All practice questions

Question 1Question →

Many urban planners argue that expanding municipal light rail systems inevitably reduces traffic congestion in suburban corridors. However, a recent comprehensive study revealed that suburban commuters rarely shift from private automobiles to light rail unless parking fees in urban business districts increase significantly. Consequently, proposing light rail expansion without simultaneous adjustments to municipal parking pricing will fail to relieve suburban traffic. Implementing higher parking fees will incentivize a sufficient number of commuters to adopt public transit, thereby achieving the desired reduction in highway congestion.

In the argument above, what are the respective roles played by the two boldfaced portions?

The first is evidence cited to challenge a position that the argument opposes; the second provides a rationale for a key condition necessary for the proposed solution to succeed.

The first is the main conclusion of the argument; the second is a premise offered in support of that conclusion.

The first is a counterargument directed against the author's primary recommendation; the second is the author's main conclusion.

The first provides background information establishing the context of transit planning; the second is an intermediate conclusion that directly refutes the urban planners' claim.

The first is evidence supporting the traditional view held by urban planners; the second is a concession made to those who oppose municipal transit funding.

Show answer & explanation

Answer: The first is evidence cited to challenge a position that the argument opposes; the second provides a rationale for a key condition necessary for the proposed solution to succeed.

Answer

The option stating that the first bolded portion is evidence cited to challenge a position that the argument opposes, and the second provides a rationale for a key condition necessary for the proposed solution to succeed.

The correct option accurately evaluates both bolded statements: the first bolded statement presents empirical study findings that counter the claim of urban planners (a position the author opposes), while the second bolded statement explains the mechanism by which higher parking fees achieve reduced highway congestion, functioning as a supporting rationale for the essential condition identified by the author.

Step-by-Step Solution

1

Analyze the overall argument structure and identify the author's main conclusion.

The argument begins with an opposing view ('Many urban planners argue...'). The author's main conclusion is that proposing light rail expansion without adjusting parking fees will fail to relieve traffic.

Establishing the main conclusion enables accurate classification of surrounding supporting statements.

2

Determine the functional role of the first bolded statement.

The first bolded statement presents study findings demonstrating that commuters do not switch to light rail unless parking fees rise. This evidence directly undermines the urban planners' traditional view and supports the author's conclusion.

The contrastive transition 'However' signals that the study evidence refutes the initial position.

3

Determine the functional role of the second bolded statement.

The second bolded statement explains why raising parking fees works—by incentivizing commuters to adopt public transit—thereby justifying the condition required for transit success.

It provides the underlying mechanism/rationale for why parking fee adjustments are essential.

4

Match the structural analysis to the correct option.

The option identifying the first statement as evidence challenging an opposed position and the second statement as a rationale for a key condition is correct.

It captures the exact logical relationship of both bolded statements to the argument.

Key Concept

Analyzing Bolded Statement Roles in Critical Reasoning

Question 2Question →

If $x$ is a nonzero real number, is $\frac{x^2 - 4x}{x} > 0$ ?

(1) $x > 5$
(2) $x^2 > 16$

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.

Simplifying the target expression

\frac{x^2 - 4x}{x}

for

x \neq 0

yields

x - 4

. Thus, the question target rephrases to 'Is

x > 4

?'. Statement (1) states

x > 5

, which guarantees

x > 4

, yielding a definitive 'Yes' answer. Statement (2) allows

x > 4

or

x < -4

, yielding both 'Yes' and 'No' outcomes. Therefore, Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Step-by-Step Solution

1

Simplify the question stem expression

Since

x \neq 0

, factor out

x

from the numerator:

\frac{x(x - 4)}{x} = x - 4

.

Simplifying the expression reveals the underlying condition required by the question stem.

2

Rephrase the target question

The original question 'Is

\frac{x^2 - 4x}{x} > 0

?' simplifies to 'Is

x - 4 > 0

?', which is equivalent to 'Is

x > 4

?'.

Target rephrasing turns a fraction inequality into a simple comparison.

3

Evaluate Statement (1):

x > 5

If

x > 5

, then

x

is strictly greater than 4. The answer to 'Is

x > 4

?' is a definitive YES.

Since Statement (1) provides a conclusive 'Yes', Statement (1) alone is sufficient.

4

Evaluate Statement (2):

x^2 > 16

Taking the square root gives

|x| > 4

, meaning

x > 4

or

x < -4

.
- If

x = 5

, then

x > 4

(YES).
- If

x = -5

, then

x < 4

(NO).

Because Statement (2) allows both 'Yes' and 'No' answers, it is not sufficient.

Key Concept

Question Stem Simplification and Target Rephrasing

Question 3Question →

Is $x$ an integer?

(1) $3x$ is an integer.
(2) $5x$ is an integer.

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.

Evaluating Statement (1) alone shows

x

could be

\frac{1}{3}

(not an integer) or

1

(an integer), so Statement (1) is insufficient. Evaluating Statement (2) alone shows

x

could be

\frac{1}{5}

(not an integer) or

1

(an integer), so Statement (2) is insufficient. Taking both statements together,

3x = a

and

5x = b

for integers

a

and

b

. Subtracting

5x

from

2(3x)

yields

6x - 5x = x = 2a - b

. Because integers are closed under multiplication and subtraction,

2a - b

must be an integer, confirming that

x

is definitively an integer.

Step-by-Step Solution

1

Evaluate Statement (1) independently

If

3x = a

where

a

is an integer, then

x = \frac{a}{3}

. If

a = 1

,

x = \frac{1}{3}

(not an integer). If

a = 3

,

x = 1

(an integer).

Since

x

can be either an integer or a non-integer, Statement (1) alone is not sufficient.

2

Evaluate Statement (2) independently

If

5x = b

where

b

is an integer, then

x = \frac{b}{5}

. If

b = 1

,

x = \frac{1}{5}

(not an integer). If

b = 5

,

x = 1

(an integer).

Since

x

can be either an integer or a non-integer, Statement (2) alone is not sufficient.

3

Evaluate Statements (1) and (2) together

Since

3x

and

5x

are both integers, their linear combination

2(3x) - 5x = 6x - 5x = x

must also be an integer.

