is more than half.

Step-by-Step Solution

1

Understand the condition and metric required

Need to calculate Revenue per employee (Revenue in dollars divided by number of employees) for each division and check if it is strictly greater than $250,000.

The statement specifies 'strictly exceeds $250,000' and applies to 'more than half' (at least 3 out of 5) of the divisions.

2

Compute Revenue per employee for each division

Alpha:

120M / 450 =

266,667; Beta:

200M / 800 =

250,000; Gamma:

80M / 250 =

320,000; Delta:

150M / 500 =

300,000; Epsilon:

300M / 1,200 =

250,000.

Performing explicit division allows precise comparison against the threshold value of $250,000.

3

Evaluate the threshold condition across all divisions

Divisions exceeding

250,000: Alpha, Gamma, Delta (Total = 3 divisions). Divisions equal to

250,000: Beta, Epsilon (Total = 2 divisions).

Values exactly equal to $250,000 do not satisfy 'strictly exceeds'.

4

Determine overall Boolean truth value

3 out of 5 divisions is 60%, which is more than half (50%). Thus, the statement evaluates to True.

Comparing the count of meeting divisions (3) against half of the dataset size (2.5).

Key Concept

Table Analysis & Boolean Statement Evaluation

Question 1614Question →

An investment fund allocates its capital between two asset classes, Class $P$ and Class $Q$ . At the beginning of a given year, the ratio of capital in Class $P$ to capital in Class $Q$ was $3 : 2$ . During the year, Class $P$ earned an annual return of $r_p\%$ and Class $Q$ earned an annual return of $r_q\%$ . At the end of the year, a management fee of $2\%$ was deducted from the total ending value of Class $P$ , and a management fee of $5\%$ was deducted from the total ending value of Class $Q$ . Was the total dollar amount of the management fee deducted from Class $P$ greater than the total dollar amount of the management fee deducted from Class $Q$ ?

(1) $r_p - r_q = 10$
(2) At the end of the year, before management fees were deducted, the total value of Class $P$ was $60\%$ greater than the total value of Class $Q$ .

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.

Statement (2) alone allows us to express both fee amounts in terms of the single variable

V_Q

, the ending value of Class

Q

. Because

F_P = 0.02(1.6 V_Q) = 0.032 V_Q

and

F_Q = 0.05 V_Q

, we know with certainty that

F_P < F_Q

. This provides a definitive 'No' answer to whether

F_P > F_Q

, which makes Statement (2) alone sufficient. Statement (1) alone leaves the relationship dependent on the unconstrained value of

r_q

, so it is not sufficient.

Step-by-Step Solution

1

Algebraically rephrase the question target.

Let initial capital be

P_0

and

Q_0

, where

P_0 = 1.5 Q_0

. Ending values before fees are

V_P = 1.5 Q_0 (1 + \frac{r_p}{100})

and

V_Q = Q_0 (1 + \frac{r_q}{100})

. The fees are

F_P = 0.02 V_P = 0.03 Q_0 (1 + \frac{r_p}{100})

and

F_Q = 0.05 V_Q = 0.05 Q_0 (1 + \frac{r_q}{100})

. The question 'Is

F_P > F_Q

?' simplifies to 'Is

0.03(100 + r_p) > 0.05(100 + r_q)

?' or 'Is

3 r_p - 5 r_q > 200

?'

Rephrased targets clarify the exact mathematical relationship required to answer the Data Sufficiency prompt.

2

Evaluate Statement (1):

r_p - r_q = 10

.

Substituting

r_p = r_q + 10

into the inequality yields

3(r_q + 10) - 5 r_q = 30 - 2 r_q > 200

, which simplifies to

r_q < -85

. Since

r_q

can be any real number (e.g.,

r_q = 0

yields 'No', while

r_q = -100

yields 'Yes'), Statement (1) alone is NOT sufficient.

Without specific values for

r_q

, the inequality cannot be answered definitively.

3

Evaluate Statement (2):

V_P = 1.6 V_Q

.

We are given that

V_P = 1.6 V_Q

. Substituting this directly into the fee expressions gives

F_P = 0.02 V_P = 0.02 (1.6 V_Q) = 0.032 V_Q

. Since

F_Q = 0.05 V_Q

and portfolio value

V_Q > 0

,

0.032 V_Q

is strictly less than

0.05 V_Q

. Thus,

F_P > F_Q

is definitively FALSE.

