All practice questions

Question 1521Question →

A pharmaceutical company plans to transition from traditional synthetic batch processing to enzyme-catalyzed continuous-flow processing to manufacture its primary hypertension medication. In small-scale laboratory trials, continuous-flow processing achieved a 40 percent reduction in raw material waste and required significantly shorter reaction times per production run. Based on these findings, company management concluded that implementing continuous-flow processing on a commercial scale will substantially reduce the overall per-unit manufacturing cost of the medication. Which of the following, if true, most seriously weakens the management's conclusion?

Raw material suppliers recently lowered the purchase price of the precursor chemicals used in both traditional batch synthesis and continuous-flow processing.

The specialized enzymes required for continuous-flow processing degrade rapidly under high-volume pressure in commercial reactors, necessitating frequent and costly replacement.

Patients taking the hypertension medication manufactured via continuous-flow processing report fewer minor side effects than those taking medication from batch synthesis.

Traditional batch synthesis requires environmental disposal permits for chemical byproducts that are not required for continuous-flow processing.

Competing pharmaceutical manufacturers are currently attempting to develop alternative continuous-flow methods for different drug compounds.

Show answer & explanation

Answer: The specialized enzymes required for continuous-flow processing degrade rapidly under high-volume pressure in commercial reactors, necessitating frequent and costly replacement.

Answer

The conclusion is most weakened by the finding that the specialized enzymes degrade rapidly under high-volume commercial pressure, requiring frequent and expensive replacements that offset raw material savings.

The correct answer demonstrates that scaling up the continuous-flow process introduces a substantial operational expense—frequent, costly enzyme replacement—that was not present or impactful during small-scale laboratory trials. This directly undermines management's assumption that laboratory savings will translate into overall per-unit cost reductions at the commercial level.

Step-by-Step Solution

1

Identify the premises and main conclusion of the argument.

Premises: Small-scale trials of continuous-flow processing reduced raw material waste by 40% and shortened reaction times. Conclusion: Full commercial implementation will significantly lower overall per-unit manufacturing costs.

Understanding the logic gap between small-scale lab success and commercial financial viability is key to finding the unstated assumption.

2

Identify the unstated assumption in the reasoning.

The argument assumes that the cost benefits observed in small-scale trials will not be negated by new, unexpected expenses that arise when scaling up to commercial production.

To weaken a plan-to-cost argument, look for a factor that introduces significant new costs unique to full-scale operations.

3

Evaluate the choices to find new information that breaks the central assumption.

The statement regarding rapid enzyme degradation under commercial pressure identifies a severe recurring cost unique to commercial scaling that directly neutralizes the efficiency gains.

This hidden operational drawback demonstrates that total per-unit manufacturing costs may actually rise rather than fall.

Key Concept

Weakening a Causal / Plan-to-Cost Argument via Unintended Scaling Costs

Question 1522Question →

The table below displays the vehicle fleet composition across four regional divisions of a logistics corporation.

Division	Electric Vehicles	Gasoline Vehicles	Total Vehicles
North	120	280	400
South	160	240	400
East	90	210	300
West	230	270	500

What percentage of the total fleet across all four divisions consists of electric vehicles?

Show answer & explanation

Answer: 37.5

Answer

The percentage of the total fleet consisting of electric vehicles across all four divisions is

37.5\%

.

To find the overall percentage of electric vehicles, sum the number of electric vehicles across all divisions (

120 + 160 + 90 + 230 = 600

) and divide by the overall total number of vehicles (

400 + 400 + 300 + 500 = 1600

). Dividing

600

by

1600

gives

0.375

, which equals

37.5\%

.

Step-by-Step Solution

1

Calculate the total number of electric vehicles across all divisions.

120 + 160 + 90 + 230 = 600

electric vehicles.

Summing the electric vehicle column values gives the total count of electric vehicles.

2

Calculate the total vehicle count across all divisions.

400 + 400 + 300 + 500 = 1600

total vehicles.

Summing the total vehicle column values provides the aggregate denominator.

3

Compute the required percentage.

\frac{600}{1600} \times 100\% = 37.5\%

.

Dividing total electric vehicles by total vehicles yields the aggregate proportion.

Key Concept

Ratio, Proportion, and Percent Calculations

Estimated Time:1m 0s

Question 1523Question →

If $m$ and $n$ are positive integers, is $m^2 - n^2$ a prime number?

(1) $m - n = 1$
(2) $m + n = 7$

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.

Rephrasing the question stem shows

m^2 - n^2 = (m - n)(m + n)

. Statement (1) alone allows

2n + 1

to be prime (for

n=1

) or composite (for

n=4

), so it is insufficient. Statement (2) alone allows pairs like

(4,3)

which gives

7

(prime) and

(5,2)

which gives

21

(composite), so it is insufficient. Combining both statements yields

m = 4

and

n = 3

, giving

m^2 - n^2 = 7

, which definitively answers 'Yes'.

Step-by-Step Solution

1

Rephrase the question stem using algebraic factorization.

m^2 - n^2 = (m - n)(m + n)

. For

m^2 - n^2

to be a prime number, since

m

and

n

are positive integers, the smaller factor

(m - n)

must equal 1 and the larger factor

(m + n)

must be a prime number.

Factoring highlights the conditions required for a product of integers to yield a prime number.

2

Evaluate Statement (1):

m - n = 1

.

Substitute

m = n + 1

into

m^2 - n^2

:

(1)(2n + 1) = 2n + 1

. If

n = 1

, then

2(1) + 1 = 3

(prime, Yes). If

n = 4

, then

2(4) + 1 = 9

(composite, No).

Since Statement (1) produces both Yes and No outcomes, it is NOT sufficient.

3

Evaluate Statement (2):

m + n = 7

.

Since

m

and

n

are positive integers, test pairs with

m > n

: If

(m, n) = (4, 3)

, then

m^2 - n^2 = 16 - 9 = 7

(prime, Yes). If

(m, n) = (5, 2)

, then

m^2 - n^2 = 25 - 4 = 21

(composite, No).

Since Statement (2) produces both Yes and No outcomes, it is NOT sufficient.

4

Evaluate Statement (1) and Statement (2) together.

System of equations:

m - n = 1

and

m + n = 7

. Adding the equations gives

2m = 8 \implies m = 4

, which leads to

n = 3

. Then

m^2 - n^2 = 4^2 - 3^2 = 7

, which is prime (Definitive Yes).