The difference between two integers is always an integer, proving conclusively that

x

is an integer.

Key Concept

Linear combinations of real numbers and integer constraints in Data Sufficiency

Estimated Time:1m 0s

Question 4Question →

In a GMAT Data Sufficiency 'Value' question asking for the numerical value of $x + y$ , a statement that establishes that $x + y$ can equal either $5$ or $-5$ is considered sufficient.

True

False

Show answer & explanation

Answer: False

Answer

False

The assertion is false because GMAT 'Value' Data Sufficiency questions require finding a single, unique numerical value for the target expression. Obtaining two possible values (

5

or

-5

) means the value is not uniquely determined, rendering the statement insufficient.

Step-by-Step Solution

1

Identify the question type as a 'Value' Data Sufficiency problem.

The target requirement is to find one unique numerical value for

x + y

.

Value DS questions require absolute numerical uniqueness.

2

Evaluate the information provided by the statement.

The statement yields two possible values:

5

and

-5

.

Having multiple values means the exact value of

x + y

cannot be uniquely determined.

3

Determine sufficiency.

Since two distinct values exist, the statement is insufficient, making the assertion false.

Sufficiency in Value DS strictly demands a single unique outcome.

Key Concept

Value Data Sufficiency Decision Logic

Estimated Time:1m 0s

Question 5Question →

Over the past year, a gourmet coffee subscription company recorded a significant increase in the total number of monthly account cancellations. However, during that same year, the company's monthly cancellation rate—defined as the percentage of total active subscribers who canceled their accounts each month—steadily decreased.

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

The total number of active subscribers to the coffee service increased substantially over the course of the year.

Customer satisfaction surveys showed that most subscribers who canceled were dissatisfied with recent delivery delays.

The subscription company increased its monthly service fees substantially at the start of the year.

The company introduced several new premium coffee roasts mid-way through the year.

Competing subscription services experienced a similar rise in the overall number of customer cancellations.

Show answer & explanation

Answer: The total number of active subscribers to the coffee service increased substantially over the course of the year.

Answer

The total number of active subscribers to the coffee service increased substantially over the course of the year.

The correct answer resolves the paradox by identifying a shift in the overall subscriber base. Total cancellations equal the cancellation rate multiplied by the total number of active subscribers. If the total subscriber base grew substantially, a lower percentage cancellation rate would still yield a higher absolute number of cancellations.

Step-by-Step Solution

1

Identify the two contradictory facts in the stimulus.

Fact 1: Total monthly cancellations increased. Fact 2: The monthly cancellation rate (percentage of active subscribers canceling) decreased.

Resolving a paradox requires finding an underlying factor that allows both facts to exist simultaneously without denying either premise.

2

Analyze the relationship between rate and total volume.

Total Cancellations = (Total Active Subscribers) × (Cancellation Rate).

If the cancellation rate drops while the total number of cancellations increases, the total number of active subscribers must have expanded.

3

Evaluate the option choices to find the statement establishing subscriber base growth.

The option stating that active subscribers increased substantially provides the missing mathematical linkage.

A much larger denominator (total active subscribers) yields a higher total count of cancellations even when the percentage fraction is smaller.

Key Concept

Resolving Rate versus Total Volume Discrepancies

Question 6Question →

Read the argument below and match each boldfaced statement to its precise structural role within the reasoning.

Some urban planners claim that the city council should not enact the proposed mandate requiring all new commercial buildings to install reflective white roofs. These planners contend that white roofs rapidly accumulate atmospheric soot, rendering them ineffective within two years. However, long-term field testing demonstrates that periodic rainfall naturally washes away over 85 percent of soot deposits from modern reflective roofing materials. Therefore, dirt accumulation does not significantly diminish the long-term cooling efficiency of white roofs, and the council should proceed with implementing the mandate.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The statement opposing the mandate matches the opposing claim; the statement regarding cooling efficiency matches the intermediate conclusion countering the opponents' objection; and the statement recommending implementation matches the main conclusion of the argument.

Matching statement 1 with the opposing claim correctly identifies the position that the author rejects. Matching statement 2 with the intermediate conclusion recognizes that it is a claim derived from rainfall evidence and used to dismantle the opponents' objection. Matching statement 3 with the main conclusion correctly isolates the primary judgment supported by the entire passage.

Step-by-Step Solution

1

Identify the overall stance and main conclusion of the author.

The author argues in favor of passing the mandate, explicitly concluding in the final statement that 'the council should proceed with implementing the mandate.'

Establishing the main conclusion clarifies the ultimate goal of the passage.

2

Analyze the role of the first boldfaced statement.

The first boldfaced statement presents the view of 'some urban planners' who argue against enacting the mandate. The author directly rejects this view.

Identifying opponent positions helps differentiate between opposing claims and the author's own premises.

3

Analyze the function of the factual evidence and the second boldfaced statement.

The author introduces premise evidence (rainfall cleaning modern materials) to draw a sub-conclusion: dirt accumulation does not significantly diminish efficiency. This sub-conclusion directly addresses and counters the opponents' soot objection.

An intermediate conclusion relies on factual evidence and serves to build logical support toward the main conclusion.

Key Concept

Identifying structural roles of statements in GMAT Critical Reasoning arguments

Question 7Question →

The following documents detail fleet operations for a regional transport firm in 2026:

Tab 1: Fleet Maintenance Policy (Section 4)
- 4.2 Preventative Maintenance Limit: Scheduled routine maintenance downtime for heavy cargo vans must not exceed an average of $8\text{ hours}$ per vehicle per quarter.
- 4.5 Emergency Exemption: Downtime resulting from emergency powertrain overhauls is classified as Unscheduled Fleet Services and is strictly exempt from the $8\text{-hour}$ preventative maintenance downtime cap.

Tab 2: Q2 Internal Audit Report
- The Heavy Cargo Van Division operated $120\text{ vehicles}$ during Q2 2026.
- Total fleet downtime recorded for maintenance during Q2 was $1,440\text{ hours}$ , yielding an average of $12\text{ hours}$ of maintenance downtime per vehicle.
- Finding: The division violated Section 4.2 by exceeding the maximum allowable routine downtime limit by $50\%$ .

