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Question 1481Question →

In a graduating class of 120120 students, each student participated in at least one of two extracurricular activities: the Science Club or the Debate Team. The mean score on a national mathematics exam for all students who participated in the Science Club was 8585, and the mean score for all students who participated in the Debate Team was 8080. What was the mean mathematics score for all 120120 students in the graduating class?

(1) Exactly 4040 students participated in both the Science Club and the Debate Team, and their mean mathematics score on the exam was 9090.
(2) The total number of students who participated in the Science Club was equal to the total number of students who participated in the Debate Team.

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.
Both statements together are sufficient. Statement (1) establishes that 4040 students are in both activities with a mean score of 9090, leaving 8080 students in only one activity, but does not specify how those 8080 students are divided between the two clubs. Statement (2) specifies that the two club sizes are equal, which implies that the number of students participating only in Science equals the number participating only in Debate. Combining these facts determines that exactly 4040 students are in Science only, 4040 in Debate only, and 4040 in both, allowing the total score sum (96009600) and overall mean (8080) to be uniquely calculated.

Step-by-Step Solution

1
Set up the algebraic model for overlapping set counts and statistics sums.
Let aa be the number of students in Science Club only, bb be the number of students in Debate Team only, and cc be the number of students in both. a+b+c=120a + b + c = 120. Total sum of scores = 85(a+c)+80(b+c)−Sum(S∩D)85(a+c) + 80(b+c) - \text{Sum}(S \cap D).
Scores of students in the intersection are counted in both club averages, so subtracting the overlap sum prevents double counting.
2
Evaluate Statement (1) independently.
Statement (1) gives c=40c = 40 and Sum(S∩D)=40×90=3600\text{Sum}(S \cap D) = 40 \times 90 = 3600. Then a+b=80a + b = 80, and Total Sum = 85a+80b+3000=5a+940085a + 80b + 3000 = 5a + 9400. Since aa can vary from 00 to 8080, Total Sum is not unique.
Statement (1) alone is insufficient because aa remains a free variable.
3
Evaluate Statement (2) independently.
Statement (2) gives a+c=b+c  ⟹  a=ba + c = b + c \implies a = b. Without cc or intersection scores, Total Sum cannot be computed.
Statement (2) alone is insufficient.
4
Evaluate Statement (1) and Statement (2) combined.
From (1), a+b=80a + b = 80 and c=40c = 40. From (2), a=ba = b. Thus 2a=80  ⟹  a=402a = 80 \implies a = 40 and b=40b = 40. Substituting a=40a = 40 gives Total Sum = 5(40)+9400=96005(40) + 9400 = 9600. Overall mean = 9600/120=809600 / 120 = 80.
The combined system yields a single unique overall average score.

Key Concept

Weighted averages in overlapping sets using principle of inclusion-exclusion for statistical sums.
Estimated Time:2m 0s
Question 1482Question →

To decrease peak-hour patient wait times, a regional healthcare provider plans to launch an automated online triage system for its urgent care clinics. The system will evaluate walk-in patients upon arrival and redirect those with minor, non-emergency symptoms to scheduled telehealth consultations later the same day. Administrators reason that transferring a substantial portion of non-urgent visits away from physical clinics will alleviate waiting room overcrowding. Which of the following would be most useful to evaluate in determining whether the provider's plan will achieve its goal?

Show answer & explanation

Answer: Whether a significant proportion of patients redirected to telehealth consultations subsequently seek in-person clinic care during peak hours because their symptoms persist or require physical examination

Answer

Evaluating whether redirected telehealth patients still end up visiting the clinic in person during peak hours is the most useful factor, as it determines whether the plan actually reduces clinic volume.
The correct option addresses whether the redirected patients actually stay out of the clinic during peak hours. If a high percentage of telehealth-redirected patients still end up visiting the clinic in person during peak hours because their condition requires physical examination, the plan will fail to alleviate peak-hour wait times. Conversely, if very few return, the plan will succeed. Passing this variance test makes this information essential for evaluating the plan.

Step-by-Step Solution

1
Identify the core goal and the proposed mechanism of the plan.
Goal: Reduce peak-hour patient wait times at urgent care clinics. Plan: Redirect non-urgent walk-in patients to same-day telehealth appointments.
Evaluating a plan requires understanding how the proposed action is supposed to lead to the intended outcome.
2
Apply the Variance Test to the key underlying assumption.
The plan assumes that redirecting patients to telehealth will permanently remove them from the peak-hour in-person clinic queue.
If redirected patients return to the physical clinic during peak hours anyway, the queue does not shrink and wait times remain high.
3
Select the option that tests whether this crucial assumption holds true.
Determining if redirected patients still require in-person care during peak hours directly determines the success or failure of the plan.
Opposite answers to this question yield opposite outcomes for the efficacy of the plan.

Key Concept

Evaluating Plan Efficacy and Variance Test
Estimated Time:1m 30s
Question 1483Question →

If aa and bb are non-zero real numbers, is ∣a+b∣>∣a−b∣|a + b| > |a - b|?

(1) ∣a+2b∣<∣a−2b∣|a + 2b| < |a - 2b|
(2) ∣a∣b+∣b∣a<0\frac{|a|}{b} + \frac{|b|}{a} < 0

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Rephrasing the question stem by squaring both sides gives ∣a+b∣2>∣a−b∣2  ⟺  (a+b)2>(a−b)2  ⟺  4ab>0  ⟺  ab>0|a + b|^2 > |a - b|^2 \iff (a + b)^2 > (a - b)^2 \iff 4ab > 0 \iff ab > 0. Statement (1) simplifies similarly by squaring both sides to (a+2b)2<(a−2b)2  ⟺  8ab<0  ⟺  ab<0(a + 2b)^2 < (a - 2b)^2 \iff 8ab < 0 \iff ab < 0. Since ab<0ab < 0 guarantees that ab>0ab > 0 is false, Statement (1) produces a definitive 'No' and is therefore sufficient. Statement (2) is satisfied when both aa and bb are negative (giving ab>0ab > 0, a 'Yes' answer) as well as when aa and bb have opposite signs with ∣a∣>∣b∣|a| > |b| (giving ab<0ab < 0, a 'No' answer). Because Statement (2) permits both outcomes, it is insufficient.