Combining the statements yields a single unique pair of values and a definitive Yes answer.

Key Concept

Difference of squares factorization and prime number properties in Data Sufficiency

Estimated Time:2m 0s

Question 1524Question →

At TechCorp, any department that implements Cloud System X must undergo a mandatory quarterly security audit. Every department undergoing a quarterly security audit is prohibited from using Legacy Software Y. Last year, the Financial Analytics division at TechCorp was authorized to use Legacy Software Y throughout all four quarters. If the statements above are true, which of the following must also be true regarding TechCorp last year?

The Financial Analytics division did not implement Cloud System X during any quarter last year.

The Financial Analytics division was the only department at TechCorp authorized to use Legacy Software Y last year.

Any department at TechCorp that did not implement Cloud System X last year was authorized to use Legacy Software Y.

The Financial Analytics division suffered no cybersecurity breaches while using Legacy Software Y last year.

If a department did not undergo a quarterly security audit last year, it was required to use Legacy Software Y.

Show answer & explanation

Answer: The Financial Analytics division did not implement Cloud System X during any quarter last year.

Answer

The Financial Analytics division did not implement Cloud System X during any quarter last year.

The correct option stating that the Financial Analytics division did not implement Cloud System X during any quarter last year is logically necessary. From the premises, implementing Cloud System X requires a quarterly security audit, which in turn forbids using Legacy Software Y. By contrapositive logic, any department using Legacy Software Y cannot undergo a quarterly security audit and therefore cannot implement Cloud System X.

Step-by-Step Solution

1

Formalize premise 1

Implement Cloud System X → Quarterly Security Audit

Establishing the conditional rule linking System X to security audits.

2

Formalize premise 2

Quarterly Security Audit → NOT Authorized to use Legacy Software Y

Establishing the conditional rule linking security audits to Legacy Software Y prohibition.

3

Chain the premises together

Implement Cloud System X → Quarterly Security Audit → NOT Authorized for Legacy Software Y

Creating a unified conditional chain.

4

Form the contrapositive

Authorized to use Legacy Software Y → NOT Quarterly Security Audit → NOT Implement Cloud System X

Taking the logical contrapositive to deduce what follows from being authorized for Legacy Software Y.

5

Apply the facts about Financial Analytics

Financial Analytics used Legacy Software Y → Financial Analytics did NOT implement Cloud System X

Directly applying the contrapositive to the fact stated in the stimulus.

Key Concept

Conditional Logic Chains and Contrapositives

Question 1525Question →

If $p$ and $q$ are positive integers, is $p^2 + 3q$ divisible by 6?

(1) $p + q$ is an odd integer.
(2) $p^2 - q^2$ is divisible by 3.

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

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

Answer

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

The question requires determining whether

p^2 + 3q

is divisible by 6, which demands divisibility by both 2 and 3. By parity rules,

p^2 \equiv p \pmod 2

and

3q \equiv q \pmod 2

, meaning

p^2 + 3q

has the same parity as

p + q

. Statement (1) specifies that

p + q

is odd, so

p^2 + 3q

is odd and cannot be divisible by 6. This gives a definitive 'No' answer, making Statement (1) alone sufficient. Statement (2) permits cases where

p^2 + 3q

is divisible by 6 (e.g.,

p=3, q=3

) and cases where it is not (e.g.,

p=4, q=1

), making Statement (2) alone insufficient.

Step-by-Step Solution

1

Rephrase the question target using number properties and parity rules.

For

p^2 + 3q

to be divisible by 6, it must be divisible by both 2 (even) and 3. For parity,

p^2 \equiv p \pmod 2

and

3q \equiv q \pmod 2

, so

p^2 + 3q \equiv p + q \pmod 2

. Thus,

p^2 + 3q

is even if and only if

p + q

is even.

Simplifying the parity constraint simplifies evaluating statements regarding divisibility by 2.

2

Evaluate Statement (1):

p + q

is an odd integer.

Since

p + q

is odd,

p^2 + 3q

must be odd. An odd integer cannot be divisible by 2, so

p^2 + 3q

CANNOT be divisible by 6. This yields a definitive 'No'.

In Data Sufficiency Yes/No questions, a definitive 'No' answer means the statement is sufficient.

3

Evaluate Statement (2):

p^2 - q^2

is divisible by 3.

Test cases:
- If

p = 3, q = 3

:

p^2 - q^2 = 0

(divisible by 3), and

p^2 + 3q = 18

(divisible by 6 -> YES).
- If

p = 4, q = 1

:

p^2 - q^2 = 15

(divisible by 3), and

p^2 + 3q = 19

(not divisible by 6 -> NO).

Since Statement (2) yields both 'Yes' and 'No' outcomes, it is insufficient.

Key Concept

Parity rephrasing and Yes/No Data Sufficiency decision logic

Question 1526Question →

Read the argument below regarding biotechnology and invasive species management, and match each statement from the text to its corresponding logical role within the overall argument.

Argument: Conservationists frequently propose gene-drive technology to eradicate invasive species on isolated islands. Critics contend that off-target genetic mutations could inadvertently spread to mainland populations, causing ecological collapse. However, recent field trials utilizing self-limiting genetic markers demonstrate that gene drives decay naturally within five generations, rendering widespread spillover biologically impossible. Although monitoring post-release ecosystems remains essential to detect unexpected ecological shifts, the fear of uncontrolled global spread is unfounded. Consequently, environmental agencies should proceed with controlled island deployments of self-limiting gene drives.

Which logical role corresponds to each statement from the argument?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match each statement to its structural role: the trial decay finding is an empirical premise; the monitoring statement is a concessionary precaution; the statement that spread fear is unfounded is an intermediate conclusion; and the call to proceed with island deployments is the main conclusion.

The main conclusion of a Critical Reasoning argument is the ultimate claim that the author seeks to prove or recommend. The author presents field trial findings as a supporting premise to establish the intermediate conclusion that global spillover fears are unfounded. That intermediate conclusion, alongside a minor concession regarding monitoring precautions, provides the justification for the author's final claim and main conclusion: environmental agencies should proceed with controlled island deployments.

Step-by-Step Solution

1

Analyze the structural direction of the argument.

Identified the author's primary goal: persuading environmental agencies to approve island deployments of self-limiting gene drives.