Tab 3: Service Maintenance Logs Excerpt
- In Q2 2026, $30$ of the $120\text{ heavy cargo vans}$ required emergency powertrain overhauls following a manufacturer recall, logging a total of $720\text{ hours}$ under emergency repairs.
- The remaining $720\text{ hours}$ of total maintenance downtime across the division were incurred for standard routine preventative maintenance.

Statement to Evaluate:
Based on the information provided across the three sources, the internal audit report's finding that the division violated the routine downtime policy in Q2 2026 is invalid because it improperly included exempt emergency repair downtime in its calculation.

True

False

Show answer & explanation

Answer: True

Answer

True. The audit finding is invalid because excluding the

720\text{ hours}

of exempt emergency powertrain repairs reduces the relevant routine maintenance downtime to

720\text{ hours}

, which averages

\le 8\text{ hours}

per vehicle and complies with Section 4.2.

The evaluated statement is correct (True) because synthesizing Section 4.5 from Tab 1 with the downtime breakdown in Tab 3 shows that

720\text{ hours}

were exempt emergency repairs. Subtracting these leaves

720\text{ routine maintenance hours}

, which meets the requirement of

\le 8\text{ hours}

per vehicle.

Step-by-Step Solution

1

Identify the conflict between the sources.

Tab 2 claims a violation based on an average of

12\text{ hours}

downtime per vehicle (

1,440\text{ total hours} / 120\text{ vans}

), whereas Tab 1 Section 4.5 outlines a specific policy exemption for emergency powertrain overhauls.

Resolving discrepancies requires checking whether reported figures conform to defined policy boundaries and exceptions.

2

Extract exempt downtime using Tab 3 maintenance logs.

Emergency powertrain overhauls accounted for

720\text{ hours}

of downtime in Q2.

Section 4.5 explicitly states emergency powertrain overhaul hours are exempt from the routine maintenance cap.

3

Calculate non-exempt routine preventative maintenance downtime.

Total downtime (

1,440\text{ hours}

) minus exempt emergency downtime (

720\text{ hours}

) =

720\text{ non-exempt routine downtime hours}

.

Only non-exempt hours should be evaluated against the Section 4.2 preventative maintenance limit.

4

Evaluate compliance against the policy threshold.

720\text{ routine hours} / 120\text{ vans} = 6\text{ hours per van}

(or

720\text{ routine hours} / 90\text{ routine vans} = 8\text{ hours per van}

). Both values are

\le 8\text{ hours}

.

Because the compliant routine average does not exceed

8\text{ hours}

, the audit report's finding of a violation was invalid.

Key Concept

Discrepancy and Conflict Resolution Between Sources

Question 8Question →

Read the following sentence regarding historical forest ecology:

"While early twentieth-century silviculturists asserted that the rapid decline of old-growth oak stands in the Baltic basin was driven primarily by overharvesting for naval shipbuilding, recent dendrochronological analysis reveals that severe decadal drought cycles in the late seventeenth century had already compromised root systems, rendering these stands uniquely susceptible to fungal pathogens prior to the onset of intensive timber extraction."

Which of the following inferences regarding the decline of Baltic oak stands is most strongly supported by the statement above?

The vulnerability of Baltic oak stands to fungal pathogens was heightened by environmental stress experienced prior to the expansion of intensive timber harvesting.

Intensive timber harvesting for naval construction posed a greater long-term ecological threat to Scandinavian forests than to Baltic basin oak stands.

Late seventeenth-century dendrochronological records confirm that naval shipbuilding was the primary driver of oak depletion, validating early silvicultural theories.

Twentieth-century silviculturists maintained that fungal pathogens, rather than drought, were responsible for compromising the root structures of Baltic oaks.

Timber extraction had absolutely no impact on the overall decline of Baltic oak stands compared to the devastating effects of fungal pathogens.

Show answer & explanation

Answer: The vulnerability of Baltic oak stands to fungal pathogens was heightened by environmental stress experienced prior to the expansion of intensive timber harvesting.

Answer

The vulnerability of Baltic oak stands to fungal pathogens was heightened by environmental stress experienced prior to the expansion of intensive timber harvesting.

The sentence specifies that drought cycles in the late seventeenth century compromised root systems and rendered oak stands uniquely susceptible to fungal pathogens prior to the onset of intensive timber extraction. This directly supports the conclusion that environmental stress occurring before expanded harvesting heightened the trees' vulnerability to pathogens.

Step-by-Step Solution

1

Analyze the logical structure of the target sentence.

The sentence contrasts an older view (silviculturists claiming shipbuilding overharvesting was the main cause) with recent dendrochronological evidence.

Identifying the main clause clarifies what the author actually asserts as factual.

2

Examine the specific temporal and causal sequence presented in the evidence.

Late 17th-century drought cycles -> compromised root systems -> made trees susceptible to pathogens -> occurred prior to intensive timber extraction.

Evaluating pre-existing conditions confirms how drought stress preceded and enabled fungal vulnerability.

3

Match the sequence to the correct inference.

The statement directly supports that pre-harvesting environmental stress (drought) increased susceptibility (vulnerability) to pathogens.

A valid GMAT single-sentence inference must rely strictly on stated facts without external assumptions.

Key Concept

Single-Sentence Logical Inference

Question 9Question →

For all integers $a$ , $b$ , and $c$ , if the expression $a^3 b - b^3 c + c^3 a$ is an odd integer, then the product $(a - b)(b - c)(c - a)$ must be divisible by 4.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False.

The statement claims that the product must be divisible by 4 for all integer inputs where the given expression is odd. However, setting two variables to odd integers and one variable to an even integer (such as

a=3, b=1, c=0

) makes the initial expression odd (

27

) while producing a product of

-6

, which is not divisible by 4.

Step-by-Step Solution

1

Simplify the expression modulo 2 to establish necessary parity conditions.

Since

x^3 \equiv x \pmod 2

for any integer

x

, the parity of

x^3 y

is identical to the parity of

xy

. Thus,

a^3b - b^3c + c^3a \equiv ab - bc + ca \pmod 2

.