Step-by-Step Solution

1
Rephrase the question stem target using algebraic properties of absolute values.
Squaring both non-negative sides of ∣a+b∣>∣a−b∣|a + b| > |a - b| yields (a+b)2>(a−b)2  ⟹  a2+2ab+b2>a2−2ab+b2  ⟹  4ab>0  ⟹  ab>0(a + b)^2 > (a - b)^2 \implies a^2 + 2ab + b^2 > a^2 - 2ab + b^2 \implies 4ab > 0 \implies ab > 0. The question asks: 'Is ab>0ab > 0?'
Simplifying the stem target into a fundamental sign constraint (ab>0ab > 0) prevents algebraic errors during statement evaluation.
2
Evaluate Statement (1): ∣a+2b∣<∣a−2b∣|a + 2b| < |a - 2b|.
Squaring both sides yields (a+2b)2<(a−2b)2  ⟹  a2+4ab+4b2<a2−4ab+4b2  ⟹  8ab<0  ⟹  ab<0(a + 2b)^2 < (a - 2b)^2 \implies a^2 + 4ab + 4b^2 < a^2 - 4ab + 4b^2 \implies 8ab < 0 \implies ab < 0.
Since ab<0ab < 0, abab cannot be greater than 00. This yields a definitive 'No' to the question 'Is ab>0ab > 0?'. A definitive 'No' is sufficient.
3
Evaluate Statement (2): ∣a∣b+∣b∣a<0\frac{|a|}{b} + \frac{|b|}{a} < 0.
Combine the fractions: a∣a∣+b∣b∣ab<0\frac{a|a| + b|b|}{ab} < 0. Test specific cases:
- Case A: a=−2,b=−2  ⟹  ∣−2∣−2+∣−2∣−2=−2<0a = -2, b = -2 \implies \frac{|-2|}{-2} + \frac{|-2|}{-2} = -2 < 0. Here ab=4>0ab = 4 > 0 (Answer: YES).
- Case B: a=3,b=−1  ⟹  ∣3∣−1+∣−1∣3=−3+13=−83<0a = 3, b = -1 \implies \frac{|3|}{-1} + \frac{|-1|}{3} = -3 + \frac{1}{3} = -\frac{8}{3} < 0. Here ab=−3<0ab = -3 < 0 (Answer: NO).
Since Statement (2) allows both a 'Yes' and a 'No' response to whether ab>0ab > 0, Statement (2) alone is not sufficient.

Key Concept

Data Sufficiency Yes/No decision logic combined with distance and squaring properties of absolute value inequalities.
Question 1484Question →

To evaluate the viability of a newly developed AI-driven inventory management software, a logistics firm tested the program across five of its highest-performing regional fulfillment centers during a six-month trial. Because all five fulfillment centers reported a 25 percent reduction in processing delays during the trial, executive management concluded that implementing the software across all fifty of the firm's fulfillment centers nationwide would yield a similar 25 percent improvement in overall operational efficiency. Which of the following best describes a flaw in the executive management's reasoning?

Show answer & explanation

Answer: It draws a broad conclusion about the entire network based on a sample of facilities that may not be representative of the firm's standard fulfillment centers.

Answer

The argument's flaw is that it draws a broad conclusion about the entire network based on a sample of facilities that may not be representative of the firm's standard fulfillment centers.
The correct answer accurately identifies an unrepresentative sample flaw. The executive management attempts to extrapolate results from five exceptionally high-performing centers to all fifty fulfillment centers. Facilities that already perform at the highest level may have better technical infrastructure, management, or personnel, making them far better equipped to integrate new AI software successfully than average or underperforming centers. Thus, generalizing these trial results to the entire network is logically flawed.

Step-by-Step Solution

1
Deconstruct the argument into premise and conclusion.
Premise: Five top-performing fulfillment centers achieved a 25% reduction in processing delays during a six-month trial. Conclusion: Implementing the software across all 50 fulfillment centers nationwide will produce a similar 25% efficiency improvement overall.
Identifying the structural gap between the evidence (sample) and the claim (population) is essential for spoting inductive reasoning errors.
2
Analyze the sample characteristics for selection bias.
The sample consists strictly of 'highest-performing' fulfillment centers, which likely possess superior infrastructure, staff expertise, or management that average or low-performing centers lack.
An unrepresentative sample invalidates inductive generalizations to a broader, more heterogeneous population.
3
Select the choice that articulates this sampling flaw directly.
The correct response points out that the conclusion relies on a sample of facilities that may not represent the typical conditions across all remaining facilities in the firm.
This directly matches the core logical vulnerability of unrepresentative sampling.

Key Concept

Sampling and Generalization Flaws
Question 1485Question →

To streamline drug delivery and eliminate physical retrieval delays, a hospital installed automated medication-dispensing kiosks directly inside every emergency department treatment room. However, despite the medications now being physically stored within arms' reach of attending nurses, official records show that the average total time elapsed between a physician prescribing a medication and the patient receiving it increased by nearly 30 percent after the kiosks were introduced. Which of the following, if true, most helps to resolve the apparent discrepancy described above?

Show answer & explanation

Answer: Under the new system, each kiosk remains locked until an off-site pharmacist performs a remote safety verification for the order, whereas previously nurses retrieved drugs immediately and logged them afterward.

Answer

The apparent paradox is resolved by the fact that under the new system, each kiosk requires off-site pharmacist remote verification before unlocking, whereas nurses previously retrieved drugs immediately and logged them afterward.
The correct answer provides a confounding operational shift that explains both facts: while the physical distance to the medication dropped to zero, a mandatory prerequisite delay (waiting for an off-site pharmacist to verify and unlock the kiosk) was added to the workflow. Previously, nurses retrieved medications first and logged them later, so patient receipt occurred prior to verification. Thus, total elapsed time from prescription to patient receipt increased despite physical proximity.

Step-by-Step Solution

1
Identify the two seemingly contradictory facts in the stimulus.
Fact 1: Automated dispensing kiosks were placed directly in treatment rooms to eliminate physical retrieval delays. Fact 2: The average elapsed time between prescribing and patient receipt of medication increased by 30%.
Resolving a discrepancy requires establishing what needs to be explained without denying either premise.
2
Determine what type of information is needed to reconcile the premises.
Look for a factor that explains how eliminating physical travel could coincide with introducing a new administrative, procedural, or verification bottleneck into the total elapsed time.
A valid resolution must account for both facts simultaneously by revealing a hidden bottleneck or shift in workflow.
3
Evaluate the option choices to find the one that introduces an overriding operational bottleneck.
The option noting that kiosks require remote pharmacist authorization prior to dispensing explains why total elapsed time grew even though physical travel distance shrank.
The added delay from waiting for remote clearance outweighs the time saved on physical walking.

Key Concept

Resolving Paradoxes and Discrepancies: Workflow Bottlenecks vs. Physical Proximity
Question 1486Question →

Tab 1: Supply Chain Audit Memorandum (Q1 2026)
The quarterly audit report concludes that Supplier Alpha achieved a 0%0\% defect rate for all 1000010{}000 units of Component X received during Q1 2026. The audit's conclusion relies strictly on receiving-stage inspection records confirming that 100%100\% of delivered batches were logged as defect-free upon arrival.

