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2195 questions

Question 381Question

Historians studying 19th-century agrarian developments have long maintained that the adoption of synthetic nitrate fertilizers was the primary catalyst for the dramatic increase in agricultural yields across Northern Europe. However, recent archival evidence indicates that the widespread implementation of tile drainage systems preceded the mass commercial availability of synthetic nitrates by nearly two decades. Because crop roots cannot absorb soil nutrients effectively in waterlogged fields, the efficiency of any added chemical fertilizer remains severely constrained without prior soil drainage. Therefore, the introduction of synthetic fertilizers merely amplified a productivity trend that was already well underway due to soil infrastructure improvements, rather than serving as its fundamental trigger.

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

Show answer & explanation

Answer: The first is factual evidence presented to undermine an established position; the second is the main conclusion of the argument.

Answer

The first boldface portion is factual evidence presented to undermine an established position, and the second is the main conclusion of the argument.
The argument opens by citing a long-held view among historians that synthetic nitrates caused the yield surge. The first bold statement introduces historical evidence about tile drainage that directly undermines this traditional view. Following an explanatory premise, the second bold statement is introduced by the conclusion indicator 'Therefore', asserting the author's central point: synthetic fertilizers merely amplified a trend already started by drainage.

Step-by-Step Solution

1
Identify the main argument components and structural pivots
The opening sentence establishes an opposing position held by historians (synthetic nitrates were the primary catalyst). The pivot word 'However' introduces a counter-finding.
Understanding the transition reveals whether the subsequent statements support or oppose the initial view.
2
Analyze the function of the first boldface statement
The statement presents archival evidence that tile drainage preceded synthetic nitrates by two decades.
This empirical evidence contradicts the historians' timeline and supports the author's critique of the traditional view.
3
Analyze the bridge premise and the second boldface statement
The author explains why drainage matters (fertilizer efficiency relies on drainage) and concludes with 'Therefore...', leading directly to the second boldface statement.
The conclusion word 'Therefore' explicitly signals that the second bold statement is the ultimate claim the author is defending.

Key Concept

Analyzing Boldface Roles in Critical Reasoning Arguments
Question 382Question

If xx is a positive integer, is xx an even number?

(1) xx is a prime number greater than 2.
(2) x+1x + 1 is an odd number.

Show answer & explanation

Answer: EACH statement ALONE is sufficient.

Answer

EACH statement ALONE is sufficient.
The correct option is the one stating that EACH statement ALONE is sufficient. Statement (1) establishes that xx is an odd prime, yielding a definitive 'No' to the stem question, which makes it sufficient. Statement (2) establishes that xx is even, yielding a definitive 'Yes' to the stem question, making it sufficient as well.

Step-by-Step Solution

1
Analyze Statement (1): xx is a prime number greater than 2.
All prime numbers greater than 2 are odd numbers (e.g., 3, 5, 7, 11). Therefore, xx cannot be an even number. The question 'Is xx an even number?' receives a definitive answer of 'No'. In Data Sufficiency, a statement that leads to a conclusive 'No' is SUFFICIENT.
In Yes/No Data Sufficiency, a consistent 'No' answer is just as sufficient as a consistent 'Yes' answer.
2
Analyze Statement (2): x+1x + 1 is an odd number.
If an integer plus 1 is odd, the integer itself must be even. Thus, xx must be an even number. The question 'Is xx an even number?' receives a definitive answer of 'Yes'. Therefore, Statement (2) is SUFFICIENT.
Direct algebraic or parity properties allow a unique 'Yes' determination.
3
Combine evaluations of both statements.
Since Statement (1) alone yields a definitive 'No' and Statement (2) alone yields a definitive 'Yes', each statement independently answers the question.
Both statements are sufficient on their own.