Reducing powers modulo 2 determines which parity combinations of

a, b,

and

c

yield an odd result.

2

Analyze all possible parity combinations for the three variables.

Case 1: All three are odd

\implies odd - odd + odd = odd

.
Case 2: Two are odd and one is even (e.g.,

a, b

odd,

c

even)

\implies odd - even + even = odd

.
Case 3: One is odd and two are even

\implies even - even + even = even

.
Case 4: All three are even

\implies even - even + even = even

.

Identifying that both Case 1 and Case 2 produce an odd value is essential for finding edge cases.

3

Test Case 2 using specific integer values to check whether

(a - b)(b - c)(c - a)

must be divisible by 4.

Set

a = 3

(odd),

b = 1

(odd), and

c = 0

(even). The given expression equals

3^3(1) - 1^3(0) + 0^3(3) = 27

, which is odd. Evaluating the product gives

(3 - 1)(1 - 0)(0 - 3) = (2)(1)(-3) = -6

.

Testing specific valid integers disproves a universal 'must be' claim.

4

Evaluate the divisibility of the resulting product by 4.

-6

is not divisible by 4 because

-6 / 4 = -1.5

, which is not an integer.

Finding a valid case where the product is not divisible by 4 proves the statement is false.

Key Concept

Parity rules for algebraic expressions and edge-case evaluation using zero as an even integer

Question 10Question →

A marine conservation agency abides by the following guidelines regarding commercial oceanic operations: An oceanic research institute will approve a coastal zone for deep-sea mining only if the zone undergoes an ecological impact assessment. An ecological impact assessment is conducted whenever a designated marine habitat contains endangered coral species, unless the habitat is classified as a protected sanctuary. Furthermore, any coastal zone that undergoes an ecological impact assessment requires the implementation of continuous acoustic monitoring.

If the statements above are true, which of the following MUST also be true?

A coastal zone cannot be approved for deep-sea mining without the implementation of continuous acoustic monitoring.

Any coastal zone in which continuous acoustic monitoring is implemented will automatically be approved for deep-sea mining.

If a designated marine habitat is classified as a protected sanctuary, an ecological impact assessment cannot be conducted under any circumstances.

Any designated marine habitat that contains endangered coral species must implement continuous acoustic monitoring.

A coastal zone that does not contain endangered coral species is not required to implement continuous acoustic monitoring under any circumstances.

Show answer & explanation

Answer: A coastal zone cannot be approved for deep-sea mining without the implementation of continuous acoustic monitoring.

Answer

A coastal zone cannot be approved for deep-sea mining without the implementation of continuous acoustic monitoring.

The passage establishes a chain of necessary conditions: approval for deep-sea mining requires an ecological impact assessment (Approval -> Assessment), and an ecological impact assessment requires continuous acoustic monitoring (Assessment -> Monitoring). Combining these transitive statements yields Approval -> Monitoring. The contrapositive of this deduction is that without continuous acoustic monitoring, a zone cannot receive approval for deep-sea mining.

Step-by-Step Solution

1

Formalize the conditional statements provided in the passage.

Statement 1: Approval -> Assessment. Statement 2: Coral AND NOT Sanctuary -> Assessment. Statement 3: Assessment -> Monitoring.

Mapping the premises into logical notation clarifies valid deductions and prevents common fallacies.

2

Chain the conditional statements linking Approval, Assessment, and Monitoring.

Approval -> Assessment -> Monitoring. Thus, Approval -> Monitoring.

Transitive logic allows combining two nested conditional rules sharing a middle term (Assessment).

3

Take the contrapositive of the combined deduction.

NOT Monitoring -> NOT Approval.

A conditional statement is logically equivalent to its contrapositive, confirming that without monitoring, approval is impossible.

Key Concept

Conditional Logic and Formal Deductions

Question 11Question →

Under municipal transit regulations, a technology firm receives a commercial testing permit for autonomous trucks on public highways only if its navigation software achieves a Tier-1 safety certification. Achieving a Tier-1 safety certification requires completing at least 500,000 miles of simulated urban driving without a single critical system disengagement. Furthermore, unless a firm holds a commercial testing permit, it is forbidden from deploying autonomous vehicles during peak traffic hours.

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

A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.

Any technology firm that completes 500,000 miles of simulated urban driving without a critical system disengagement will automatically receive a commercial testing permit.

A technology firm that has not been permitted to deploy autonomous vehicles during peak traffic hours has failed to achieve a Tier-1 safety certification.

Autonomous trucks that have logged 500,000 miles of simulated urban driving are safer than conventional commercial trucks operated by human drivers.

Technology firms holding a commercial testing permit deploy autonomous trucks exclusively during non-peak traffic hours.

Show answer & explanation

Answer: A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.

Answer

A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.

The passage establishes a chain of necessary conditions: to deploy during peak traffic hours, a firm must hold a commercial testing permit; to have that permit, it must hold Tier-1 certification; and to achieve Tier-1 certification, it must complete 500,000 simulated miles without a critical disengagement. Therefore, any firm deploying vehicles during peak hours must have completed those 500,000 simulated miles.

Step-by-Step Solution

1

Formalize the conditional statements given in the passage

Statement 1: Commercial Permit -> Tier-1 Certification. Statement 2: Tier-1 Certification -> 500,000 Simulated Miles without critical disengagement. Statement 3: Deploy Peak Hours -> Commercial Permit.

Translating natural language indicators ('only if', 'requires', 'unless') into formal logic clarifies necessary and sufficient conditions.

2

Chain the conditional statements together transitively

Deploy Peak Hours -> Commercial Permit -> Tier-1 Certification -> 500,000 Simulated Miles.

Because each condition is necessary for the preceding one, the entire chain must hold true.

3

Deduce the logically necessary conclusion

Deploying during peak traffic hours necessarily implies having completed at least 500,000 miles of simulated driving without a critical disengagement.

If the antecedent of the chain is true, all necessary conditions down the chain must also be true.