A definitive 'No' answer is sufficient in Data Sufficiency decision logic.

Key Concept

Data Sufficiency Yes/No decision logic and algebraic target rephrasing for percentage adjustments and fee calculations.

Estimated Time:2m 0s

Question 1615Question →

[Tab 1: Municipal Adaptive Reuse Policy (2026 Directive)]
City Urban Redevelopment Authority Guidelines:
- Base Conversion Rebate: $50 per square foot of converted space for projects transforming Commercial Class B or Class C office space into residential housing.
- Environmental Standard Bonus: Projects achieving Tier-1 Green Certification receive an additional 20% bonus applied directly to their base conversion rebate.
- Affordable Housing Requirement & Exception: To qualify for any rebate, at least 15% of converted residential units must be designated as affordable housing for 20 years. *Exception*: Projects where the total converted space is under 40,000 square feet are exempt from this affordable housing quota while remaining fully eligible for base rebates and environmental bonuses.

[Tab 2: Project Portfolio Submissions (Q2 2026)]

Project ID	Original Property Class	Total Converted Space (sq ft)	Designated Affordable Units (% of total)	Environmental Certification Level
Project Alpha	Class B	35,000	10%	Tier-1 Green
Project Beta	Class A	50,000	20%	Tier-1 Green
Project Gamma	Class C	60,000	18%	Standard (Non-Tier-1)
Project Delta	Class B	45,000	12%	Tier-1 Green

[Tab 3: Zoning Board Audit Memorandum]
Memo from Chief Zoning Inspector:
- Project Alpha: Base space verified. Exempt from affordable housing quota due to square footage (< 40,000 sq ft). Approved for full rebate and applicable bonuses.
- Project Beta: Disqualified from the rebate program because the original property class was Class A (policy strictly limits base rebates to Class B/C properties).
- Project Delta: Audit confirms affordable housing quota of 12% is below the required 15% threshold for projects of 40,000 sq ft or larger; application denied.

Based on the Municipal Adaptive Reuse Policy, the Project Portfolio Submissions, and the Zoning Board Audit Memorandum, what is the total dollar amount of conversion rebates approved across all eligible projects submitted in Q2 2026?

$3,000,000

$4,750,000

$5,100,000

$4,800,000

$8,100,000

Show answer & explanation

Answer: $5,100,000

Answer

$5,100,000 total approved conversion rebates

The correct total of

5,100,000 is derived by synthesizing information across all three tabs. Project Alpha qualifies under the size exemption (< 40,000 sq ft) for a base rebate of

1,750,000 plus a 20% Tier-1 Green bonus (

350,000), giving

2,100,000. Project Beta is disqualified per Tab 3 because it is a Class A property. Project Gamma meets all criteria (Class C, >= 15% affordable units) for a base rebate of

3,000,000 without bonus. Project Delta is denied per Tab 3 due to insufficient affordable units. Summing Alpha (

2,100,000) and Gamma (

3,000,000) gives

5,100,000.

Step-by-Step Solution

1

Evaluate Project Alpha eligibility and rebate

Approved for $2,100,000 total

Tab 2 shows 35,000 sq ft Class B property. Tab 1 & Tab 3 state size < 40,000 sq ft exempts it from the 15% affordable housing quota (10% is acceptable). Base rebate =

35,000 \times

50 =

1,750,000

. Tier-1 Green certification adds a 20% bonus (

1,750,000 \times 0.20 =

350,000

). Total =

2,100,000$.

2

Evaluate Project Beta eligibility

Disqualified ($0)

Tab 3 audit memo explicitly states Project Beta is disqualified because its original property class was Class A.

3

Evaluate Project Gamma eligibility and rebate

Approved for $3,000,000 total

Tab 2 shows Class C property of 60,000 sq ft (>= 40,000 sq ft). Designated affordable units = 18% (>= 15% requirement). Base rebate =

60,000 \times

50 =

3,000,000

. Standard certification level means no Tier-1 bonus.

4

Evaluate Project Delta eligibility

Denied ($0)

Tab 3 audit memo confirms Delta is denied because 12% affordable units is below the mandatory 15% threshold for properties over 40,000 sq ft.

5

Sum total approved rebates across all projects

2,100,000 +

3,000,000 =

5,100,000

Adding the approved amounts for Project Alpha (

2,100,000) and Project Gamma (

3,000,000) yields $5,100,000.