Tab 2: Quality Control Standard Operating Procedure
Standard receiving protocol requires all precision electronic parts to undergo Quality Check 1 (QC-1) for visual/physical integrity and Quality Check 2 (QC-2) for thermal stress resistance before entry into inventory. However, components procured under "Express Procurement" status bypass QC-2 at receiving and are immediately marked as "Cleared at Entry." For Express Procurement items, thermal stress defects are recorded later during final post-assembly stress testing.

Tab 3: Plant Operations Defect Log (Q1 2026)
All 1000010{}000 units of Component X supplied by Supplier Alpha in Q1 2026 were procured under Express Procurement contracts. During final post-assembly stress testing of finished products, 400400 units of Component X suffered thermal breakdown and failed inspection.

Based on the information provided across the three tabs, which of the following statements help reconcile the apparent contradiction between the receiving audit's 0%0\% defect rate in Tab 1 and the 400400 thermal failures reported in Tab 3? Select all that apply.

Select all that apply

Show answer & explanation

Answer: The 0%0\% defect rate in the receiving audit reflects only initial QC-1 clearance, which Express Procurement shipments pass without receiving-stage thermal stress testing.; Thermal stress defects in Component X were captured only during final assembly testing because Express Procurement policy defers thermal testing for such shipments to the post-assembly stage.

Answer

The statements explaining that the receiving audit only reflects initial QC-1 clearance without receiving-stage thermal testing, and that thermal stress defects were logged post-assembly due to Express Procurement policy deferral, correctly reconcile the discrepancy.
The apparent contradiction between the 0%0\% defect rate at receiving (Tab 1) and the 400400 thermal breakdowns during assembly (Tab 3) is resolved by Tab 2. Because Supplier Alpha's shipment was made under Express Procurement status, the parts bypassed receiving-stage thermal testing (QC-2) and were logged as 'Cleared' based solely on QC-1. Thermal stress failures were only revealed when testing occurred at final assembly. Thus, both the statement noting that receiving audit logs reflect only QC-1 clearance and the statement noting that thermal defects were deferred to post-assembly testing under Express Procurement policy correctly explain the discrepancy.

Step-by-Step Solution

1
Identify the core discrepancy between Tab 1 and Tab 3.
Tab 1 reports a 0%0\% defect rate at receiving for 1000010{}000 units of Component X. Tab 3 reports 400400 thermal failures (4%4\%) of Component X during final assembly testing.
Resolving a discrepancy requires contrasting the scope and metrics of the conflicting reports.
2
Analyze Tab 2 for policy rules that bridge receiving data and assembly data.
Standard receiving requires QC-1 (physical) and QC-2 (thermal). Express Procurement items skip receiving QC-2 and are marked 'Cleared at Entry', while thermal defects are logged later in final assembly testing.
Understanding testing protocol exceptions explains why receiving logs miss specific failure modes.
3
Evaluate the statements to select valid reconciliation mechanisms.
The statement highlighting that receiving-stage records included only QC-1 clearance for Express Procurement items, and the statement highlighting that thermal defects defer to post-assembly logs under Express Procurement policy, both correctly reconcile the conflicting reports.
Both selected statements accurately synthesize the procedural exception in Tab 2 with the observational scope differences between Tab 1 and Tab 3.

Key Concept

Discrepancy Resolution via Scope and Procedural Exceptions Across Multiple Sources
Question 1487Question →

[Tab 1: Reimbursement Policy]
Apex Logistics Freight Reimbursement Rules:
- Standard shipments delivered to Region A or Region B qualify for a 50basereimbursement.−ShipmentsdeliveredtoRegionCqualifyfora50 base reimbursement. - Shipments delivered to Region C qualify for a 50 base reimbursement ONLY IF the total package weight exceeds 20 kg. Otherwise, 0basereimbursementisgranted.−Anefficiencybonusof0 base reimbursement is granted. - An efficiency bonus of 15 is awarded to any shipment delivered in under 24 hours, regardless of destination region or package weight.

[Tab 2: Shipment Log]
Shipment IDDestination RegionPackage WeightDelivery Time
Shipment 101Region A15 kg18 hours
Shipment 102Region C25 kg30 hours
Shipment 103Region C12 kg20 hours
Shipment 104Region B18 kg26 hours

Based on the information in the Reimbursement Policy and Shipment Log tabs, what is the total reimbursement amount awarded for Shipment 103?

Show answer & explanation

Answer: $15

Answer

The total reimbursement amount awarded for Shipment 103 is $15.
To find the total reimbursement for Shipment 103, synthesize information from both tabs. From Tab 2, Shipment 103 is sent to Region C, weighs 12 kg, and takes 20 hours. Cross-referencing Tab 1: Region C shipments only receive the 50basereimbursementiftheirweightexceeds20kg.Because12kgdoesnotexceed20kg,thebasereimbursementis50 base reimbursement if their weight exceeds 20 kg. Because 12 kg does not exceed 20 kg, the base reimbursement is 0. However, Tab 1 also awards a 15bonusforanyshipmentdeliveredunder24hours.Because20hoursislessthan24hours,Shipment103receivesthe15 bonus for any shipment delivered under 24 hours. Because 20 hours is less than 24 hours, Shipment 103 receives the 15 bonus. Adding 0base+0 base + 15 bonus yields $15.

Step-by-Step Solution

1
Evaluate base reimbursement eligibility from Tab 1 and Tab 2
Shipment 103 goes to Region C and weighs 12 kg. According to Tab 1, Region C shipments require a weight over 20 kg to qualify for the 50basereimbursement.Since12kgisnotgreaterthan20kg,basereimbursement=50 base reimbursement. Since 12 kg is not greater than 20 kg, base reimbursement = 0.
Policy rules specify a strict conditional weight threshold for Region C.
2
Evaluate efficiency bonus eligibility from Tab 1 and Tab 2
Shipment 103 was delivered in 20 hours. Tab 1 states any shipment delivered in under 24 hours receives a 15efficiencybonus,regardlessofregionorweight.Since20hours<24hours,efficiencybonus=15 efficiency bonus, regardless of region or weight. Since 20 hours < 24 hours, efficiency bonus = 15.
The delivery time threshold applies universally across all regions.
3
Sum base reimbursement and efficiency bonus
0basereimbursement+0 base reimbursement + 15 efficiency bonus = $15 total.
Combining synthesized data across both tabs yields the final total payout.

Key Concept

Multi-Source Policy and Quantitative Data Synthesis
Estimated Time:1m 0s
Question 1488Question →

At a technical conference, a total of 150150 software engineers attended at least one of two technical sessions: System Architecture or Distributed Systems. Exactly 9090 engineers attended the System Architecture session. If the mean years of experience for all 150150 engineers combined was 88 years, what was the mean years of experience for the engineers who attended ONLY the Distributed Systems session?