Key Concept

Transitive Chaining of Necessary Conditions

Question 12Question →

A bag contains 5 red marbles and 5 blue marbles. If 2 marbles are randomly selected from the bag one after another without replacement, what is the probability that at least one of the selected marbles is red?

\frac{7}{9}

\frac{2}{9}

\frac{5}{9}

\frac{3}{4}

\frac{1}{4}

Show answer & explanation

Answer: $\frac{7}{9}$

Answer

\frac{7}{9}

To find the probability of drawing at least one red marble, calculate the probability of the complementary event (drawing two blue marbles) and subtract it from 1. The probability of selecting a blue marble on the first draw is

\frac{5}{10}

, and on the second draw without replacement it is

\frac{4}{9}

. The probability of both marbles being blue is

\frac{5}{10} \times \frac{4}{9} = \frac{2}{9}

. Subtracting this from 1 gives

1 - \frac{2}{9} = \frac{7}{9}

.

Step-by-Step Solution

1

Identify the complementary outcome

The event 'at least one marble is red' is complementary to the event 'no marbles are red' (i.e., 'both marbles are blue').

Using the relationship

P(\text{at least one red}) = 1 - P(\text{both blue})

is simpler than summing individual favorable cases.

2

Calculate the probability of drawing two blue marbles without replacement

The probability that the first marble is blue is

\frac{5}{10} = \frac{1}{2}

. The probability that the second marble is blue is

\frac{4}{9}

. Therefore,

P(\text{both blue}) = \frac{5}{10} \times \frac{4}{9} = \frac{20}{90} = \frac{2}{9}

.

Since draws are without replacement, the sample space and number of blue marbles decrease by 1 after the first draw.

3

Subtract the complementary probability from 1

P(\text{at least one red}) = 1 - \frac{2}{9} = \frac{7}{9}

.

The sum of complementary probabilities is always equal to 1.

Key Concept

Complementary Probability:

P(\text{at least one}) = 1 - P(\text{none})

Question 13Question →

A rectangular tabletop measuring $126\text{ centimeters}$ by $180\text{ centimeters}$ is to be completely covered by non-overlapping, identical square tiles of the maximum possible side length, such that no tiles need to be cut. How many such square tiles are required to cover the entire tabletop?

Show answer & explanation

Answer: 70

Answer

70 tiles are required to cover the tabletop.

To cover a

126\text{ cm} \times 180\text{ cm}

surface with identical square tiles of maximum side length without cutting, the side length of each square tile must be the greatest common divisor of

126

and

180

, which is

18\text{ cm}

. Dividing the surface dimensions by

18\text{ cm}

gives

7

tiles along one side and

10

tiles along the other, yielding a total of

70

tiles.

Step-by-Step Solution

1

Determine the prime factorizations of the tabletop dimensions 126 and 180.

126 = 2^1 \times 3^2 \times 7^1

and

180 = 2^2 \times 3^2 \times 5^1

Prime factorization allows systematic extraction of the greatest common divisor.

2

Calculate the Greatest Common Divisor (GCD) of 126 and 180.

\text{GCD}(126, 180) = 2^{\min(1,2)} \times 3^{\min(2,2)} = 2^1 \times 3^2 = 18

The maximum side length of a square tile that fits evenly without cutting is the GCD of the two dimensions.

3

Find the total number of tiles required.

\text{Total tiles} = \left(\frac{126}{18}\right) \times \left(\frac{180}{18}\right) = 7 \times 10 = 70

The total area divided by the area of one tile gives the number of tiles needed.

Key Concept

Greatest Common Divisor (GCD) application in geometric spatial partitioning

Question 14Question →

For all non-zero real numbers $a$ and $b$ with $|a| \neq |b|$ , the Data Sufficiency Yes/No target question "Is $\frac{a^2 - b^2}{ab} > 0$ ?" is algebraically equivalent to asking whether $a$ and $b$ have the same sign when $|a| > |b|$ , or different signs when $|a| < |b|$ .

True

False

Show answer & explanation

Answer: True

Answer

True. The rephrased question accurately state the necessary and sufficient conditions for the fraction

\frac{a^2 - b^2}{ab}

to be positive.

The quotient

\frac{a^2 - b^2}{ab}

is positive when both

a^2 - b^2

and

ab

are positive, or when both are negative. If

a

and

b

have the same sign (

ab > 0

), then

a^2 - b^2 > 0

, which simplifies to

a^2 > b^2

or

|a| > |b|

. If

a

and

b

have different signs (

ab < 0

), then

a^2 - b^2 < 0

, which simplifies to

a^2 < b^2

or

|a| < |b|

. Hence, the statement correctly describes the target simplification.

Step-by-Step Solution

1

Set up the quotient inequality condition

The fraction

\frac{a^2 - b^2}{ab} > 0

holds when numerator

a^2 - b^2

and denominator

ab

have matching signs.

For any real fraction

\frac{N}{D} > 0

, either (

N > 0

and

D > 0

) or (

N < 0

and

D < 0

).

2

Analyze Case 1 where denominator

ab > 0

a

and

b

have the same sign. In this case,

\frac{a^2 - b^2}{ab} > 0 \implies a^2 - b^2 > 0 \implies |a| > |b|

.

When

ab > 0

, multiplying both sides of the inequality by

ab

preserves the inequality sign.

3

Analyze Case 2 where denominator

ab < 0

a

and

b

have different signs. In this case,

\frac{a^2 - b^2}{ab} > 0 \implies a^2 - b^2 < 0 \implies |a| < |b|

.

When

ab < 0

, multiplying both sides of the inequality by

ab

flips the inequality direction.

4

Combine the cases to evaluate the target rephrasing

The target question simplifies to: "Do

a

and

b

have the same sign with

|a| > |b|

, or opposite signs with

|a| < |b|

?"

Both cases together form the complete rephrased condition for the original statement to be true.

Key Concept

Algebraic Rephrasing of Quotients involving Absolute Values and Variable Signs

Question 15Question →

If $x$ is a positive real number, is $x$ an integer?

(1) $x^3$ is an integer.
(2) $x^5$ is an integer.

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.