Key Concept

Definitive Yes/No Sufficiency Rule
Question 383Question

Agricultural technology firms have recently advocated for nationwide tax credits to promote biochar application in commercial farming, contending that soil carbon storage is essential for meeting climate targets. However, verifying long-term carbon sequestration in varied soil microbiomes remains technically imprecise and prone to significant measurement error. Consequently, issuing standardized credits based on current measurement protocols will inevitably lead to overcrediting unverified carbon sinks. Therefore, the government should defer the implementation of biochar-based carbon tax credits until higher-precision auditing technologies are commercially deployed.

Based on the passage above, match each numbered claim on the left to its exact structural role in the argument on the right.

Click a left item, then click its matching right item

Items

Soil carbon storage is essential for meeting climate targets.
Verifying long-term carbon sequestration in varied soil microbiomes remains technically imprecise and prone to significant measurement error.
Issuing standardized credits based on current measurement protocols will inevitably lead to overcrediting unverified carbon sinks.
The government should defer the implementation of biochar-based carbon tax credits until higher-precision auditing technologies are commercially deployed.

Matches

Show answer & explanation

Answer

The statement regarding the inevitable overcrediting of unverified carbon sinks functions as the intermediate (subsidiary) conclusion. It is inferred from the premise concerning measurement imprecision and directly supports the main policy recommendation to defer tax credits.
The argument builds a multi-tiered logical structure. The statement describing technical measurement errors serves as an un-derived factual premise. From this premise, the author infers that issuing credits based on current protocols will lead to overcrediting (the intermediate conclusion). That intermediate conclusion then serves as the direct logical support for the main conclusion, which recommends deferring the tax credits until better technology exists.

Step-by-Step Solution

1
Identify the main conclusion of the passage
The final sentence ('Therefore, the government should defer...') is the author's ultimate normative recommendation and primary claim.
It is signaled by the conclusion indicator 'Therefore' and expresses the final policy stance that the entire argument seeks to prove.
2
Locate raw empirical premises that do not depend on prior claims
The statement that verification in soil microbiomes 'remains technically imprecise' acts as an underlying factual premise.
This claim is presented as a foundational factual observation without any supporting sub-arguments within the text.
3
Analyze the claim linking the factual premise to the main conclusion
The assertion that standardized credits 'will inevitably lead to overcrediting' is derived from technical imprecision ('Consequently') and provides the rationale for deferring policy.
Because it acts both as a conclusion relative to the measurement error premise and as a premise supporting the final deferral recommendation, it is the intermediate (subsidiary) conclusion.
4
Categorize remaining contextual claims
The claim that soil carbon storage is essential for climate targets represents background context detailing the ag-tech firms' stance.
It provides the backdrop against which the author presents a caveat and counter-proposal.

Key Concept

Identifying Intermediate and Subsidiary Conclusions
Question 384Question

An executive at an online retail company stated: 'To reverse our recent increase in shopping cart abandonment rates, we must either eliminate standard delivery charges for all orders or offer free return shipping. Because offering free return shipping on all orders would create unsustainable logistics costs, we must eliminate standard delivery charges.'

Statement: The executive's argument relies on a false dilemma fallacy by taking for granted that eliminating standard delivery charges and offering free return shipping are the only two viable strategies for reducing shopping cart abandonment.

Show answer & explanation

Answer: True

Answer

The statement is True.
The statement is correct because the executive's reasoning exhibits a classic false dilemma flaw: it assumes that only two possible actions exist to resolve shopping cart abandonment, overlooking reasonable middle-ground or alternative approaches.

Step-by-Step Solution

1
Analyze the structure of the argument in the passage.
The author presents two options ('either eliminate standard delivery charges... or offer free return shipping') and rules out one option based on financial cost, concluding that the remaining option must be implemented.
Understanding the premise-to-conclusion structure identifies how the argument limits potential solutions.
2
Identify the unstated assumption or logical flaw.
The author assumes without proof that no third option exists to address the problem of cart abandonment.
Artificially restricting possibilities to a binary choice without demonstrating that those choices are mutually exhaustive is a classic false dilemma.
3
Evaluate the accuracy of the provided statement.
The statement correctly describes the flaw as a false dilemma resulting from an unwarranted assumption about the exclusivity of the options.
Because the statement accurately diagnoses the argument's reasoning flaw, it is true.