Key Concept

Cross-tab multi-source synthesis incorporating policy rules, data tables, and explicit audit exclusions

Estimated Time:2m 30s

Question 1616Question →

The table below displays quarterly logistics metrics for five regional distribution hubs of a global shipping enterprise in 2025:

Hub	Total Units Shipped	Air Freight Share (%)	Q1 Avg Shipping Cost per Unit ($)	Q4 Avg Shipping Cost per Unit ($)
North	50,000	30%	120	168
South	60,000	40%	200	260
East	40,000	25%	150	213
West	75,000	20%	160	192
Central	30,000	35%	80	108

For the hub that experienced the greatest percentage increase in average shipping cost per unit from Q1 to Q4, what is the ratio of its air freight unit volume to the non-air freight unit volume of the hub with the highest total overall expenditure in Q4?

5 : 18

1 : 6

5 : 12

10 : 9

2 : 3

Show answer & explanation

Answer: $5 : 18$

Answer

The ratio of the air freight unit volume of the hub with the greatest percentage cost increase (East) to the non-air freight unit volume of the hub with the highest Q4 expenditure (South) is 5 : 18.

East has the greatest percentage cost increase (

42.0\%

), yielding

10,000

air freight units. South has the highest total Q4 expenditure (

\$15,600,000

), with a non-air freight unit volume of

36,000

. The simplified ratio of these two quantities is

10,000 : 36,000 = 5 : 18

.

Step-by-Step Solution

1

Calculate the percentage increase in average shipping cost per unit from Q1 to Q4 for each hub.

North:

\frac{168 - 120}{120} = 40.0\%

South:

\frac{260 - 200}{200} = 30.0\%

East:

\frac{213 - 150}{150} = 42.0\%

West:

\frac{192 - 160}{160} = 20.0\%

Central:

\frac{108 - 80}{80} = 35.0\%

Identify which hub achieved the greatest percentage increase in per-unit cost.

2

Identify the target hub and calculate its air freight unit volume.

The hub with the highest percentage increase is East (42.0%). Its air freight unit volume is

25\%

of

40,000 = 10,000

units.

Formulate the numerator for the final ratio.

3

Calculate total Q4 expenditure for each hub to find the hub with the highest overall expenditure.

North:

50,000 \times \$168 = \$8,400,000

South:

60,000 \times \$260 = \$15,600,000

East:

40,000 \times \$213 = \$8,520,000

West:

75,000 \times \$192 = \$14,400,000

Central:

30,000 \times \$108 = \$3,240,000

The hub with the highest total Q4 expenditure is South ($15,600,000).

4

Calculate the non-air freight unit volume for South.

South non-air freight share

= 100\% - 40\% = 60\%

. Non-air freight volume

= 60\%

of

60,000 = 36,000

units.

Formulate the denominator for the final ratio.

5

Compute and simplify the final ratio.

\frac{10,000}{36,000} = \frac{10}{36} = \frac{5}{18}

or

5 : 18

.

Express the relationship in simplest integer ratio form.

Key Concept

Multi-Step Tabular Ratio and Percentage Analysis

Question 1617Question →

Under regional environmental regulation protocols, a coastal marine sanctuary receives Tier-1 Protection status if and only if it contains a documented coral spawning site and strictly prohibits all commercial fishing activities. Based on these regulations, evaluate the following statement:

A coastal marine sanctuary that lacks a documented coral spawning site cannot receive Tier-1 Protection status.

True

False

Show answer & explanation

Answer: True

Answer

True. The statement is a valid deduction because a documented coral spawning site is a necessary condition for receiving Tier-1 Protection status.

The term 'if and only if' establishes a biconditional link, making a documented coral spawning site a strictly necessary condition for Tier-1 Protection status. Consequently, any sanctuary lacking such a site cannot meet the criteria for Tier-1 status, rendering the statement definitively True.

Step-by-Step Solution

1

Analyze the conditional structure of the stimulus premise.

Tier-1 Status

\iff

(Documented Coral Spawning Site AND Commercial Fishing Prohibited).

The phrase 'if and only if' denotes a biconditional relationship where both components are mutually necessary and sufficient.

2

Evaluate the condition presented in the statement.

The sanctuary lacks a documented coral spawning site.

We need to test what happens when one of the necessary conditions is negated.

3

Deduce the logical outcome based on the premise.