Evaluating each statement independently leaves open the possibility that

x

is an irrational root like

\sqrt[3]{2}

or

\sqrt[5]{2}

, making neither statement alone sufficient. Combining both statements allows us to express

x

as

\frac{(x^3)^2}{x^5}

. Because both

x^3

and

x^5

are integers,

x

must be a rational number. For any rational number whose cube is an integer, its denominator must equal 1, which proves conclusively that

x

is an integer. Thus, both statements together are sufficient.

Step-by-Step Solution

1

Evaluate Statement (1) independently.

Statement (1) is insufficient.

If

x = 2

, then

x^3 = 8

(an integer), so

x

is an integer (Yes). However, if

x = \sqrt[3]{2}

, then

x^3 = 2

(an integer), but

x

is not an integer (No). Since both Yes and No answers are possible, Statement (1) alone is not sufficient.

2

Evaluate Statement (2) independently.

Statement (2) is insufficient.

If

x = 2

, then

x^5 = 32

(an integer), so

x

is an integer (Yes). However, if

x = \sqrt[5]{2}

, then

x^5 = 2

(an integer), but

x

is not an integer (No). Since both Yes and No answers are possible, Statement (2) alone is not sufficient.

3

Combine Statement (1) and Statement (2).

The combined statements are sufficient.

Notice that

\frac{(x^3)^2}{x^5} = \frac{x^6}{x^5} = x

. Since

x^3

is an integer,

(x^3)^2

is also an integer. Since

x^5

is an integer,

x = \frac{(x^3)^2}{x^5}

is the ratio of two integers, meaning

x

must be a rational number. If

x = \frac{a}{b}

in simplest form where

a

and

b

are positive integers with

\gcd(a,b)=1

, then

x^3 = \frac{a^3}{b^3}

being an integer implies

b^3 = 1

, so

b = 1

. Thus,

x = a

, which means

x

must be an integer. This yields a definitive 'Yes' answer.

Key Concept

Integer constraints versus real numbers in Data Sufficiency and quotient relationships of exponent powers

Question 16Question →

To combat declining municipal revenues from downtown parking meters, the city council of Elmridge plans to eliminate the two-hour parking limit on all downtown streets. Council members argue that allowing drivers to park indefinitely will encourage visitors to spend more time dining and shopping in the downtown district, thereby increasing local business sales and boosting the city's sales tax revenues.

Which of the following, if true, most seriously weakens the city council's argument?

Eliminating time limits causes downtown office commuters to occupy parking spaces early in the morning for full workdays, drastically reducing space availability for shoppers and diners.

A recent survey of downtown shoppers indicated that over seventy percent of respondents cited fear of receiving a parking ticket as their main reason for cutting trips short.

Neighboring municipalities that recently increased their parking violation fines experienced a fifteen percent decrease in overall downtown vehicle traffic.

Sales tax rates in Elmridge are slightly higher than those in surrounding suburban commercial shopping centers.

A clear majority of downtown retail merchants currently favor the city council's proposed parking modification.

Show answer & explanation

Answer: Eliminating time limits causes downtown office commuters to occupy parking spaces early in the morning for full workdays, drastically reducing space availability for shoppers and diners.

Answer

The argument is most seriously weakened by the finding that removing parking time limits will cause full-day office commuters to occupy downtown parking spaces early in the morning, thereby reducing space availability for shoppers and diners throughout the day.

The correct answer weakens the argument by demonstrating an unintended side effect of the plan: full-day office commuters will park early and occupy downtown spaces all day. This severely reduces parking availability for retail customers and diners, neutralizing the intended revenue increase.

Step-by-Step Solution

1

Deconstruct the core argument

Premise: Eliminating the 2-hour parking limit allows drivers to park indefinitely. Conclusion: Visitors will stay longer to shop/dine, raising local business sales and city sales tax revenues.

Identifying the link between the plan (removing time limits) and the intended outcome (increased shopper visits and revenue) is essential to finding the unstated assumption.

2

Identify the unstated assumption

The argument assumes that shoppers and diners will be the primary beneficiaries of open-ended parking and will find available spaces easily.

A plan-to-goal argument relies on the assumption that the implementation will operate as intended without creating obstacles that defeat the goal.

3

Evaluate the impact of new evidence

If commuters occupy the spaces all day before shoppers arrive, overall customer turnover drops and shoppers cannot park downtown.

Introducing an alternative user group (commuters monopolizing spaces) invalidates the key assumption and demonstrates that the plan will decrease shopper access, directly undermining the conclusion.

Key Concept

Weakening Arguments - Plan Implementation and Unintended Consequences

Question 17Question →

[Tab 1: Export Tariff Rebate Policy (2026 Directive)]
Regional Grain Stabilization Board Regulations:
- Base Export Rebate: All agricultural exporters receive a base tariff rebate of 8.0% on the net shipment value.
- Quality Grade Premium: Shipments certified as Grade Tier S receive an additional 3.0% rebate (total 11.0%), provided the total shipment volume exceeds 10,000 metric tons (MT). Shipments of 10,000 MT or less receive only the base rebate regardless of grade.
- Moisture Content Penalty & Exemption: Any shipment with a moisture content exceeding 14.0% is subject to a 2.0% rebate reduction penalty. However, under the Maritime Exemption rule, all shipments processed through Port Apex are fully exempt from moisture content penalties.

Statement: Based on the policy directive and shipment logs, AgroCorp's total export tariff rebate for Shipment SH-101 is $220,000.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. AgroCorp's total export tariff rebate for Shipment SH-101 is $220,000.

The statement is correct because synthesizing Tab 1 rules and Tab 2 shipment metrics confirms that Shipment SH-101 qualifies for both the 8.0% base rebate and the 3.0% Tier S premium (volume 12,000 MT > 10,000 MT threshold), while avoiding the 2.0% moisture penalty via the Port Apex Maritime Exemption. The resulting 11.0% rate applied to

2,000,000 gives

220,000.

Step-by-Step Solution

1

Determine base rebate and quality tier qualification across Tab 1 and Tab 2

Base rate is 8.0%. Shipment SH-101 is Grade Tier S and its volume (12,000 MT) exceeds the 10,000 MT threshold specified in Tab 1, adding a 3.0% premium.