Determining the overall objective separates main claims from subsidiary arguments and supporting data.

2

Differentiate premises, concessions, and intermediate claims.

The five-generation decay finding provides raw empirical evidence (premise). The statement about monitoring admits a ongoing requirement (concession). The deduction that global spread fears are unfounded synthesizes trial findings to address critics (intermediate conclusion).

Each statement supports a different tier of the logical chain leading to the ultimate conclusion.

3

Map each statement to its logical definition.

Statement 1 maps to premise; Statement 2 maps to concession; Statement 3 maps to intermediate conclusion; Statement 4 maps to main conclusion.

Establishes precise alignment between text excerpts and structural definitions.

Key Concept

Identifying Main Conclusions and Structural Roles in Arguments

Question 1527Question →

[Tab 1: Clinical Protocol & Regulatory Guidelines]
BioVax Phase III Clinical Trial Operations Policy (2026 Revision):
- Cohort Balance Rule: To ensure demographic representation, no single age group ( $<50$ years vs. $\ge 50$ years) may exceed $60\%$ of total enrolled participants at any trial site during a given quarter.
- Mandatory Audit Freeze: If a trial site experiences a quarterly participant dropout rate exceeding $15\%$ AND fails the Cohort Balance Rule in the same quarter, a mandatory 30-day participant enrollment freeze takes effect on the first day of the subsequent quarter.
- Waiver Exception Policy: A mandatory enrollment freeze is waived ONLY IF the site receives written approval from the Lead Investigator prior to the start of the subsequent quarter AND achieves an overall quarterly Patient Satisfaction Score of at least $4.2$ out of $5.0$ .

[Tab 2: Q3 Site Performance Audit Data]

Site ID	Location	Total Enrolled (Q3)	Enrolled Age <50	Enrolled Age ≥50	Q3 Dropouts	Patient Satisfaction Score	Written Waiver Date
Site 101	Boston	120	78	42	20	4.4	Sept 28
Site 102	Chicago	150	93	57	24	4.1	Sept 30
Site 103	Atlanta	100	62	38	17	4.5	None
Site 104	Denver	200	110	90	28	4.0	None

[Tab 3: Executive Operations Memorandum]
To: Regional Clinical Operations Monitors
From: Dr. E. Vance, Clinical Trial Director
Date: October 2, 2026
Subject: Q4 Enrollment Readiness & Freeze Enforcement
Final Q3 data reconciliation is complete. All mandatory 30-day enrollment freezes triggered by Q3 audit failures take effect October 1. Note that while Site 102 submitted a written waiver from the Lead Investigator dated September 30, regional monitors must strictly verify that all protocol prerequisites specified in the Clinical Protocol are satisfied before validating any waiver.

Based on the information provided across the three tabs, evaluate the following statement:
Site 102 was required to undergo a mandatory 30-day enrollment freeze starting October 1.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. Site 102 met both failure triggers for a mandatory audit freeze and failed to satisfy the satisfaction score threshold required for a valid waiver exemption.

The correct evaluation shows that Site 102 triggered a mandatory freeze by exceeding both the 60% demographic threshold (achieving 62%) and the 15% dropout limit (achieving 16%). Furthermore, its waiver was invalid because its Patient Satisfaction Score of 4.1 failed the strict 4.2 minimum threshold mandated by protocol.

Step-by-Step Solution

1

Calculate the Q3 demographic proportion and dropout rate for Site 102 using Tab 2 data.

Age <50 proportion =

\frac{93}{150} = 62\%

. Dropout rate =

\frac{24}{150} = 16\%

.

Determine if Site 102 triggered the Mandatory Audit Freeze criteria specified in Tab 1.

2

Compare Site 102's calculated metrics against Tab 1 Mandatory Audit Freeze rules.

Both conditions are met:

62\% > 60\%

(Cohort Balance failure) and

16\% > 15\%

(Dropout threshold exceeded). A freeze was triggered.

Verify if an enrollment freeze was required prior to waiver considerations.

3

Evaluate Site 102's waiver eligibility against both criteria in Tab 1.

Written approval date (Sept 30) was before Oct 1 (Met), but Patient Satisfaction Score (

4.1

) was below the required

4.2

minimum (Failed).

Check if the written waiver granted to Site 102 effectively exempted it from the freeze.

4

Synthesize results with Tab 3 guidelines to form final determination.

Because the satisfaction score requirement was not met, the waiver is invalid under Tab 3 directives, confirming the statement as True.

Ensure all policy constraints across text and tabular sources are reconciled.

Key Concept

Multi-Source Policy Exception Synthesis

Question 1528Question →

[Tab 1: Compliance Standard]
Commercial Fleet Maintenance Policy (2026 Audit Standards):
- Category A Aircraft (Long-Haul): Heavy maintenance (C-Check) is required whenever an aircraft reaches 24 elapsed months since its last C-Check OR accumulates 6,000 total flight hours, whichever occurs first. The standard base inspection fee is $120,000. - Category B Aircraft (Regional): Heavy maintenance (C-Check) is required whenever an aircraft reaches 18 elapsed months since its last C-Check OR accumulates 4,000 total flight hours, whichever occurs first. The standard base inspection fee is$ 80,000.
- Overhaul Surcharge (Rule 4.2): If an aircraft has logged more than 75% of its total flight hours in high-corrosion maritime environments, a 15% surcharge is added to its base inspection fee. However, this surcharge is waived if the aircraft completed an anti-corrosion hull upgrade within the preceding 12 months.

[Tab 2: Fleet Utilization Log]
| Aircraft ID | Category | Months Since Last C-Check | Total Flight Hours | Maritime Flight Hours (%) | Last Anti-Corrosion Upgrade |
| N-101 | Category A | 20 | 5,800 | 80% | 14 months ago |
| N-202 | Category A | 22 | 6,100 | 70% | 8 months ago |
| N-303 | Category B | 16 | 4,200 | 82% | 10 months ago |
| N-404 | Category B | 19 | 3,900 | 60% | Never |

Based on the policy guidelines and utilization data provided across both tabs, what is the total dollar amount in base inspection fees and applicable surcharges that the airline must allocate immediately for aircraft currently requiring a mandatory C-Check?