Key Concept

False Dilemma and Unwarranted Assumptions
Question 385Question

For all real numbers xx, the identity x2=x\sqrt{x^2} = x holds true.

Show answer & explanation

Answer: False

Answer

The statement is false because the principal square root x2\sqrt{x^2} is defined as the absolute value of xx, x|x|, which equals x-x when x<0x < 0.
The statement is false because the expression x2\sqrt{x^2} represents the principal (non-negative) square root of x2x^2, which simplifies to x|x|. When xx is negative, x=x|x| = -x, which is not equal to xx.

Step-by-Step Solution

1
Recall the definition of the principal square root radical symbol x\sqrt{\vphantom{x}}
By definition, a0\sqrt{a} \ge 0 for any real number a0a \ge 0.
The principal square root function always yields a non-negative output.
2
Test a negative value for the variable xx
Let x=3x = -3. Then (3)2=9=3\sqrt{(-3)^2} = \sqrt{9} = 3.
Evaluating a specific negative number tests if the equality holds universally for all real numbers.
3
Compare the evaluated result with the original value of xx
Since 333 \neq -3, x2x\sqrt{x^2} \neq x when x<0x < 0.
A single counterexample disproves a universal mathematical identity statement.

Key Concept

Principal Square Root and Absolute Value Property (\sqrt{x^2} = |x|)
Estimated Time:45s
Question 386Question

If xx is a real number, is x>0x > 0?

(1) x=5|x| = 5
(2) x+3>5x + 3 > 5

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 choice stating that Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient, is correct because Statement (1) yields two possible values for xx (55 and 5-5), resulting in both 'Yes' and 'No' answers. In contrast, Statement (2) simplifies to x>2x > 2, which guarantees that x>0x > 0 with a definitive 'Yes'.

Step-by-Step Solution

1
Rephrase the target question
The target asks whether xx lies to the right of 00 on the real number line (a Yes/No question).
Establishing clear sufficiency criteria requires identifying what yields a definitive 'Yes' or definitive 'No'.
2
Evaluate Statement (1): x=5|x| = 5
xx can be 55 or 5-5. If x=5x = 5, the answer is Yes (5>05 > 0). If x=5x = -5, the answer is No (50-5 \ngtr 0).
Since Statement (1) allows both a 'Yes' and a 'No' response, it is NOT sufficient.
3
Evaluate Statement (2): x+3>5x + 3 > 5
Subtracting 33 from both sides gives x>2x > 2. Any number strictly greater than 22 is automatically greater than 00.
Statement (2) provides a definitive 'Yes' answer to the question x>0x > 0, so Statement (2) ALONE is sufficient.

Key Concept

Absolute Value Definition and Single-Variable Inequality Simplification in Data Sufficiency
Question 387Question

In a GMAT Data Sufficiency 'Value' question asking for the specific numerical value of a variable xx, a statement that narrows xx down to exactly two distinct numerical solutions provides sufficient information.

Show answer & explanation

Answer: False

Answer

False
The statement is False. GMAT Data Sufficiency questions are divided into two structural categories: Value questions and Yes/No questions. For a 'Value' question, a statement is sufficient only if it allows you to determine one single, unambiguous numerical value. If a statement results in two or more distinct possible values, the exact value of the target cannot be determined, so the statement is insufficient.