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The correct answer is Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Rephrasing the question stem reveals that the total group of 150 engineers is divided into two disjoint subsets: the 90 engineers in the System Architecture session and the 60 engineers who attended ONLY the Distributed Systems session. Because the total experience of all 150 engineers is fixed at 1200 years (150 × 8), knowing the mean experience of the 90 System Architecture engineers in Statement (1) allows calculation of their total experience sum (90 × 7.5 = 675), which directly yields the remaining experience sum (1200 - 675 = 525) and mean (525 / 60 = 8.75) for the engineers in ONLY the Distributed Systems session. Statement (2) gives information about the overlap group but leaves the experience sum of the engineers in ONLY the System Architecture session unknown.

Step-by-Step Solution

1
Rephrase the question stem using set relationships and statistics formulas.
Let SS be System Architecture attendees (∣S∣=90|S| = 90) and DD be Distributed Systems attendees. The total combined group is S∪DS \cup D with ∣S∪D∣=150|S \cup D| = 150. The number of engineers attending ONLY Distributed Systems is ∣D∖S∣=∣S∪D∣−∣S∣=150−90=60|D \setminus S| = |S \cup D| - |S| = 150 - 90 = 60.
Since every attendee is in at least one session, the total group consists of all attendees in SS plus those in D∖SD \setminus S, which are mutually disjoint sets.
2
Express the total sum of experience and set up the target equation.
Total combined experience sum Ttotal=150×8=1200T_{\text{total}} = 150 \times 8 = 1200. Since SS and D∖SD \setminus S partition the entire population, Ttotal=TS+TD∖ST_{\text{total}} = T_S + T_{D \setminus S}, where TST_S is the sum of experience of all 9090 engineers in SS. Therefore, TD∖S=1200−TST_{D \setminus S} = 1200 - T_S, and the target mean is TD∖S60=1200−TS60\frac{T_{D \setminus S}}{60} = \frac{1200 - T_S}{60}.
Finding the mean experience for D∖SD \setminus S depends entirely on finding the total experience sum TST_S of the 9090 engineers in System Architecture.
3
Evaluate Statement (1): The mean years of experience for the engineers who attended the System Architecture session was 7.57.5 years.
TS=90×7.5=675T_S = 90 \times 7.5 = 675. Then TD∖S=1200−675=525T_{D \setminus S} = 1200 - 675 = 525. Target mean =52560=8.75= \frac{525}{60} = 8.75 years. Statement (1) is SUFFICIENT.
Statement (1) directly gives the mean of set SS, allowing exact computation of TST_S and thus the target mean.
4
Evaluate Statement (2): Exactly 4040 engineers attended BOTH sessions, and their mean years of experience was 99 years.
This gives ∣S∩D∣=40|S \cap D| = 40 and sum TS∩D=40×9=360T_{S \cap D} = 40 \times 9 = 360. Set SS is divided into S∖DS \setminus D (size 5050) and S∩DS \cap D (size 4040). TS=TS∖D+360T_S = T_{S \setminus D} + 360. Since TS∖DT_{S \setminus D} remains unknown, TST_S cannot be determined. Statement (2) is INSUFFICIENT.
Without the experience sum or mean of the engineers who attended ONLY System Architecture, we cannot determine TST_S.

Key Concept

Partitioning combined sets in weighted averages and Data Sufficiency rephrasing
Question 1489Question →

The table below displays performance metrics for six employees at a technology firm:

EmployeeDepartmentExperience (Years)Completed Projects
AlexMarketing412
BiancaSales615
CarlosMarketing58
DianaEngineering314
EvanSales710
FionaMarketing818

How many employees work in the Marketing department AND have completed more than 10 projects?

Show answer & explanation

Answer: 2

Answer

2 employees meet both conditions.
To satisfy the criteria, an employee must meet both conditions: Department must be 'Marketing' AND Completed Projects must be strictly greater than 10. Evaluating each employee: Alex (Marketing, 12 projects) meets both conditions; Carlos (Marketing, 8 projects) fails the project threshold; Fiona (Marketing, 18 projects) meets both conditions. No other employees belong to Marketing. Thus, exactly 2 employees qualify.

Step-by-Step Solution

1
Identify the multi-column filter criteria from the question stem.
The criteria require Department = 'Marketing' AND Completed Projects > 10.
Both conditions must be simultaneously true for an employee to qualify.
2
Evaluate each row against both conditions.
- Alex: Marketing (Yes), 12 Projects > 10 (Yes) → Qualifies
- Bianca: Sales (No), 15 Projects > 10 (Yes) → Does not qualify
- Carlos: Marketing (Yes), 8 Projects > 10 (No) → Does not qualify
- Diana: Engineering (No), 14 Projects > 10 (Yes) → Does not qualify
- Evan: Sales (No), 10 Projects > 10 (No) → Does not qualify
- Fiona: Marketing (Yes), 18 Projects > 10 (Yes) → Qualifies
Systematic row-by-row verification prevents missed criteria.
3
Count the qualifying rows.
Alex and Fiona qualify, giving a total count of 2.
Only rows satisfying both conditions are included in the final sum.

Key Concept

Conjunctive (AND) Multi-Column Table Filtering
Question 1490Question →

A logistics company analyzed the operational downtime of a fleet of 8080 delivery trucks over a one-month period. Each truck in the fleet completed at least one of two specialized maintenance programs: Program A or Program B. The arithmetic mean downtime for trucks that completed only Program A was 1212 hours, and the arithmetic mean downtime for trucks that completed only Program B was 1818 hours. What was the average downtime per truck, in hours, for all 8080 trucks in the fleet?

(1) Exactly 5050 trucks completed Program A, and exactly 4545 trucks completed Program B.
(2) The total downtime of all trucks in the fleet that completed Program B was 765765 hours.

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 response identifies that both statements together provide complementary pieces of required information: the first statement determines the number of trucks in the 'only A' group (3535 trucks), while the second statement provides the combined downtime of all trucks in the 'Program B' group (765765 hours). Together, they uniquely specify the fleet's total downtime as 12(35)+765=118512(35) + 765 = 1185 hours, giving a single average of 14.812514.8125 hours.