$200,000

$280,000

$292,000

$322,000

$418,000

Show answer & explanation

Answer: $280,000

Answer

$280,000

Evaluating both tabs demonstrates that aircraft N-202, N-303, and N-404 exceed their operational threshold criteria (N-202 and N-303 on flight hours, N-404 on elapsed months). Aircraft N-202 and N-404 do not exceed the 75% maritime threshold, incurring base fees of

120,000 and

80,000 respectively. Aircraft N-303 exceeds the 75% maritime threshold, but because its anti-corrosion upgrade was completed 10 months ago (within the 12-month window), the 15% surcharge is waived, resulting in a base fee of

80,000. Summing these values gives

280,000.

Step-by-Step Solution

1

Evaluate mandatory C-Check threshold compliance for each aircraft combining rules from Tab 1 and data from Tab 2.

N-101 (Cat A): 20 months (< 24) and 5,800 hours (< 6,000) -> No check required.
N-202 (Cat A): 22 months (< 24) but 6,100 hours (>= 6,000) -> MANDATORY CHECK REQUIRED.
N-303 (Cat B): 16 months (< 18) but 4,200 hours (>= 4,000) -> MANDATORY CHECK REQUIRED.
N-404 (Cat B): 19 months (>= 18) and 3,900 hours (< 4,000) -> MANDATORY CHECK REQUIRED.

An aircraft requires an immediate C-Check if it meets or exceeds EITHER the monthly limit OR the flight hour limit for its specific category.

2

Calculate inspection fees and evaluate Rule 4.2 surcharge conditions for required aircraft.

N-202: Base

120,000. Maritime is 70% (<= 75%), so no surcharge applies. Total =

120,000.
N-303: Base

80,000. Maritime is 82% (> 75%), but anti-corrosion upgrade was 10 months ago (<= 12 months), waiving the surcharge. Total =

80,000.
N-404: Base

80,000. Maritime is 60% (<= 75%), so no surcharge applies. Total =

80,000.

Tab 1 specifies that the 15% surcharge applies only when maritime hours exceed 75%, and is explicitly waived if an upgrade occurred within the last 12 months.

3

Sum the fee allocations for all non-compliant aircraft.

120,000 +

80,000 +

80,000 =

280,000.

Combining the calculated costs yields the total immediate budget allocation required.

Key Concept

Multi-Source Inference and Rule Exception Synthesis

Question 1529Question →

If $a$ and $b$ are positive real numbers, what is the value of $a^2 + b^2$ ?

(1) $a^4 - b^4 = 5(a^2 - b^2)$
(2) $ab = 6$ and $a + b = 5$

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

Answer: Statement (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 (1) simplifies to

(a^2 - b^2)(a^2 + b^2 - 5) = 0

, which allows

a^2 + b^2 = 5

when

a \neq b

, but allows infinitely many values for

a^2 + b^2

when

a = b

. Hence, Statement (1) alone is insufficient. Statement (2) provides

a + b = 5

and

ab = 6

, allowing us to use

(a + b)^2 = a^2 + b^2 + 2ab

to find

a^2 + b^2 = 25 - 12 = 13

uniquely. Therefore, Statement (2) alone is sufficient.

Step-by-Step Solution

1

Analyze Statement (1) algebraically.

Factor the left side as

(a^2 - b^2)(a^2 + b^2) = 5(a^2 - b^2)

. Rearranging yields

(a^2 - b^2)(a^2 + b^2 - 5) = 0

.

Dividing by

(a^2 - b^2)

is valid only if

a \neq b

.

2

Evaluate sufficiency of Statement (1).

If

a \neq b

, then

a^2 + b^2 = 5

. However, if

a = b > 0

, then

a^2 - b^2 = 0

, which makes the equation true for any positive value of

a

, meaning

a^2 + b^2 = 2a^2

can take infinitely many values (e.g., if

a=b=1

,

a^2+b^2=2

; if

a=b=3

,

a^2+b^2=18

). Thus, a unique value cannot be determined.

Multiple possible values mean Statement (1) is not sufficient.

3

Evaluate sufficiency of Statement (2).

Use the algebraic identity

(a + b)^2 = a^2 + 2ab + b^2

. Substituting

a + b = 5

and

ab = 6

gives

5^2 = a^2 + 2(6) + b^2

, so

25 = a^2 + b^2 + 12 \implies a^2 + b^2 = 13

.

This determines a single, unique numerical value for

a^2 + b^2

.

4

Conclude overall sufficiency.

Statement (1) is NOT sufficient, but Statement (2) IS sufficient.

Statement (2) alone resolves the target question.

Key Concept

Algebraic Equations and Systems in Data Sufficiency

Question 1530Question →

### Tab 1: International Travel Policy
Employees are eligible for Business Class reimbursement only on international flights with a continuous flight duration exceeding $8$ hours, provided that Vice President approval is secured at least $14$ days prior to departure.

### Tab 2: Financial Compliance Addendum
Any Vice President approval for a travel reimbursement upgrade secured fewer than $14$ days prior to departure is automatically routed to the Finance Audit Committee for mandatory review prior to disbursement.

Based on the policy documents in Tab 1 and Tab 2, which of the following reimbursement requests will be automatically routed to the Finance Audit Committee for mandatory review?

A request for a 10-hour flight with Vice President approval secured 10 days prior to departure

A request for a 10-hour flight with Vice President approval secured 20 days prior to departure

A request for a 6-hour flight with Vice President approval secured 18 days prior to departure

A request for an Economy Class flight on a 5-hour route booked 7 days prior to departure

A request for a 12-hour flight without Vice President approval booked 15 days prior to departure

Show answer & explanation

Answer: A request for a 10-hour flight with Vice President approval secured 10 days prior to departure

Answer

A request for a 10-hour flight with Vice President approval secured 10 days prior to departure.

The correct answer combines the flight duration rule from Tab 1 (

10\text{ hours} > 8\text{ hours}

) with the audit review trigger from Tab 2 (

10\text{ days} < 14\text{ days}

). Because the Vice President approval was obtained fewer than 14 days before departure, Tab 2 specifies that the request must be automatically routed to the Finance Audit Committee.

Step-by-Step Solution

1

Analyze Tab 1 for baseline eligibility criteria

Business Class reimbursement requires a continuous flight duration of

> 8

hours and Vice President approval secured

\ge 14

days prior.

Establishes the core rules for flight upgrades.

2

Analyze Tab 2 for compliance exception criteria

If Vice President approval for an upgrade is secured

< 14

days prior to departure, the request is automatically routed to the Finance Audit Committee.