Step-by-Step Solution

1
Identify the standard for sufficiency in a GMAT Data Sufficiency 'Value' question.
A statement must produce a single, unique numerical value for the target variable or expression.
Value questions require determinacy; if more than one value is possible from the statement alone, the specific value is unknown.
2
Evaluate the condition where a statement yields exactly two distinct numerical solutions.
Since two distinct values exist, the statement fails to provide a unique value, rendering it insufficient.
Having a finite set of two solutions (e.g., x=2x = 2 or x=2x = -2) does not satisfy the unique value requirement of Value Data Sufficiency questions.

Key Concept

Value Data Sufficiency Decision Logic
Question 388Question

Municipal planners in City K recently installed permeable asphalt along downtown sidewalks to reduce surface runoff during storm events. During the first rainy season following installation, measured runoff volume entering the local river decreased by 30 percent compared to the historical seasonal average. The planners concluded that expanding the installation of permeable asphalt throughout all municipal districts will significantly mitigate urban flooding during future severe storms.

Which of the following, if true, provides the strongest support for the municipal planners' conclusion?

Show answer & explanation

Answer: The total volume and intensity of rainfall during the first rainy season were typical of severe storm conditions, and no other runoff control measures were introduced in the downtown area during that period.

Answer

The argument is most strongly supported by the statement showing that the total volume and intensity of rainfall during the trial period were typical of severe storm conditions and that no alternative runoff control measures were active.
The correct answer strengthens the argument by demonstrating that the test period was representative of severe storm conditions and by ruling out alternative explanations (such as other flood control projects or light rainfall) for the observed reduction in runoff.

Step-by-Step Solution

1
Deconstruct the argument into premise and conclusion.
Premise: Permeable asphalt installed downtown coincided with a 30% drop in river runoff during one rainy season. Conclusion: Expanding permeable asphalt citywide will significantly mitigate future urban flooding.
Identifying the gap between a single limited trial and a broader causal claim is essential for evaluating strengthening statements.
2
Identify potential vulnerabilities in the author's reasoning.
The 30% drop could have been caused by lighter-than-usual rain or other unmentioned flood control interventions, or the trial conditions might not represent true severe storm conditions.
Strengthening questions often require ruling out alternative causes or confirming that trial conditions mirror the target conditions.
3
Evaluate the choices to find the statement that addresses these vulnerabilities.
Confirming that rainfall intensity matched severe storm conditions and that no other interventions occurred eliminates confounding variables and supports the claim that permeable asphalt caused the reduction.
Ruling out confounding variables directly increases confidence in the causal relationship asserted by the conclusion.

Key Concept

Strengthening Arguments by Ruling Out Confounding Variables
Question 389Question

In January, electricity comprised 0.450.45 of a facility's total energy consumption. In February, electricity comprised 35\frac{3}{5} of its total energy consumption. If the facility's total energy consumption was constant at 1,2001,200 kilowatt-hours in each of the two months, by how many kilowatt-hours did its electricity consumption increase from January to February?

Show answer & explanation

Answer: 180180 kilowatt-hours

Answer

The electricity consumption increased by 180180 kilowatt-hours from January to February.
The correct answer of 180180 kilowatt-hours is found by converting both fractions and decimals into comparable parts of the 1,2001,200 kilowatt-hour base. January electricity usage is 0.45×1,200=5400.45 \times 1,200 = 540 kWh. February electricity usage is 35×1,200=720\frac{3}{5} \times 1,200 = 720 kWh. The difference is 720540=180720 - 540 = 180 kWh. Alternatively, subtracting the proportions first gives 350.45=0.600.45=0.15\frac{3}{5} - 0.45 = 0.60 - 0.45 = 0.15, and 0.15×1,200=1800.15 \times 1,200 = 180 kWh.

Step-by-Step Solution

1
Calculate the January electricity consumption
0.45×1,200=5400.45 \times 1,200 = 540 kilowatt-hours
Electricity represented 0.450.45 of the 1,2001,200 kilowatt-hour total.
2
Calculate the February electricity consumption
35×1,200=0.60×1,200=720\frac{3}{5} \times 1,200 = 0.60 \times 1,200 = 720 kilowatt-hours
Electricity represented 35\frac{3}{5} (or 0.600.60) of the 1,2001,200 kilowatt-hour total.
3
Find the difference between February and January consumption
720540=180720 - 540 = 180 kilowatt-hours
Subtracting January usage from February usage yields the net increase.