Step-by-Step Solution

1
Define set variables and express the target fleet average in terms of known and unknown quantities.
Let nAn_A be the number of trucks completing only Program A, nBn_B be the number of trucks completing only Program B, and nABn_{AB} be the number of trucks completing both programs. The total number of trucks is nA+nB+nAB=80n_A + n_B + n_{AB} = 80. The total downtime of the fleet is Ttotal=(12⋅nA)+TBT_{total} = (12 \cdot n_A) + T_B, where TBT_B is the total downtime of all trucks that completed Program B (which comprises trucks completing only B and trucks completing both A and B).
Partitioning the fleet into trucks completing only Program A and trucks completing Program B allows us to rephrase the total downtime simply as 12nA+TB12 n_A + T_B.
2
Evaluate Statement (1) independently.
Statement (1) states that nA+nAB=50n_A + n_{AB} = 50 and nB+nAB=45n_B + n_{AB} = 45. Since (nA+nAB)+(nB+nAB)−nAB=80(n_A + n_{AB}) + (n_B + n_{AB}) - n_{AB} = 80, we get 50+45−nAB=80⇒nAB=1550 + 45 - n_{AB} = 80 \Rightarrow n_{AB} = 15. This yields nA=35n_A = 35 and nB=30n_B = 30. However, we do not know TBT_B or the downtime of the 1515 trucks in both programs, so the fleet average cannot be calculated. Statement (1) alone is NOT sufficient.
Knowing set counts alone does not supply the necessary downtime data for the overlapping region.
3
Evaluate Statement (2) independently.
Statement (2) gives TB=765T_B = 765 hours. Substituting this into our total downtime expression yields Ttotal=12nA+765T_{total} = 12 n_A + 765. Since nAn_A (the number of trucks completing only Program A) is unknown, TtotalT_{total} cannot be uniquely calculated. Statement (2) alone is NOT sufficient.
Without knowing nAn_A, the contribution of trucks completing only Program A to total downtime cannot be determined.
4
Evaluate Statements (1) and (2) together.
From Statement (1), nA=35n_A = 35. From Statement (2), TB=765T_B = 765. Thus, Ttotal=12(35)+765=420+765=1185T_{total} = 12(35) + 765 = 420 + 765 = 1185 hours. The average downtime per truck is 118580=14.8125\frac{1185}{80} = 14.8125 hours, which is a unique numerical value. Both statements together are SUFFICIENT.
Combining nA=35n_A = 35 with TB=765T_B = 765 uniquely determines the fleet's total downtime and overall average.

Key Concept

Overlapping set partitioning and weighted averages in Data Sufficiency
Question 1491Question →

To address declining attendance, the city history museum recently eliminated its admission fee, expecting the policy to attract first-time visitors. Six months after the policy took effect, total monthly attendance figures were identical to those recorded during the same period in the previous year. Museum administrators concluded that free admission failed to attract first-time visitors because local residents simply lack interest in regional history.

Which of the following, if true, most seriously weakens the administrators' conclusion?

Show answer & explanation

Answer: During the six-month period following the policy change, major road construction rendered the museum's primary parking area inaccessible, causing a sharp drop in visits by regular patrons.

Answer

The statement regarding road construction rendering the parking area inaccessible weakens the conclusion by demonstrating that total attendance could remain flat even if first-time visitor numbers increased.
The conclusion relies on equating flat total attendance with a failure to attract first-time visitors. The correct option demonstrates that regular patron attendance dropped significantly due to parking accessibility issues. Consequently, total attendance could remain unchanged even if a substantial number of first-time visitors responded to the free admission offer, thereby exposing a flaw in the administrators' reasoning.

Step-by-Step Solution

1
Identify the argument's premises and conclusion
Premise: Total attendance remained identical before and after eliminating entry fees. Conclusion: Free admission failed to attract first-time visitors because local residents lack interest.
Understanding the logic gap requires clearly isolating what evidence was used to justify the conclusion.
2
Identify the unstated assumption
The argument assumes that no other factor reduced attendance among existing regular visitors during the same six-month period.
If regular attendance dropped simultaneously, total attendance numbers could mask a rise in first-time visitors.
3
Evaluate the correct weakening option
The option noting that road construction disrupted parking and caused a sharp drop in regular patrons shows that first-time visitor numbers could have increased while total attendance stayed constant.
Demonstrating an offsetting decline in another segment of visitors breaks the link between static overall attendance and the supposed failure to attract new visitors.

Key Concept

Evaluating alternative causes and offsetting variables in causal argument evaluation
Question 1492Question →

If nn is a positive real number, is nn an integer?

(1) n+6nn + \frac{6}{n} is an integer.
(2) n2+36n2n^2 + \frac{36}{n^2} is an integer.

Show answer & explanation

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

Answer

Statements (1) and (2) TOGETHER are NOT sufficient to determine whether nn is an integer.
The correct answer identifies that neither statement alone is sufficient, and combining them offers no additional constraint because the second statement is algebraically derived by squaring the first. Since non-integer real numbers such as n=3+3n = 3 + \sqrt{3} satisfy both statements, the statements together remain insufficient.

Step-by-Step Solution

1
Evaluate Statement (1) by setting n+6n=kn + \frac{6}{n} = k, where kk is an integer.
Multiplying by nn gives n2−kn+6=0n^2 - kn + 6 = 0, which yields n=k±k2−242n = \frac{k \pm \sqrt{k^2 - 24}}{2}. For nn to be a real number, we need k2≥24k^2 \ge 24, so k≥5k \ge 5.
We must test whether all positive real solutions for nn under this condition are integers.
2
Test specific integer values for kk in Statement (1).
If k=5k = 5, then n=5±12n = \frac{5 \pm 1}{2}, giving n=3n = 3 or n=2n = 2 (both are integers, yielding a YES answer). However, if k=6k = 6, then n=6±122=3±3n = \frac{6 \pm \sqrt{12}}{2} = 3 \pm \sqrt{3}, which is a positive real number but NOT an integer (yielding a NO answer).
Since Statement (1) permits both integer and non-integer values for nn, Statement (1) ALONE is NOT sufficient.
3
Evaluate Statement (2) independently and analyze its algebraic relationship to Statement (1).
If n+6n=kn + \frac{6}{n} = k, then squaring both sides gives (n+6n)2=n2+12+36n2=k2\left(n + \frac{6}{n}\right)^2 = n^2 + 12 + \frac{36}{n^2} = k^2, which implies n2+36n2=k2−12n^2 + \frac{36}{n^2} = k^2 - 12. If kk is an integer, k2−12k^2 - 12 is automatically an integer.
This shows Statement (2) is logically and algebraically implied by Statement (1).
4
Evaluate Statements (1) and (2) together.
Because Statement (2) provides zero new information beyond Statement (1), combining them does not eliminate the non-integer solution n=3+3n = 3 + \sqrt{3}. Thus, the question cannot be answered definitively.
Redundant statements cannot resolve insufficiency present in the individual statements.

Key Concept

Number Properties and Integer Constraints in Data Sufficiency
Estimated Time:2m 30s
Question 1493Question →

Read the argument below regarding environmental policy and marine mining, then match each statement from the text to its corresponding logical role within the argument:

"Proponents of deep-sea polymetallic nodule mining argue that extracting seabed minerals is essential to supply metals for green technology transitions without expanding terrestrial mining's ecological footprint. However, recent oceanographic surveys indicate that benthic ecosystems recover far more slowly from physical disturbance than land-based biomes do. Because deep-sea sediment plumes can travel hundreds of kilometers, disrupting midwater marine food webs, the environmental costs of abyssal mining are likely to exceed those of conventional land extraction. Therefore, international regulators should institute an immediate moratorium on commercial seabed mining, regardless of projected economic benefits."