Identifies the specific condition triggering committee review.

3

Synthesize conditions across both tabs to find the matching scenario

A 10-hour flight meets the

> 8

hour threshold from Tab 1. Obtaining VP approval 10 days prior meets the

< 14

days condition from Tab 2, resulting in automatic routing to the audit committee.

Directly answers the stem question by combining constraints from both sources.

Key Concept

Cross-document synthesis of policy conditions and conditional exception rules

Question 1531Question →

If $n$ is a positive integer, is $n$ a multiple of 18?

(1) $n^2$ is divisible by 108.
(2) $n^3$ is divisible by 243.

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

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

Answer

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

Statement (1) alone is sufficient because prime factor analysis of

n^2

being divisible by

108 = 2^2 \times 3^3

requires the exponent of 3 in

n^2

to be at least 4 (since

n

is an integer and exponents in

n^2

must be even). This guarantees

n

is divisible by

2^1 \times 3^2 = 18

. Statement (2) alone is not sufficient because

n^3

being divisible by

243 = 3^5

only guarantees

n

is a multiple of 9, allowing

n = 9

(not a multiple of 18) or

n = 18

(a multiple of 18).

Step-by-Step Solution

1

Rephrase the target question using prime factorizations.

The target asks if

n

is a multiple of

18 = 2^1 \times 3^2

. For

n

to be a multiple of 18, its prime factorization must contain at least one factor of 2 and at least two factors of 3.

Decomposing into prime factors simplifies the condition required for sufficiency.

2

Evaluate Statement (1):

n^2

is divisible by

108 = 2^2 \times 3^3

.

Since

n

is a positive integer, any prime factor in the prime factorization of

n^2

must have an even exponent. For

n^2

to be divisible by

2^2 \times 3^3

, the power of 2 in

n^2

must be at least 2, so

n

has at least one factor of 2. The power of 3 in

n^2

must be an even integer greater than or equal to 3, meaning it must be at least 4. Thus,

n

must contain at least two factors of 3 (

3^2 = 9

). Consequently,

n

must be divisible by

2^1 \times 3^2 = 18

. Statement (1) alone yields a definitive 'Yes'.

An integer's square must have even exponents for all its prime factors.

3

Evaluate Statement (2):

n^3

is divisible by

243 = 3^5

.

For

n^3

to be divisible by

3^5

, the exponent of 3 in

n^3

must be a multiple of 3 greater than or equal to 5, which means it must be at least 6. Therefore,

n

must contain at least two factors of 3 (

3^2 = 9

). However, statement (2) places no restriction on whether

n

is even. If

n = 9

,

n^3 = 729 = 243 \times 3

(divisible by 243), but 9 is NOT a multiple of 18. If

n = 18

,

n^3 = 5832 = 243 \times 24

(divisible by 243), and 18 IS a multiple of 18. Since

n

can yield both 'No' and 'Yes', Statement (2) alone is insufficient.

Testing specific values demonstrates that

n

may or may not be even.

Key Concept

Prime Factor Exponents in Integer Powers and Data Sufficiency Sufficiency Logic

Estimated Time:2m 0s

Question 1532Question →

A summer academic camp has a total of $120$ enrolled students. Every student participates in at least one of two workshops: Data Analysis or Public Speaking. Exactly $70$ students participate in Data Analysis and exactly $80$ students participate in Public Speaking. What is the average (arithmetic mean) test score of the students who participate ONLY in Public Speaking?

Statement (1): The average test score of all $120$ students in the camp is $84$ .
Statement (2): The average test score of the students who participate in BOTH workshops is $90$ , and the average test score of the students who participate ONLY in Data Analysis is $78$ .

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 to uniquely determine the average score of the students participating only in Public Speaking, but neither statement alone is sufficient.

The correct response identifies that both statements together provide enough information to solve for the target average, whereas neither statement alone is sufficient. By deconstructing the overlapping sets into three distinct groups (Data Analysis only = 40, Both = 30, Public Speaking only = 50), the weighted average equation connects the overall average to the three subgroup averages. Statement (1) supplies only the overall average, leaving two unknown subgroup averages. Statement (2) supplies two subgroup averages, leaving the overall average unknown. Combining both statements yields a single equation with only one unknown (

A_{P\text{-only}} = 85.2

), producing a unique numerical solution.

Step-by-Step Solution

1

Rephrase the question stem by calculating the exact number of students in each mutually exclusive subset.

Using the overlapping sets formula

N(D \cup P) = N(D) + N(P) - N(D \cap P)

, we get

120 = 70 + 80 - N(D \cap P)

, so

N(D \cap P) = 30

students in both workshops. Therefore, students in Data Analysis only =

70 - 30 = 40

, students in Public Speaking only =

80 - 30 = 50

, and students in both =

30

.

Deconstructing the overlapping sets into three distinct, non-overlapping groups (Data Analysis only, Both, Public Speaking only) is essential for formulating a weighted average equation.

2

Formulate the weighted average equation relating all subset averages to the total average.

Total Score Sum =

120 \cdot A_{total} = 40 \cdot A_{D\text{-only}} + 30 \cdot A_{both} + 50 \cdot A_{P\text{-only}}

, where

A_{P\text{-only}}

is the target value.

The total sum of all scores is the weighted sum of scores from the three mutually exclusive subsets.

3

Evaluate Statement (1) independently.

Statement (1) gives

A_{total} = 84

. Substituting gives

120(84) = 10080 = 40 \cdot A_{D\text{-only}} + 30 \cdot A_{both} + 50 \cdot A_{P\text{-only}}

. Since

A_{D\text{-only}}

and

A_{both}

remain unknown,

A_{P\text{-only}}

cannot be uniquely solved.

One linear equation with three unknown variables does not yield a unique solution. Statement (1) alone is NOT sufficient.

4

Evaluate Statement (2) independently.

Statement (2) gives

A_{both} = 90

and

A_{D\text{-only}} = 78

. Substituting gives

120 \cdot A_{total} = 40(78) + 30(90) + 50 \cdot A_{P\text{-only}} = 5820 + 50 \cdot A_{P\text{-only}}

. Since

A_{total}

is unknown,

A_{P\text{-only}}

cannot be uniquely solved.

One linear equation with two unknown variables does not yield a unique solution. Statement (2) alone is NOT sufficient.