Key Concept

Fraction and Decimal Conversions and Amount Computations
Question 390Question

If kk is a positive integer such that kk is a multiple of 66 and a factor of 120120, how many possible values are there for kk?

Show answer & explanation

Answer: 6

Answer

6
The correct answer is 6. First, express 120 in prime factored form as 23×31×512^3 \times 3^1 \times 5^1. Any factor of 120 has the form 2a×3b×5c2^a \times 3^b \times 5^c where 0a30 \le a \le 3, 0b10 \le b \le 1, and 0c10 \le c \le 1. To also be a multiple of 6 (21×312^1 \times 3^1), kk must contain at least one factor of 2 and at least one factor of 3. This restricts aa to 1, 2, or 3 (3 possibilities), bb to 1 (1 possibility), and cc to 0 or 1 (2 possibilities). The total number of valid values for kk is 3×1×2=63 \times 1 \times 2 = 6.

Step-by-Step Solution

1
Find the prime factorization of 120 and 6
120=23×31×51120 = 2^3 \times 3^1 \times 5^1 and 6=21×316 = 2^1 \times 3^1
Prime factorization allows us to express divisibility constraints in terms of exponent bounds.
2
Determine the exponent constraints for k=2a×3b×5ck = 2^a \times 3^b \times 5^c
For kk to be a factor of 120, 0a30 \le a \le 3, 0b10 \le b \le 1, and 0c10 \le c \le 1. For kk to be a multiple of 6, a1a \ge 1 and b1b \ge 1. Thus: 1a31 \le a \le 3, b=1b = 1, 0c10 \le c \le 1.
Combining factor and multiple requirements yields the exact set of possible exponents.
3
Calculate the total number of combinations for (a,b,c)(a, b, c)
Number of choices for aa is 3 (1, 2, or 3). Number of choices for bb is 1 (must be 1). Number of choices for cc is 2 (0 or 1). Total possible values = 3×1×2=63 \times 1 \times 2 = 6.
By the fundamental counting principle, multiplying the number of choices for each exponent gives the total number of valid integers kk.

Key Concept

Determining the number of factors of an integer that meet specific divisibility constraints using prime factorization.
Question 391Question

A global shipping line recently introduced smart refrigerated containers equipped with automated sensors that adjust cooling levels based on cargo respiration rates, reducing energy consumption by 25 percent during ocean transit. The company expected this innovation to significantly cut total operational expenses for shipping perishable produce. However, logistics analysts point out that refrigerated containers spend over 60 percent of their total voyage time idling at port terminals or waiting at customs checkpoints, where power is supplied by third-party grid connections at fixed hourly tariffs rather than generated by the vessel's engines. Consequently, analysts conclude that the adoption of these smart containers will __________.

Which of the following statements most logically fills the blank in the argument above?

Show answer & explanation

Answer: yield a significantly smaller percentage reduction in total shipping expenses than the company anticipated.

Answer

The statement asserting that the adoption of smart containers will yield a significantly smaller percentage reduction in total shipping expenses than the company anticipated.
The correct option correctly synthesizes two key facts: the 25 percent energy savings apply only during ocean transit, but ocean transit constitutes less than 40 percent of total voyage time (since over 60 percent is spent at port under fixed hourly tariffs). Therefore, applying a partial savings rate to less than half of the total voyage time leads to a much smaller total percentage reduction in costs than anticipated.