Since a necessary condition is negated, Tier-1 Status cannot be achieved (

\neg\text{Spawning Site} \implies \neg\text{Tier-1 Status}

).

Negating a necessary condition guarantees the negation of the outcome.

Key Concept

Necessary and sufficient conditions in biconditional logic statements

Question 1618Question →

If $a$ and $b$ are positive integers, is $a^2b$ divisible by $12$ ?

(1) $ab^2$ is divisible by $18$ .
(2) $a^3b$ is divisible by $72$ .

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.

Statement (2) alone guarantees that

a^3b

contains at least three factors of

2

and two factors of

3

. Analyzing the exponent bounds for non-negative integers proves that

a^2b

must contain at least two factors of

2

and one factor of

3

, ensuring

a^2b

is divisible by

12

. Statement (1) alone is insufficient because

a=3, b=6

makes

ab^2=108

(divisible by

18

) but

a^2b=54

(not divisible by

12

). Thus, Statement (2) ALONE is sufficient.

Step-by-Step Solution

1

Rephrase the target question in terms of prime factorization

For

a^2b

to be divisible by

12 = 2^2 \times 3^1

, we need

2 v_2(a) + v_2(b) \ge 2

and

2 v_3(a) + v_3(b) \ge 1

, where

v_p(n)

is the exponent of prime

p

in the prime factorization of

n

.

Decomposing divisibility into prime factor exponent inequalities allows definitive evaluation of sufficiency.

2

Evaluate Statement (1):

ab^2

is divisible by

18 = 2^1 \times 3^2

This gives

v_2(a) + 2 v_2(b) \ge 1

and

v_3(a) + 2 v_3(b) \ge 2

. Test counterexample

a=3, b=6

:

ab^2 = 3 \times 36 = 108

(divisible by 18), but

a^2b = 9 \times 6 = 54

, which is not divisible by 12.

A single valid counterexample proves Statement (1) is NOT sufficient.

3

Evaluate Statement (2):

a^3b

is divisible by

72 = 2^3 \times 3^2

This gives

3 v_2(a) + v_2(b) \ge 3

and

3 v_3(a) + v_3(b) \ge 2

. If

v_2(a) = 0

, then

v_2(b) \ge 3 \implies 2 v_2(a) + v_2(b) \ge 3 \ge 2

. If

v_2(a) \ge 1

, then

2 v_2(a) + v_2(b) \ge 2(1) + 0 = 2

. Similarly for prime 3: if

v_3(a) = 0

,

v_3(b) \ge 2 \implies 2 v_3(a) + v_3(b) \ge 2 \ge 1

; if

v_3(a) \ge 1

,

2 v_3(a) + v_3(b) \ge 2 \ge 1

. Thus

a^2b

is always divisible by 12.

Statement (2) strictly guarantees that the prime factor counts for 2 and 3 in

a^2b

meet or exceed the required thresholds, yielding a definitive 'Yes'.

Key Concept

Divisibility analysis using prime factor exponent inequalities in Data Sufficiency.

Question 1619Question →

A retailer sold standard boxes at $\$s$ each and premium boxes at $\$p$ each yesterday, generating a total revenue of $\$900$ . If the retailer sold $x$ standard boxes and $y$ premium boxes, where $x$ and $y$ are positive integers, did the retailer sell more standard boxes than premium boxes?

(1) Standard boxes cost $\$15$ each and premium boxes cost $\$25$ each.
(2) The average (arithmetic mean) price of all boxes sold yesterday was $\$18$ , and premium boxes cost $\$10$ more per box than standard boxes.

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

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

Answer

Both statements together are sufficient, but neither statement alone is sufficient.

The correct option is the one stating that both statements together are sufficient, but neither statement alone is sufficient. Statement (1) allows multiple positive integer pairs for

(x, y)

such that

x > y

in some cases and

x < y

in others, making it insufficient on its own. Statement (2) alone leaves the base price

s

unknown, so the ratio of standard to premium boxes cannot be determined without Statement (1). Combining

s = 15

from Statement (1) with Statement (2) establishes that

\frac{x}{y} = \frac{7}{3}

, which definitively proves

x > y

.

Step-by-Step Solution

1

Evaluate Statement (1) independently.