5

Evaluate Statement (1) and Statement (2) combined.

Combining both statements provides

A_{total} = 84

,

A_{both} = 90

, and

A_{D\text{-only}} = 78

. The equation becomes

120(84) = 40(78) + 30(90) + 50 \cdot A_{P\text{-only}}

, which simplifies to

10080 = 5820 + 50 \cdot A_{P\text{-only}} \implies 4260 = 50 \cdot A_{P\text{-only}} \implies A_{P\text{-only}} = 85.2

.

We have one linear equation with only one unknown variable, giving a single unique numerical value. Both statements together are SUFFICIENT.

Key Concept

Combining overlapping set cardinalities with group weighted averages in Data Sufficiency

Estimated Time:2m 0s

Question 1533Question →

At an ongoing archaeological excavation of an ancient Mediterranean trading port, researchers have established two strict origin rules for artifact classification: first, any ceramic vessel containing traces of refined pine resin was manufactured in Coastal Region K. Second, every ceramic vessel manufactured in Coastal Region K that dates to the 4th century BCE features a specialized lead-based sealant glaze.

Statement: Based on the rules above, if an excavated ceramic vessel dates to the 4th century BCE but does not feature a lead-based sealant glaze, it cannot contain traces of refined pine resin.

True

False

Show answer & explanation

Answer: True

Answer

True. The deduction is logically valid and guaranteed by combining the contrapositives of the two premise rules.

The statement must be true. Combining the given conditional premises demonstrates that any 4th-century BCE vessel with pine resin would necessarily require the lead-based glaze. Therefore, the absence of the glaze on a 4th-century BCE vessel guarantees the absence of pine resin.

Step-by-Step Solution

1

Represent the premises using conditional logic statements.

Rule 1: Pine Resin

\rightarrow

Region K. Rule 2: (Region K

\land

4th Century BCE)

\rightarrow

Lead-based Glaze.

Formalizing the premises clarifies the required chain of logic.

2

Take the contrapositive of Rule 2 for artifacts from the 4th century BCE.

If an artifact is from the 4th century BCE and lacks a Lead-based Glaze, it was NOT manufactured in Region K.

The contrapositive of

A \rightarrow B

is

\neg B \rightarrow \neg A

, which is logically equivalent.

3

Apply the contrapositive of Rule 1 to the result of Step 2.

Rule 1 Contrapositive: NOT Region K

\rightarrow

NO Pine Resin.

Since the artifact was not manufactured in Region K, it cannot possess the characteristic unique to Region K vessels.

4

Synthesize the conclusion.

A 4th-century BCE vessel without lead-based glaze cannot contain refined pine resin. Thus, the statement MUST BE TRUE.

The conclusion is 100% guaranteed by the given premises.

Key Concept

Conditional Logic & Contrapositive Chain Deductions

Question 1534Question →

If $n$ is a positive integer, is $n^2 + 3n + 2$ divisible by 12?

(1) $n$ is a multiple of 3.
(2) $n + 1$ is a prime number.

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

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

Answer

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

Factoring the stem expression gives

n^2 + 3n + 2 = (n + 1)(n + 2)

. Statement (1) tells us

n

is a multiple of 3, which implies neither

n + 1

nor

n + 2

is a multiple of 3. Consequently, their product can never be divisible by 3, and thus can never be divisible by 12. Because Statement (1) conclusively answers 'No' to the question stem, Statement (1) ALONE is sufficient. Statement (2) allows

n = 2

(giving 12, divisible by 12) and

n = 4

(giving 30, not divisible by 12), yielding both 'Yes' and 'No' responses, making Statement (2) alone insufficient.

Step-by-Step Solution

1

Rephrase the question stem target using factoring.

The expression

n^2 + 3n + 2

factors into

(n + 1)(n + 2)

. The question asks whether

(n + 1)(n + 2)

is divisible by

12 = 2^2 \times 3

.

Factoring quadratic expressions helps reveal divisibility properties of consecutive integers.

2

Evaluate Statement (1):

n

is a multiple of 3.

If

n = 3k

for some positive integer

k

, then

n + 1 = 3k + 1

and

n + 2 = 3k + 2

. Neither factor contains 3 as a prime factor, so their product

(3k + 1)(3k + 2)

leaves a remainder of

1 \times 2 = 2

when divided by 3. Since the product is never divisible by 3, it can NEVER be divisible by 12.

In a Yes/No Data Sufficiency question, a statement that yields a definitive 'No' to the question is SUFFICIENT.

3

Evaluate Statement (2):

n + 1

is a prime number.

If

n = 2

, then

n + 1 = 3

(prime). The expression

(2+1)(2+2) = 12

, which is divisible by 12 (Answer: YES). If

n = 4

, then

n + 1 = 5

(prime). The expression

(4+1)(4+2) = 30

, which is not divisible by 12 (Answer: NO). Since both 'Yes' and 'No' are possible, Statement (2) is NOT sufficient.

Testing specific values shows that Statement (2) does not yield a consistent answer.

Key Concept

Definitive Yes/No decision logic in Data Sufficiency combined with divisibility and prime factor properties of consecutive integers.

Question 1535Question →

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

(1) $a^2 b < a b^2$
(2) $\frac{a}{b} + \frac{b}{a} < 0$

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 option states that both statements together are sufficient, but neither statement alone is sufficient. Statement (1) simplifies to

ab(a - b) < 0

, which is insufficient by itself because the sign of

(a - b)

depends on whether

ab

is positive or negative. Statement (2) simplifies to

ab < 0

(since

a^2 + b^2 > 0

), which alone does not reveal whether

a

or

b

is the larger number. When evaluated together, knowing

ab < 0

allows us to divide

ab(a - b) < 0

by the negative value

ab

and flip the inequality sign, yielding

a - b > 0

(i.e.,

a > b

) definitively.

Step-by-Step Solution

1

Analyze the target question and simplify Statement (1) algebraically.

Statement (1) can be rewritten as

a^2 b - a b^2 < 0

, which factors into

ab(a - b) < 0

.

Factoring isolates the relationship between

ab

and

(a - b)

.

2

Test Statement (1) independently.

If

a = 1

and

b = 2

, then

ab(a - b) = 2(-1) = -2 < 0

, giving

a < b

(No). If

a = 2

and

b = -1

, then

ab(a - b) = -2(3) = -6 < 0

, giving

a > b

(Yes).