Step-by-Step Solution

1
Identify the main premises and key contrast in the passage
Premise 1: Smart containers cut energy consumption by 25% during ocean transit. Premise 2: Over 60% of total voyage time occurs at ports under fixed hourly tariffs, meaning transit represents less than 40% of voyage time.
Understanding the distribution of time and costs is necessary to evaluate the total financial impact.
2
Synthesize the premises to draw the logical conclusion
Because energy efficiency applies to less than 40% of the trip time while 60%+ remains bound by fixed port tariffs, the overall reduction in total trip expenses will be diluted.
The conclusion must logically bridge the gap created by the contrast word 'However'.

Key Concept

Completing the Passage Logically (Synthesis of Quantitative Trade-offs)
Estimated Time:1m 50s
Question 392Question

To protect centuries-old parchment manuscripts from humidity-induced decay, the curators of a national archive recently replaced the facility's traditional refrigeration-based cooling coils with advanced chemical desiccant air-drying units. Over the six months following the replacement, sensor logs confirmed that relative humidity in the vault remained perfectly stabilized within the ideal target range of 45% to 50%. Nevertheless, physical inspections conducted at the end of the period revealed that the rate of structural fiber cracking on the parchment manuscripts was twice as high as it had been during the six months prior to the equipment change. Concluding that the new desiccant units were directly responsible for the accelerated deterioration, the lead conservator recommended re-installing the original refrigeration-based system.

Which of the following, if true, most strengthens the lead conservator's argument?

Show answer & explanation

Answer: During the six months following the equipment change, manuscripts stored in an adjacent vault served by the original refrigeration-based system experienced no increase in fiber cracking, despite being handled with the same frequency as those in the updated vault.

Answer

The argument is most strengthened by the evidence that manuscripts stored under the original refrigeration system in an adjacent vault suffered no increase in damage under identical handling conditions.
The correct response introduces a control group: identical manuscripts in an adjacent room kept under the old refrigeration system experienced no increase in cracking while being handled at the same rate. By keeping external conditions and handling constant between the two groups, this finding effectively rules out alternative explanations (such as seasonal shifts or handling damage) and provides strong empirical evidence that the new desiccant system caused the accelerated deterioration.

Step-by-Step Solution

1
Identify the author's premise and conclusion
Premise: Fiber cracking doubled after replacing refrigeration coils with chemical desiccant units, even though relative humidity remained constant. Conclusion: The chemical desiccant units caused the damage, so the original refrigeration system should be restored.
Understanding the precise causal link claimed by the author is essential to identifying strengthening evidence.
2
Evaluate potential logical gaps or alternative explanations
The increase in cracking could have been caused by unmeasured external variables (e.g., seasonal weather shifts, increased archival handling, ambient temperature fluctuation) rather than the desiccant units themselves.
Strengthening a causal argument requires ruling out plausible alternative causes or providing a control group.
3
Select the option that confirms causality by controlling for confounding variables
Showing that manuscripts in a control vault equipped with the old system suffered no increase in damage under identical conditions rules out general environmental or handling causes and isolates the desiccant system as the driver of the damage.
A controlled comparative setup eliminates alternative explanations, directly validating the lead conservator's causal claim.

Key Concept

Causal Argument Strengthening via Control Group / Elimination of Alternative Causes
Question 393Question

Prior to 2022, any corporate entity acquiring more than a 15 percent stake in a domestic renewable energy producer in Nation X was subject to mandatory federal antitrust review unless the acquiring entity was a state-backed entity. In 2022, Nation X amended its regulations such that all corporate acquisitions of domestic energy producers, regardless of the acquiring entity's state-backed status or stake size, require mandatory federal antitrust review if the target firm holds exclusive regional distribution rights. Last year, Solis Corp, a private non-state-backed corporation, acquired a 12 percent stake in Terra Energy, a domestic renewable energy producer in Nation X, without undergoing a federal antitrust review.

Which of the following statements must be true based on the information provided above? Select all that apply.