The volume condition for the Tier S quality premium is satisfied (

12,000 > 10,000

MT).

2

Evaluate moisture content rules and regional exceptions

Moisture content is 14.5%, which exceeds 14.0%. However, because the shipment was processed at Port Apex, the Maritime Exemption applies, resulting in no penalty.

Tab 1 explicitly states that all shipments processed at Port Apex are exempt from moisture penalties.

3

Calculate the final rebate percentage and dollar amount

Effective rebate rate =

8.0\% + 3.0\% - 0.0\% = 11.0\%

. Rebate amount =

11.0\% \times \$2,000,000 = \$220,000

.

Multiplying the calculated effective rate by the net shipment value gives the total rebate.

Key Concept

Multi-Source Inference and Synthesis with Conditional Policy Rules and Exceptions

Question 18Question →

A long-term agricultural study in a semi-arid basin established that whenever seasonal rainfall drops below 250 millimeters, farmers who irrigate their crops using unlined soil canals lose at least 35 percent of their diverted water to seepage. Conversely, any farm in the basin that adopts high-efficiency drip irrigation retains at least 85 percent of its diverted water regardless of seasonal rainfall levels. Last season, seasonal rainfall in the basin was 210 millimeters, yet Farm X lost less than 20 percent of its diverted water.

If the statements above are true, which of the following MUST also be true regarding Farm X last season?

Farm X did not rely on unlined soil canals to irrigate its crops last season.

Farm X used high-efficiency drip irrigation to irrigate its crops last season.

If Farm X had received more than 250 millimeters of rainfall last season, its diverted water loss would have been greater than 35 percent.

Farm X diverted a greater total volume of water last season than did neighboring farms using unlined soil canals.

Any farm in the basin that loses less than 35 percent of its diverted water during a low-rainfall season must be using high-efficiency drip irrigation.

Show answer & explanation

Answer: Farm X did not rely on unlined soil canals to irrigate its crops last season.

Answer

Farm X did not rely on unlined soil canals to irrigate its crops last season.

The correct answer is derived using formal conditional logic. The stimulus establishes that when rainfall is under 250 mm, using unlined soil canals guarantees a water loss of at least 35%. Since the rainfall was 210 mm and Farm X lost less than 20% of its diverted water, Farm X cannot have used unlined soil canals. By contrapositive reasoning, if the outcome (loss ≥ 35%) did not occur despite the trigger condition (rainfall < 250 mm) being met, the requirement for that outcome (unlined soil canals) must have been absent.

Step-by-Step Solution

1

Analyze the conditional rule for unlined soil canals.

If (Rainfall < 250 mm) AND (Unlined Soil Canals), then (Water Loss ≥ 35%).

This is a direct premise established by the study.

2

Evaluate the conditions given for Farm X last season.

Rainfall was 210 mm (which is strictly less than 250 mm), and Farm X's Water Loss was strictly less than 20%.

These are the explicit facts provided about Farm X.

3

Apply the contrapositive of the conditional rule.

Since Water Loss was NOT ≥ 35% (it was < 20%) while Rainfall was < 250 mm, the condition 'Unlined Soil Canals' must be FALSE for Farm X.

If P and Q imply R, then P and not-R implies not-Q.

Key Concept

Applying Contrapositive Logic in Must-Be-True Deductions

Question 19Question →

### Tab 1: Pharmaceutical Compliance & Clinical Trial Approval Rules
- High Compliance Risk Criteria: A Phase III clinical trial is classified as *High Compliance Risk* if it satisfies at least one of the following conditions: (1) more than 2 protocol amendments, or (2) a patient dropout rate strictly greater than 5.0%.
- Sign-off Requirement: If a Phase III trial is classified as *High Compliance Risk*, all quarterly reporting requires dual sign-off from both the Lead Investigator and the Independent Ethics Board (IEB). Without dual sign-off on file, the trial's reported efficacy metric is automatically suspended from board valuation.
- Emergency Exemption: Clinical trials operating under Emergency Expedited Authorization (EEA) are exempt from the dual sign-off requirement regardless of risk status, provided total patient enrollment exceeds 500.

### Tab 2: Q2 Clinical Trial Audit Summary

Trial Code	Phase	Protocol Amendments	Patient Enrollment	Patient Dropout Rate	EEA Status	Sign-off On File	Reported Efficacy
Trial-Alpha	Phase III	3	600	4.0%	Yes	Lead Investigator Only	84%
Trial-Beta	Phase III	1	400	6.2%	No	Lead Investigator & IEB	91%
Trial-Gamma	Phase II	4	250	8.0%	Yes	Lead Investigator Only	78%
Trial-Delta	Phase III	2	550	5.5%	No	Lead Investigator Only	88%

### Tab 3: Board Valuation Standards
- To be included in the Q3 R&D pipeline valuation as Pipeline Qualified, a trial must be a Phase III trial, must have a valid (non-suspended) reported efficacy metric under Tab 1 rules, and must achieve a reported efficacy of at least 85%.

Statement for Evaluation:
Based on the information provided across all three tabs, evaluate whether the following statement is True or False:
"Exactly two of the four audited trials (Trial-Alpha, Trial-Beta, Trial-Gamma, Trial-Delta) meet all criteria to be classified as 'Pipeline Qualified' for the Q3 R&D pipeline valuation."

True

False

Show answer & explanation

Answer: False

Answer

The statement is False because exactly one trial (Trial-Beta) qualifies for the Q3 R&D pipeline valuation, rather than two.

Evaluating all conditions shows that only Trial-Beta satisfies all criteria (Phase III, high risk accompanied by required dual sign-off, and non-suspended efficacy of 91% >= 85%). Trial-Alpha fails the efficacy threshold (84% < 85%), Trial-Gamma is Phase II with insufficient efficacy (78%), and Trial-Delta's 88% efficacy is suspended due to non-compliance with Tab 1 sign-off rules. Therefore, exactly one trial qualifies, making the assertion that 'exactly two' qualify false.