Since Statement (1) permits both a 'Yes' and a 'No' response depending on the signs of

a

and

b

, it is NOT sufficient alone.

3

Evaluate Statement (2) strictly in isolation without using information from Statement (1).

Combining terms gives

\frac{a^2 + b^2}{ab} < 0

. Because

a^2 + b^2 > 0

for non-zero real numbers, the denominator must be negative, so

ab < 0

.

Knowing

ab < 0

implies

a

and

b

have opposite signs, but it does not specify which variable is positive and which is negative (e.g.,

a = 2, b = -1 \implies a > b

, whereas

a = -1, b = 2 \implies a < b

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

4

Combine Statement (1) and Statement (2).

From Statement (2),

ab < 0

. From Statement (1),

ab(a - b) < 0

. Dividing

ab(a - b) < 0

by the negative quantity

ab

requires flipping the inequality sign, yielding

a - b > 0

, or

a > b

.

This establishes a definitive 'Yes' answer to the question, making the statements together sufficient.

Key Concept

Statement Independence Evaluation and Statement Combination in Data Sufficiency

Question 1536Question →

In 2021, Phase III trials constituted exactly 15 percent of all clinical drug trials conducted by Apex BioTech. By 2025, Phase III trials represented 25 percent of the company's total clinical drug trials. If the total number of clinical drug trials conducted by Apex BioTech that were NOT Phase III trials increased by 20 percent from 2021 to 2025, which of the following statements must be true based on the information above?

Apex BioTech conducted a greater total number of Phase III clinical drug trials in 2025 than it did in 2021.

The absolute expenditure on Phase III clinical trials at Apex BioTech increased by exactly 10 percentage points between 2021 and 2025.

Apex BioTech conducted fewer total clinical drug trials across all phases in 2025 than it conducted in 2021.

Phase III clinical trials conducted in 2025 were significantly more likely to yield successful market approvals than those conducted in 2021.

The proportion of non-Phase III trials that successfully advanced to Phase III status doubled between 2021 and 2025.

Show answer & explanation

Answer: Apex BioTech conducted a greater total number of Phase III clinical drug trials in 2025 than it did in 2021.

Answer

Apex BioTech conducted a greater total number of Phase III clinical drug trials in 2025 than it did in 2021.

The correct option is mathematically mandatory. Let total trials in 2021 equal 100. Non-Phase III trials in 2021 equal 85, and Phase III trials equal 15. In 2025, non-Phase III trials increased by 20% to

85 \times 1.20 = 102

. Since non-Phase III trials represent 75% of the 2025 total, the total number of trials in 2025 is

\frac{102}{0.75} = 136

. Consequently, Phase III trials in 2025 equal

136 - 102 = 34

. Because 34 is greater than 15, the company undeniably conducted more Phase III trials in 2025 than in 2021.

Step-by-Step Solution

1

Define variables for the total trial counts in 2021 (

T_{2021}

) and 2025 (

T_{2025}

).

In 2021, Phase III trials =

0.15 T_{2021}

and non-Phase III trials =

0.85 T_{2021}

. In 2025, Phase III trials =

0.25 T_{2025}

and non-Phase III trials =

0.75 T_{2025}

.

Establishing exact mathematical representations of the given proportions allows for direct structural comparison.

2

Relate the non-Phase III trial volume of 2025 to 2021 using the given 20% increase.

0.75 T_{2025} = 1.20 \times (0.85 T_{2021}) = 1.02 T_{2021}

. Solving for

T_{2025}

yields

T_{2025} = \frac{1.02}{0.75} T_{2021} = 1.36 T_{2021}

.

This proves that the total number of clinical trials increased by 36% overall from 2021 to 2025.

3

Calculate the absolute change in the number of Phase III trials.

In 2021, Phase III volume =

0.15 T_{2021}

. In 2025, Phase III volume =

0.25 T_{2025} = 0.25 \times (1.36 T_{2021}) = 0.34 T_{2021}

.

Comparing

0.34 T_{2021}

to

0.15 T_{2021}

shows that the absolute count of Phase III trials increased from 15% to 34% of the 2021 baseline total, confirming an undeniable increase.

Key Concept

Inferring absolute numerical shifts from proportional changes and base rate adjustments

Question 1537Question →

A metropolitan transit authority introduced micro-transit shuttle vans operating on flexible, demand-responsive routes to serve low-density suburban neighborhoods, hoping to boost overall public transit ridership. During the first year of operation, the shuttle service successfully attracted thousands of suburban residents who previously commuted exclusively by private automobiles. Nevertheless, total public transit ridership across the metropolitan area experienced a measurable decline over the same period.

Which of the following, if true, most helps to resolve the apparent paradox described above?

Because the flexible shuttle vans frequently drew vehicles and drivers from established fixed-route suburban bus lines, service frequency on those bus lines dropped significantly, causing a far greater number of regular bus riders to switch to private driving than the number of new commuters gained by the shuttles.

Suburban commuters who switched to the micro-transit shuttle vans reported higher satisfaction levels regarding trip comfort and door-to-door convenience compared to traditional municipal buses.

During the same year, the transit authority lowered fares on municipal bus lines throughout the metropolitan area to encourage broader public transit adoption.

High-density urban centers within the metropolitan area experienced slight population growth due to the construction of several new residential apartment complexes.

Private automobile ownership rates in the suburban neighborhoods served by the shuttle vans remained steady throughout the year.

Show answer & explanation

Answer: Because the flexible shuttle vans frequently drew vehicles and drivers from established fixed-route suburban bus lines, service frequency on those bus lines dropped significantly, causing a far greater number of regular bus riders to switch to private driving than the number of new commuters gained by the shuttles.

Answer

The statement explaining that shuttle vans drew drivers and vehicles away from fixed-route bus lines, causing a larger loss of bus riders than the gain in shuttle riders, resolves the paradox.

The correct choice reconciles both premises by identifying a trade-off in resource allocation. While the shuttle service attracted new suburban commuters, pulling vehicles and drivers from established bus lines degraded service quality on those lines. The resulting loss of regular bus riders outweighed the addition of new shuttle riders, explaining how total ridership could fall despite the new service's popularity.

Step-by-Step Solution

1

Identify the two contradictory facts in the stimulus.

Fact 1: The new suburban shuttle service successfully attracted thousands of former car drivers to public transit. Fact 2: Total metropolitan public transit ridership decreased overall.