Select all that apply

Show answer & explanation

Answer: If Terra Energy holds exclusive regional distribution rights in Nation X, Solis Corp's acquisition must have occurred prior to the 2022 regulatory amendment.; Prior to 2022, state-backed entities acquiring more than a 15 percent stake in a domestic renewable energy producer in Nation X were exempt from mandatory federal antitrust review.

Answer

The correct statements are: 1) 'If Terra Energy holds exclusive regional distribution rights in Nation X, Solis Corp's acquisition must have occurred prior to the 2022 regulatory amendment' and 2) 'Prior to 2022, state-backed entities acquiring more than a 15 percent stake in a domestic renewable energy producer in Nation X were exempt from mandatory federal antitrust review.'
The conclusion regarding state-backed entities being exempt prior to 2022 follows directly from the exception clause ('unless the acquiring entity was a state-backed entity'). The conditional conclusion regarding exclusive regional distribution rights follows by contrapositive reasoning: post-2022 rules mandate reviews for any acquisition of a firm with exclusive distribution rights regardless of stake size; since Solis Corp's acquisition of a 12 percent stake was unreviewed, if Terra Energy possesses exclusive distribution rights, the transaction could not have occurred under the post-2022 rules and must have taken place prior to the amendment.

Step-by-Step Solution

1
Analyze the pre-2022 regulatory framework premises.
Before 2022, mandatory antitrust review applied ONLY IF (stake > 15%) AND (acquiring entity is NOT state-backed). State-backed entities were explicitly exempt.
Establishes the boundary conditions for acquisitions occurring prior to 2022.
2
Analyze the post-2022 regulatory framework premises.
After the 2022 amendment, mandatory review applies to ALL corporate acquisitions IF target holds exclusive regional distribution rights (regardless of state-backed status or stake percentage).
Establishes the strict conditional trigger for post-2022 transactions.
3
Apply formal logic (contrapositive) to the unreviewed acquisition of Terra Energy by Solis Corp.
Solis Corp (private) acquired 12% of Terra Energy (domestic renewable producer) with NO review. If Terra Energy has exclusive distribution rights, the transaction CANNOT be post-2022 (since post-2022 requires review for any stake if exclusive rights exist). Thus, if exclusive rights exist, the transaction MUST be pre-2022.
Synthesizes the specific factual scenario with the conditional rules to deduce valid conclusions.

Key Concept

Drawing Valid Conditional Inferences and Contrapositive Deduction
Question 394Question

Historically, municipal governments relied on property taxes to fund public transit expansion, operating under the assumption that infrastructure investment directly drives commercial real estate appreciation. However, recent economic analyses reveal that modern commercial enterprises prioritize digital infrastructure over physical proximity to transit hubs. Therefore, urban economists argue that issuing new municipal bonds to expand city bus lines will yield diminishing returns for the local tax base. Since property values have already stagnated across commercial sectors, funding transit expansion through property tax increases will burden local businesses without generating the anticipated economic growth.

In the argument presented, the bolded statement plays which of the following roles?

Show answer & explanation

Answer: It provides contextual background information about a traditional practice and belief, establishing the situation that the argument's main conclusion evaluates.

Answer

The bolded statement provides contextual background information about a traditional practice and belief, establishing the situation that the argument's main conclusion evaluates.
The correct answer accurately describes the structural role of the bolded statement. The first sentence presents historical context regarding how cities funded transit and what they assumed about real estate value. This historical context sets up the scenario that the author and urban economists evaluate in the rest of the passage.

Step-by-Step Solution

1
Analyze the structural components of the passage
Identified four key parts: (1) Bolded statement = historical context/assumption, (2) Pivot premise = modern commercial priority on digital infrastructure, (3) Main conclusion = bus line expansion will yield diminishing returns, (4) Supporting premise = property taxes will burden businesses.
Deconstructing the argument structure allows precise classification of each sentence's function.
2
Evaluate the specific role of the bolded statement
The bolded statement describes how municipalities traditionally operated and what they assumed. It sets the stage for the argument but does not serve as evidence for why expanding bus lines today is a bad investment.
Background information establishes circumstances or historical beliefs that frame the main argument without acting as an active premise or conclusion.
3
Match the identified structural role with the option choices
The statement functions as background context establishing the situation evaluated by the conclusion.
This description accurately aligns with GMAT Critical Reasoning terminology for non-premise background claims.