Click a left item, then click its matching right item

Items

Deep-sea polymetallic nodule mining is essential to supply metals for green technology transitions without expanding terrestrial mining's ecological footprint.
Benthic ecosystems recover far more slowly from physical disturbance than land-based biomes do.
The environmental costs of abyssal mining are likely to exceed those of conventional land extraction.
International regulators should institute an immediate moratorium on commercial seabed mining.

Matches

Show answer & explanation

Answer

The statement regarding green technology needs corresponds to the opposing viewpoint; the statement about benthic recovery rates corresponds to a premise offering empirical evidence; the statement asserting environmental costs will exceed terrestrial mining corresponds to an intermediate conclusion; the statement advocating a moratorium corresponds to the main conclusion.
The author uses survey evidence regarding benthic recovery rates and sediment plume movement to support the sub-claim that deep-sea mining costs will exceed terrestrial mining costs. This sub-claim directly justifies the author's primary final claim: that regulators should enact an immediate moratorium on commercial seabed mining. The opening assertion about green technology needs represents the opposing claim being refuted.

Step-by-Step Solution

1
Identify the author's ultimate goal or main conclusion in the passage.
The final sentence introduced by 'Therefore' recommends that international regulators institute an immediate moratorium on commercial seabed mining.
This is the ultimate recommendation of the passage that all preceding evidence and sub-claims work together to justify.
2
Analyze intermediate claims that connect foundational evidence to the main conclusion.
The claim that abyssal mining costs will exceed land extraction costs is derived from facts about benthic recovery and sediment plumes, but it acts as a supporting reason for the moratorium.
A claim that is inferred from factual premises and simultaneously used to support the final recommendation acts as an intermediate conclusion.
3
Classify remaining premises and background claims.
Survey findings on benthic recovery rates serve as direct empirical evidence (premise), while the opening sentence presents the proponents' claim (opposing viewpoint).
Empirical survey results provide foundational support for the sub-conclusion, whereas proponents' views provide the counter-position being challenged.

Key Concept

Distinguishing Main Conclusions from Intermediate Conclusions, Premises, and Counterarguments
Question 1494Question →

To reduce its overall operational expenditures, a commercial food distribution company plans to replace its fleet of diesel-powered refrigerated delivery trucks with electric refrigerated trucks. Company directors base this strategy on data demonstrating that electric delivery vehicles incur significantly lower per-mile energy and routine maintenance expenses than diesel vehicles. Which of the following would be most useful to evaluate in order to determine whether implementing the plan will achieve the company's goal?

Show answer & explanation

Answer: Whether the continuous power demand of the refrigeration units reduces the battery lifespan of the electric trucks enough to require costly battery pack replacements prior to the end of the vehicles' intended operational service.

Answer

Determining whether the continuous power demand of the refrigeration units reduces battery lifespan enough to require costly battery pack replacements before the end of the vehicles' operational service.
The correct answer identifies a factor that directly impacts whether the projected operating savings will be realized. Under the Variance Test: if the refrigeration units rapidly degrade the electric truck batteries, the substantial cost of recurring battery replacements will exceed the per-mile energy and routine maintenance savings, defeating the plan's goal. Conversely, if battery life is not severely compromised, the expected cost reductions will occur. Because opposing answers to this question dictate whether the plan succeeds or fails, this information is critical for evaluation.

Step-by-Step Solution

1
Identify the plan and the stated goal
The plan is to replace diesel refrigerated trucks with electric refrigerated trucks. The goal is to reduce overall operational expenditures.
Evaluating a plan requires clear identification of the proposed mechanism and the intended outcome.
2
Identify the underlying assumption of the plan
The plan assumes that lower per-mile energy and routine maintenance costs for electric vehicles will translate into lower net operating costs overall.
Plans fail if hidden, unconsidered expenses offset projected cost savings.
3
Apply the Variance Test to evaluate useful information
If refrigeration units cause premature battery failure, battery replacement costs will negate energy and maintenance savings (plan fails). If refrigeration units do not significantly degrade battery life, projected savings will materialize (plan succeeds).
An information item is relevant to plan evaluation if opposite answers to the underlying question produce opposite conclusions about the plan's success.

Key Concept

Evaluating Plans and Strategies using the Variance Test
Question 1495Question →

If aa and bb are non-zero real numbers such that a2≠b2a^2 \neq b^2, is a2b+ab2a3b−ab3>0\frac{a^2 b + a b^2}{a^3 b - a b^3} > 0?

(1) a>ba > b
(2) a+b>0a + b > 0

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The target question asks whether a2b+ab2a3b−ab3>0\frac{a^2 b + a b^2}{a^3 b - a b^3} > 0. Factoring the numerator as ab(a+b)ab(a+b) and the denominator as ab(a+b)(a−b)ab(a+b)(a-b) allows us to cancel common non-zero factors, simplifying the target question to 'Is 1a−b>0\frac{1}{a-b} > 0?', which is equivalent to 'Is a>ba > b?'. Statement (1) directly states that a>ba > b, answering the rephrased question with a definitive 'Yes'. Statement (2) states that a+b>0a+b > 0, which gives no information regarding whether a>ba > b. Therefore, Statement (1) alone is sufficient, while Statement (2) alone is not.

Step-by-Step Solution

1
Rephrase the target question stem algebraically by factoring numerator and denominator.
Numerator: a2b+ab2=ab(a+b)a^2 b + a b^2 = a b(a + b). Denominator: a3b−ab3=ab(a2−b2)=ab(a+b)(a−b)a^3 b - a b^3 = a b(a^2 - b^2) = a b(a + b)(a - b). The expression becomes ab(a+b)ab(a+b)(a−b)\frac{a b(a + b)}{a b(a + b)(a - b)}.
Simplifying complex rational expressions before evaluating statements prevents misinterpretation of necessary conditions.
2
Cancel non-zero common terms in the simplified fraction.
Since ab≠0a b \neq 0 and a+b≠0a + b \neq 0 (given a2≠b2a^2 \neq b^2), common terms cancel out to yield 1a−b>0\frac{1}{a - b} > 0.
The sign of 1a−b\frac{1}{a - b} is strictly positive if and only if a−b>0a - b > 0, which is equivalent to a>ba > b.
3
Evaluate Statement (1): a>ba > b.
This directly yields a−b>0a - b > 0, so 1a−b>0\frac{1}{a - b} > 0. This provides a definitive 'Yes' answer.
Statement (1) alone provides sufficient information.
4
Evaluate Statement (2): a+b>0a + b > 0.
Knowing a+b>0a + b > 0 gives no information about whether a>ba > b or a<ba < b (e.g., if a=5,b=2a=5, b=2, a>ba > b; if a=2,b=5a=2, b=5, a<ba < b).
Statement (2) alone is not sufficient to determine if a>ba > b.