Resolving a paradox requires finding a factor that allows both facts to be true simultaneously without denying either premise.

2

Evaluate the mechanism provided by the correct explanation.

By shifting resources away from existing bus lines to run the new shuttles, service on those bus lines degraded. This caused existing transit users to abandon public transit in numbers exceeding the new riders gained by the shuttle service.

This establishes a cause-and-effect relationship that accounts for both the localized success of the shuttle service and the net overall drop in transit system ridership.

Key Concept

Resolving Paradoxes and Discrepancies

Estimated Time:1m 30s

Question 1538Question →

### Tab 1: Vendor Contracting Policy
Vendor contracts exceeding $50,000 require formal approval from the Department Head. Additionally, any vendor contract involving external data processing or third-party sharing of customer data requires approval from the Data Privacy Officer, regardless of the contract's total monetary value.

### Tab 2: Legal Department Memorandum
The procurement request for Project Alpha specifies a new vendor contract valued at $35,000. Under the terms of the agreement, the vendor will perform a third-party audit of consumer behavioral data.

Statement: Based on the provided documents, the vendor contract for Project Alpha requires approval from the Data Privacy Officer but does not require approval from the Department Head.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True.

Synthesizing Tab 1 and Tab 2 confirms that the contract value (

35,000) does not meet the

50,000 threshold for Department Head review, but its scope (third-party audit of consumer behavioral data) mandates Data Privacy Officer review regardless of dollar amount.

Step-by-Step Solution

1

Evaluate the requirement for Department Head approval using Tab 1 and Tab 2.

Tab 1 states that contracts exceeding

50,000 require Department Head approval. Tab 2 shows the Project Alpha contract value is

35,000, so Department Head approval is not required.

The monetary value is below the policy threshold.

2

Evaluate the requirement for Data Privacy Officer approval using Tab 1 and Tab 2.

Tab 1 requires Data Privacy Officer approval for any contract involving third-party sharing of customer data regardless of value. Tab 2 specifies the contract includes a third-party audit of consumer behavioral data, so Data Privacy Officer approval is required.

The nature of the work triggers the mandatory data privacy policy condition.

3

Synthesize findings to confirm the validity of the statement.

The contract requires Data Privacy Officer approval and does not require Department Head approval, making the statement True.

Both conditions evaluated match the statement exactly.

Key Concept

Tabbed Text Document Analysis

Question 1539Question →

Read the following argument carefully, then match each key term from the argument to the specific shift in meaning it undergoes between the premise context and the conclusion context:

'To ensure market stability, regulatory boards must foster fair competition among competing energy firms. However, fair competition exists only when no firm holds an unfair advantage over its rivals. Because companies holding proprietary patents on green technology possess a clear operational advantage not shared by competitors, patent enforcement violates fair competition. Thus, patent protections undermine market stability.'

Click a left item, then click its matching right item

Show answer & explanation

Answer

The terms 'Fair competition', 'Unfair advantage', and 'Market stability' each shift from standard regulatory definitions in the premises to overly restrictive, outcome-focused definitions in the conclusion.

The correct pairings accurately pinpoint how each term's scope changes to make an invalid conclusion appear logically valid. 'Fair competition' shifts from impartial rules to equal capabilities; 'unfair advantage' shifts from illegal practice to legal patent ownership; and 'market stability' shifts from structural order to protection from competitive innovation.

Step-by-Step Solution

1

Analyze how 'fair competition' is introduced in the premise versus how it is applied to patent holders.

The argument moves from procedural fairness (equal rules) to outcome equality (no technological gaps).

This establishes the primary equivocation regarding competitive fairness.

2

Trace the implicit definition of 'unfair advantage'.

The premise implies improper advantage, but the argument equates this with holding valid intellectual property rights.

This shows how a term with negative normative connotations is improperly applied to legal research outcomes.

3

Examine the shift in 'market stability'.

Systemic stability is conflated with insulating existing market actors from competitive pressure.

This completes the logical flaw, demonstrating that the final conclusion rests on shifting definitions rather than sound premises.

Key Concept

Equivocation and Shift in Term Meaning

Estimated Time:2m 0s

Question 1540Question →

If $x$ and $y$ are real numbers such that $x \neq y$ , what is the value of $x + y$ ?

(1) $x^3 - y^3 = 7(x - y)$
(2) $x^2 - y^2 = 3(x - y)$

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

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

Answer

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

The question stem explicitly states that

x \neq y

, establishing that

x - y \neq 0

. In Statement (2), factoring

x^2 - y^2

into

(x - y)(x + y) = 3(x - y)

and dividing by non-zero

(x - y)

directly yields the unique value

x + y = 3

. In Statement (1), factoring gives

x^2 + xy + y^2 = 7

, which leaves

x + y

undetermined because

xy

can vary. Consequently, Statement (2) alone is sufficient, while Statement (1) alone is not.

Step-by-Step Solution

1

Analyze the question stem constraints and target expression.

We are given that

x

and

y

are real numbers with

x \neq y

, which implies

x - y \neq 0

. The goal is to determine a single unique value for

x + y

.

Establishing

x - y \neq 0

allows valid algebraic division by

(x - y)

in the given statements.

2

Evaluate Statement (1) independently:

x^3 - y^3 = 7(x - y)

.

Factor the left side using the difference of cubes identity:

(x - y)(x^2 + xy + y^2) = 7(x - y)

. Since

x - y \neq 0

, divide both sides by

(x - y)

to get

x^2 + xy + y^2 = 7

, which rewrites to

(x + y)^2 - xy = 7

.

Because

xy

is unknown and variable,

(x + y)

can take multiple values. For instance,

(x, y) = (2, 1)

gives

x+y=3

and

4+2+1=7

, whereas

(x, y) = (\sqrt{7}, -\sqrt{7})

gives

x+y=0

and

7-7+7=7

. Thus, Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) independently:

x^2 - y^2 = 3(x - y)

.

Factor the left side using the difference of squares identity:

(x - y)(x + y) = 3(x - y)

. Since

x - y \neq 0

, divide both sides by

(x - y)

to yield

x + y = 3

.

This provides a single, unambiguous numerical value for

x + y

. Therefore, Statement (2) alone IS sufficient.

Key Concept

Algebraic expression simplification using stem constraints in Data Sufficiency

Answer

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