Step-by-Step Solution

1

Evaluate risk status and sign-off compliance for each trial using Tab 1 and Tab 2 criteria.

Trial-Alpha: Phase III, 3 amendments (> 2) -> High Risk. Has EEA=Yes & Enrollment=600 (> 500), so exempt from dual sign-off requirement; efficacy (84%) is valid.
Trial-Beta: Phase III, 6.2% dropout (> 5.0%) -> High Risk. Has Lead & IEB dual sign-off; efficacy (91%) is valid.
Trial-Gamma: Phase II trial, efficacy (78%) is valid but not Phase III.
Trial-Delta: Phase III, 5.5% dropout (> 5.0%) -> High Risk. Has Lead Investigator Only sign-off, EEA=No (not exempt). Efficacy (88%) is suspended under Tab 1 rules.

Correctly applying conditional rules and policy exceptions across tabs determines which efficacy figures are eligible for evaluation.

2

Check Tab 3 requirements (Phase III, valid efficacy, efficacy >= 85%) for each trial to determine 'Pipeline Qualified' status.

Trial-Alpha: Valid efficacy (84%), but 84% < 85% -> NOT Qualified.
Trial-Beta: Valid efficacy (91%), 91% >= 85%, Phase III -> QUALIFIED.
Trial-Gamma: Phase II, efficacy 78% < 85% -> NOT Qualified.
Trial-Delta: Suspended efficacy -> NOT Qualified.

Synthesizing constraints across all three tabs yields exactly 1 qualified trial (Trial-Beta).

3

Compare the actual number of qualified trials against the statement's assertion.

The statement asserts exactly two trials qualify, but only one trial (Trial-Beta) qualifies.

Since 1 != 2, the statement is false.

Key Concept

Multi-source dichotomous reasoning requires integrating multi-tab rules, conditional exemptions, and quantitative thresholds to evaluate complex statement assertions accurately.

Estimated Time:2m 30s

Question 20Question →

[Tab 1: Municipal Resilience Grant Policy (2026 Directive)]

Regional Infrastructure Authority Guidelines:
- Standard Eligibility: A municipal project is eligible for a base grant equal to 40% of its projected cost if it has a Resilience Index of at least 70 (out of 100) AND serves a target population of at least 50,000 residents.
- High-Impact Bonus: Projects that meet standard eligibility AND serve a target population exceeding 100,000 residents receive an additional 10% bonus grant (total grant of 50% of projected cost).
- High Flood Risk Exception: Any project located in a designated High Flood Risk zone has its Resilience Index requirement reduced to a minimum of 60. However, the maximum total grant funding awarded to any single project under this exception is strictly capped at $2,000,000 regardless of percentage calculations.

[Tab 2: Fiscal Year 2026 Project Applications]

Project ID	Project Type	Projected Cost	Resilience Index	Target Population	Location Zone
Project Alpha	Sea Wall Construction	$6,000,000	65	120,000	Zone R2
Project Beta	Grid Storage Backup	$4,500,000	72	80,000	Zone R1
Project Gamma	Urban Drainage System	$5,000,000	62	60,000	Zone R3
Project Delta	Bridge Structural Retrofit	$3,000,000	75	45,000	Zone R1

[Tab 3: Environmental Audit Memorandum]

Environmental Protection Board Assessment:
- Zone R1: Classified as Low Flood Risk.
- Zone R2: Classified as High Flood Risk due to coastal storm surge exposure.
- Zone R3: Classified as Moderate Flood Risk.
- Special Variance Note: No population threshold exceptions or policy variances were approved for any project in the 2026 funding cycle.

Based on the policy guidelines, project application data, and environmental audit memorandum, what is the total dollar amount of grant funding awarded across all four municipal project applications?

$1,800,000

$3,800,000

$4,800,000

$5,000,000

$6,800,000

Show answer & explanation

Answer: $3,800,000

Answer

$3,800,000

Synthesizing data across all three tabs demonstrates that Project Alpha qualifies under the High Flood Risk exception (Zone R2 per Tab 3) for a capped grant of

2,000,000. Project Beta qualifies under standard policy (Zone R1 per Tab 3) for a grant of 40% of

4,500,000 =

1,800,000. Projects Gamma and Delta fail eligibility criteria. Total funding awarded equals

3,800,000.

Step-by-Step Solution

1

Evaluate Project Alpha eligibility and grant amount by synthesizing data across Tab 1, Tab 2, and Tab 3.

Project Alpha is in Zone R2 (High Flood Risk per Tab 3). Tab 1 lowers the required Resilience Index from 70 to 60 for High Flood Risk zones. Project Alpha's Resilience Index of 65 satisfies this reduced threshold. Its population of 120,000 (>100,000) would qualify for a 50% grant (

3,000,000), but Tab 1 mandates a strict cap of

2,000,000 for High Flood Risk exception grants. Thus, Project Alpha receives $2,000,000.

Applying the conditional exception and maximum cap rules specified in Tab 1.

2

Evaluate Project Beta eligibility and grant amount.

Project Beta is in Zone R1 (Low Flood Risk per Tab 3). Standard policy applies. Its Resilience Index of 72 (>=70) and target population of 80,000 (>=50,000) meet standard criteria. It receives 40% of its

4,500,000 cost =

1,800,000.

Standard eligibility criteria check for non-high-risk projects.

3

Evaluate Project Gamma and Project Delta eligibility.

Project Gamma (Zone R3, Moderate Flood Risk) has a Resilience Index of 62, which is below the standard threshold of 70 (the reduced 60 threshold applies ONLY to High Flood Risk zones). Thus, Project Gamma receives

0. Project Delta has a population of 45,000, which is below the minimum threshold of 50,000 (and Tab 3 confirms no variances were approved). Thus, Project Delta receives

0.

Checking standard rule compliance and boundary conditions.

4

Calculate the total grant funding awarded.

2,000,000 (Project Alpha) +

1,800,000 (Project Beta) = $3,800,000.

Summing approved funding across all four applications.

Key Concept

Multi-Source Reasoning requiring cross-tab synthesis of policy rules, quantitative tables, and environmental risk classifications.

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