Key Concept

Question Stem Simplification and Target Rephrasing
Estimated Time:1m 40s
Question 1496Question →

If kk is a real number, is kk an integer?

(1) k2−kk^2 - k is an integer.
(2) k3−kk^3 - k is an integer.

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.
Neither statement alone is sufficient because non-integer real numbers can produce integer outputs for k2−kk^2 - k or k3−kk^3 - k. However, when both statements are combined, expressing k3−kk^3 - k as m(k+1)m(k + 1) proves that kk must be a rational number. For any rational number ab\frac{a}{b} in lowest terms, (ab)2−ab\left(\frac{a}{b}\right)^2 - \frac{a}{b} can only be an integer if the denominator b=1b = 1, which proves definitively that kk must be an integer.

Step-by-Step Solution

1
Evaluate Statement (1) independently.
Statement (1) is NOT sufficient.
We are given that k2−k=mk^2 - k = m for some integer mm. If m=1m = 1, then k2−k−1=0k^2 - k - 1 = 0, which gives k=1+52k = \frac{1 + \sqrt{5}}{2}. Here, kk is not an integer, but k2−k=1k^2 - k = 1 is an integer. Thus, Statement (1) alone does not determine whether kk is an integer.
2
Evaluate Statement (2) independently.
Statement (2) is NOT sufficient.
We are given that k3−k=nk^3 - k = n for some integer nn. If n=1n = 1, then k3−k−1=0k^3 - k - 1 = 0. By the Intermediate Value Theorem, there exists a real number k∈(1,2)k \in (1, 2) satisfying this equation. Since 1<k<21 < k < 2, kk cannot be an integer, yet k3−k=1k^3 - k = 1 is an integer. Thus, Statement (2) alone does not determine whether kk is an integer.
3
Evaluate Statements (1) and (2) combined.
The combined statements are SUFFICIENT.
Let k2−k=m∈Zk^2 - k = m \in \mathbb{Z} and k3−k=n∈Zk^3 - k = n \in \mathbb{Z}. Note that k3−k=k(k2−1)=k(k2−k+k−1)=k(m+k−1)=mk+k2−k=mk+m=m(k+1)k^3 - k = k(k^2 - 1) = k(k^2 - k + k - 1) = k(m + k - 1) = mk + k^2 - k = mk + m = m(k + 1). Thus, n=m(k+1)n = m(k + 1). If m=0m = 0, then k2−k=0  ⟹  k=0k^2 - k = 0 \implies k = 0 or k=1k = 1, both of which are integers. If m≠0m \neq 0, then mk=n−m  ⟹  k=n−mmmk = n - m \implies k = \frac{n - m}{m}. Since mm and nn are integers, kk must be a rational number. Let k=abk = \frac{a}{b} in reduced form with gcd⁡(a,b)=1\gcd(a, b) = 1 and b≥1b \ge 1. Substituting into k2−k=mk^2 - k = m yields a2−abb2=m  ⟹  a(a−b)=mb2\frac{a^2 - ab}{b^2} = m \implies a(a - b) = m b^2. This means b2b^2 must divide a(a−b)a(a - b). Since gcd⁡(a,b2)=1\gcd(a, b^2) = 1, b2b^2 must divide a−ba - b, which implies b=1b = 1. Therefore, k=ak = a, so kk MUST be an integer.

Key Concept

Testing implicit real number constraints vs integer constraints using polynomial reduction and rational root properties.
Question 1497Question →

To combat fraudulent crop loss claims, a national agricultural insurer plans to require all policyholders to submit high-resolution satellite imagery of their farmland taken immediately before and after any reported severe weather event. The insurer reasons that comparing these images will enable claims adjusters to verify whether physical crop damage actually occurred as a direct result of the weather event, thereby eliminating payouts for pre-existing crop degradation or unverified losses.

Which of the following is an assumption on which the insurer's plan depends?

Show answer & explanation

Answer: High-resolution satellite imagery can provide enough detail to distinguish pre-existing crop degradation from physical damage caused by a severe weather event.

Answer

The insurer's plan relies on the assumption that high-resolution satellite imagery can provide enough detail to distinguish pre-existing crop degradation from physical damage caused by a severe weather event.
The conclusion asserts that comparing satellite images will eliminate payouts for pre-existing crop degradation by verifying whether damage resulted directly from a weather event. For this verification process to work, the satellite images must possess sufficient resolution and detail to differentiate between crop degradation present before the storm and new damage caused by the storm. If the images cannot distinguish between these two states, adjusters cannot verify causality, and the plan fails. Therefore, this statement is a necessary unstated assumption.

Step-by-Step Solution

1
Deconstruct the argument into premises and main conclusion.
Premise: Insurers will require satellite imagery immediately before and after severe weather. Premise: Adjusters will compare images to verify if damage was directly caused by the storm. Conclusion: The plan will eliminate payouts for pre-existing degradation or unverified losses.
Identifying the logic gap requires clearly isolating what the premises establish versus what the conclusion claims.
2
Identify the unstated logical gap between the premise and conclusion.
The premises state that images will be compared, but assume that comparing these images actually enables adjusters to tell pre-existing damage apart from new weather damage.
An assumption is an unstated premise required to bridge the gap between the evidence provided and the outcome claimed.
3
Apply the Negation Test to confirm logical necessity.
Negated statement: 'High-resolution satellite imagery CANNOT provide enough detail to distinguish pre-existing degradation from weather damage.' If true, comparing images fails to verify causality, shattering the conclusion that fraudulent payouts will be eliminated.
If the negated version of a choice causes the argument to collapse, that choice is a strictly necessary assumption.

Key Concept

Identifying Unstated Assumptions using the Negation Test
Estimated Time:1m 50s
Question 1498Question →

[Tab 1: Travel & Expense Policy]
Global Logistics Corp Standard Policy:
- Standard domestic daily meal per diem is $80.
- Employees with Executive titles (Vice President, Executive Director, or C-Level) receive a 50% increase on standard meal per diems.
- All expense claims must be equal to or less than the designated allowance to be considered compliant.

[Tab 2: Q1 Expense Summary Log]
- Employee A (Senior Manager): Domestic travel claim of 75perday.−EmployeeB(ExecutiveDirector):Domestictravelclaimof75 per day. - Employee B (Executive Director): Domestic travel claim of 115 per day.

Based on the policy rules in Tab 1 and the expense log in Tab 2, evaluate the following statement: Employee B's expense claim of $115 per day is compliant with corporate travel policy.