Statement (1) provides

s = 15

and

p = 25

, yielding the equation

15x + 25y = 900

, which simplifies to

3x + 5y = 180

. Testing positive integer solutions gives multiple valid pairs: for instance,

(x, y) = (55, 3)

yields

x > y

(Yes), while

(x, y) = (10, 30)

yields

x < y

(No). Because both Yes and No are possible, Statement (1) alone is NOT sufficient.

A statement must yield a single definitive Yes or No answer to be sufficient.

2

Evaluate Statement (2) independently without using information from Statement (1).

Statement (2) states that

p = s + 10

and the average price is

\frac{sx + py}{x + y} = 18

. Substituting

p = s + 10

gives

\frac{sx + (s + 10)y}{x + y} = 18

, which simplifies to

s + \frac{10y}{x + y} = 18

. Because the individual box price

s

is unknown,

\frac{y}{x + y}

can vary depending on

s

(e.g., if

s = 10

,

x < y

; if

s = 15

,

x > y

). Thus, Statement (2) alone is NOT sufficient.

Information from Statement (1) must never be carried over when testing Statement (2) independently.

3

Combine Statements (1) and (2).

From Statement (1),

s = 15

. Substituting

s = 15

into the simplified average equation from Statement (2),

15 + \frac{10y}{x + y} = 18

, gives

\frac{10y}{x + y} = 3 \implies 10y = 3x + 3y \implies 7y = 3x \implies \frac{x}{y} = \frac{7}{3}

. Since

x

and

y

are positive integers,

\frac{x}{y} > 1

, which definitively proves that

x > y

(Yes).

Combining the known price from Statement (1) with the weighted average equation from Statement (2) uniquely determines the ratio of

x

to

y

.

Key Concept

Statement Independence and Statement Combination in Data Sufficiency

Question 1620Question →

To revitalize downtown retail commerce, the city of Vaelen converted a five-block stretch of Main Street from a vehicle-accessible thoroughfare into a pedestrian-only zone. City officials reasoned that eliminating car traffic would encourage visitors to spend more time browsing local shops, thereby increasing total retail sales in the district. However, three months after the conversion, total retail sales along Main Street were 15 percent lower than during the same three-month period last year. Consequently, city officials concluded that the pedestrian zone failed to attract shoppers and directly harmed retail commerce. Which of the following, if true, most seriously weakens the city officials' conclusion?

Several boutique shop owners on Main Street reported that parking availability on adjacent side streets decreased significantly after the conversion.

During the three-month period following the conversion, overall retail sales throughout the entire city dropped by 35 percent due to a major regional economic downturn.

Suburban shopping malls located outside the city limits experienced a modest increase in customer traffic over the past year.

The city council originally planned to install additional outdoor seating and greenery along the promenade but postponed those physical improvements until next year.

Eliminating vehicle traffic on Main Street led to a measurable reduction in ambient air pollution levels within the downtown district.

Show answer & explanation

Answer: During the three-month period following the conversion, overall retail sales throughout the entire city dropped by 35 percent due to a major regional economic downturn.

Answer

The argument is most weakened by establishing that citywide retail sales fell by 35 percent during the same period, showing that Main Street actually outperformed the regional trend.

The conclusion asserts a direct causal relationship: the pedestrian conversion caused the 15 percent drop in retail sales. Showing that overall citywide retail sales plunged by 35 percent during the exact same timeframe provides crucial baseline context. It demonstrates that sales on Main Street actually declined far less than expected given the severe regional downturn, which strongly suggests the pedestrian zone buffered Main Street from a worse fate rather than causing the decline.

Step-by-Step Solution

1

Identify the main conclusion and premises.

Premise: Main Street sales fell 15% after pedestrian conversion. Conclusion: The conversion failed to attract shoppers and directly caused the sales decline.

Understanding the precise causal link asserted by the author is necessary to weaken it.

2

Identify the unstated assumption in the author's causal leap.

The author assumes no external factor (such as a broader economic slump) was responsible for the 15% drop in sales.

A weakening answer choice will often present an alternative cause or show that the baseline performance was affected by outside variables.

3

Evaluate the choices to find evidence undermining the assumed cause.

Showing that citywide retail sales dropped 35% demonstrates that Main Street's 15% drop was actually a relative success, undermining the claim that the pedestrian zone harmed commerce.

If the broader market fell much more sharply, the pedestrian zone likely helped protect Main Street from an even steeper decline.

Key Concept

Causal Fallacy and Baseline Confounding Variables

Answer

Step-by-Step Solution

Key Concept

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