Show answer & explanation

Answer: True

Answer

The statement is True. Employee B's daily claim of 115iscompliantbecausetheallowablemealperdiemforExecutivepositionsis115 is compliant because the allowable meal per diem for Executive positions is 120 per day.
Synthesizing Tab 1 and Tab 2 shows that Executive Directors qualify for a 50% meal per diem increase, raising their maximum daily allowance to 120(120 ( 80 × 1.50). Employee B's daily claim of $115 is within this threshold, making the statement true.

Step-by-Step Solution

1
Extract base allowance and conditional exception rules from Tab 1.
Standard per diem = $80 per day. Executive title bonus = 50% increase.
Identify the policy baseline and applicable adjustment terms.
2
Calculate the executive per diem threshold.
80×(1+0.50)=80 \times (1 + 0.50) = 120 per day.
Apply the 50% conditional exception to determine the maximum allowed claim for an Executive Director.
3
Synthesize data with Tab 2 to verify compliance.
Employee B claimed 115perday,whichis115 per day, which is \le $120.
Comparing the claimed amount from Tab 2 against the synthesized policy cap from Tab 1 proves compliance.

Key Concept

Multi-Source Inference and Policy Rule Integration
Question 1499Question →

In a financial firm, a total of 100100 portfolio audits were conducted last year. Each audit was classified as High-Risk, International, or both. Exactly 6060 audits were classified as High-Risk, and exactly 5050 audits were classified as International. What was the average (arithmetic mean) duration, in days, of the 100100 portfolio audits?

(1) The average duration of the High-Risk audits was 1414 days, and the average duration of the International audits was 1818 days.
(2) The average duration of the audits classified as both High-Risk and International was 2020 days.

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 states that both statements together are sufficient, but neither statement alone is sufficient. By set theory, the number of audits in both categories is 60+50−100=1060 + 50 - 100 = 10. The total sum of days across all 100100 audits satisfies Stotal=SHigh-Risk+SInternational−SBothS_{\text{total}} = S_{\text{High-Risk}} + S_{\text{International}} - S_{\text{Both}}. Statement (1) gives SHigh-Risk=60×14=840S_{\text{High-Risk}} = 60 \times 14 = 840 and SInternational=50×18=900S_{\text{International}} = 50 \times 18 = 900, yielding Stotal=1740−SBothS_{\text{total}} = 1740 - S_{\text{Both}}, which is insufficient alone. Statement (2) gives SBoth=10×20=200S_{\text{Both}} = 10 \times 20 = 200, which is insufficient alone. Combining both gives Stotal=1740−200=1540S_{\text{total}} = 1740 - 200 = 1540 days, allowing us to find a unique overall mean of 15.415.4 days.

Step-by-Step Solution

1
Determine set sizes using Principle of Inclusion-Exclusion.
Total N=100N = 100. N(H)=60N(H) = 60, N(I)=50N(I) = 50. Since every audit is in HH, II, or both, N(H∪I)=100=60+50−N(H∩I)  ⟹  N(H∩I)=10N(H \cup I) = 100 = 60 + 50 - N(H \cap I) \implies N(H \cap I) = 10.
Identify the count of audits in the overlapping set (both High-Risk and International).
2
Formulate total duration sum in terms of set sums.
Stotal=SH+SI−SH∩IS_{\text{total}} = S_H + S_I - S_{H \cap I}, where SHS_H is sum of High-Risk durations, SIS_I is sum of International durations, and SH∩IS_{H \cap I} is sum of durations in both categories.
Double counting principle applies to the sum of values across sets.
3
Evaluate Statement (1) alone.
SH=60×14=840S_H = 60 \times 14 = 840 days, SI=50×18=900S_I = 50 \times 18 = 900 days. Stotal=840+900−SH∩I=1740−SH∩IS_{\text{total}} = 840 + 900 - S_{H \cap I} = 1740 - S_{H \cap I}.
Since SH∩IS_{H \cap I} is unknown, StotalS_{\text{total}} cannot be calculated. Statement (1) alone is insufficient.
4
Evaluate Statement (2) alone.
SH∩I=10×20=200S_{H \cap I} = 10 \times 20 = 200 days.
Without SHS_H or SIS_I, StotalS_{\text{total}} cannot be calculated. Statement (2) alone is insufficient.
5
Evaluate Statements (1) and (2) together.
Stotal=1740−200=1540S_{\text{total}} = 1740 - 200 = 1540 days. Mean duration = 1540/100=15.41540 / 100 = 15.4 days.
A unique value for the overall mean is obtained. Both statements together are sufficient.

Key Concept

Overlapping Sets and Weighted Averages (Sum Double Counting)
Estimated Time:2m 0s
Question 1500Question →

To reduce long-term municipal energy expenses, the city of Varna plans to replace standard double-pane glass with advanced electrochromic smart glass across all municipal office buildings. The smart glass automatically darkens in response to intense sunlight, significantly reducing the energy needed to power air-conditioning systems during warm months. City planners estimate that the resulting energy savings will fully offset the initial purchase and installation costs within four years. Therefore, the planners conclude that adopting smart glass will reduce the city's total administrative operating costs over the next ten years. Which of the following, if true, most seriously weakens the planners' argument?

Show answer & explanation

Answer: Electrochromic smart glass blocks a substantial portion of natural visible light when darkened, requiring office buildings to run internal electric lighting at full capacity during daylight hours.

Answer

The argument is most seriously weakened by the statement that electrochromic smart glass blocks natural visible light when darkened, forcing municipal office buildings to run internal electric lighting at full capacity during daylight hours.
The correct answer identifies a major counterproductive side effect of the proposed plan. If the smart glass reduces natural light entry when darkened, artificial lighting must be operated at full capacity during peak daylight hours. This added electrical load directly offsets the energy saved on air conditioning, undermining the planners' conclusion that total administrative operating costs will decrease over the ten-year period.

Step-by-Step Solution

1
Deconstruct the argument structure
Premise: Smart glass darkens in sunlight, reducing summer air-conditioning energy use. Premise: Energy savings offset purchase and installation costs in 4 years. Conclusion: Smart glass installation will reduce total administrative operating costs over 10 years.
Identifying the explicit premises and conclusion reveals the core assumption.
2
Identify the central unstated assumption
The planners assume that reducing air-conditioning energy use will yield a net reduction in overall energy expenses without creating offsetting operational costs during the 10-year timeframe.
A plan-to-goal argument relies on the assumption that hidden side effects or secondary costs will not negate the projected benefits.
3
Evaluate the impact of new factual information
If darkening the glass necessitates running electric lights at full capacity throughout the day, the electricity cost for lighting increases significantly whenever air-conditioning savings occur, negating the expected net cost reduction.
Showing a direct, counteracting financial cost undermines the conclusion that net administrative expenses will decline.

Key Concept

Weakening a Plan-to-Goal Causal Argument via Unintended Side Effects
Estimated Time:2m 0s
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