Key Concept

Identifying Background Information and Contextual Claims
Question 395Question

Dr. Aris: "To reduce municipal water waste during droughts, the city council should implement a tiered pricing structure that charges commercial users higher rates per gallon once their consumption exceeds baseline operational needs."

Council Member: "Dr. Aris's proposal is entirely unviable. If we completely prohibit commercial enterprises from using city water, local manufacturing will collapse and thousands of residents will lose their jobs."

Which of the following best describes the logical flaw in the council member's response?

Show answer & explanation

Answer: It distorts the original proposal into an extreme position that is easier to refute.

Answer

The council member's argument distorts the original proposal into an extreme position that is easier to refute.
The correct answer accurately identifies the Straw Man flaw. Dr. Aris recommends higher pricing for consumption exceeding baseline operational needs. The council member responds by claiming Dr. Aris wants to 'completely prohibit' commercial water use. By attacking an extreme version of the plan that was never suggested, the council member commits a classic Straw Man fallacy.

Step-by-Step Solution

1
Analyze Dr. Aris's position
Dr. Aris proposes a tiered pricing structure where commercial users pay higher rates only after exceeding baseline needs.
Establishing the precise scope of the initial proposal is necessary to evaluate counterarguments.
2
Analyze the Council Member's response
The council member claims Dr. Aris wants to 'completely prohibit commercial enterprises from using city water.'
Comparing the rebuttal to the premise reveals whether the speaker engaged with the actual proposal or distorted it.
3
Identify the logical flaw archetype
The council member reframes a moderate policy (higher rates for excess usage) as a total ban, which is a classic Straw Man flaw.
Exaggerating an opponent's position to make it easier to attack constitutes a straw man fallacy.

Key Concept

Straw Man Fallacy
Question 396Question

A renewable energy company recently installed ultrasonic anti-scaling transducers along the fluid conduits of its geothermal power plant. Management hypothesized that high-frequency sound waves from these devices would prevent mineral deposits from adhering to the interior of heat exchanger pipes, thereby eliminating the need for periodic chemical cleaning shutdowns. Over the subsequent six-month evaluation period, the plant operated continuously without requiring a single descaling shutdown, and net electricity output remained constant. Management concluded that the ultrasonic transducers were directly responsible for preventing mineral scale accumulation during this period.

Which of the following, if true, most strengthens management's conclusion?

Show answer & explanation

Answer: An adjacent geothermal well drawing from the identical fluid reservoir, operating without ultrasonic transducers, experienced severe mineral scaling that required three cleaning shutdowns during the same six-month period.

Answer

The argument is most strengthened by the finding that an adjacent, identical well lacking transducers suffered severe scaling under the same conditions.
The conclusion asserts a direct cause-and-effect relationship between the installation of ultrasonic transducers and the absence of mineral scale buildup. The option referencing the adjacent well drawing from the same fluid reservoir acts as a controlled experiment. By demonstrating that scaling still occurred in the absence of transducers under identical fluid conditions, it rules out the alternative explanation that fluid composition naturally prevented scaling, thereby strongly supporting the conclusion that the transducers caused the observed result.

Step-by-Step Solution

1
Identify the conclusion and underlying causal logic.
Conclusion: Ultrasonic transducers prevented mineral scale accumulation. Causal premise: Transducers were installed, and no scaling shutdowns occurred for six months.
To strengthen a causal conclusion, one must demonstrate that the cause produced the effect and rule out alternative causes (e.g., natural drop in mineral levels).
2
Evaluate the impact of establishing a comparative control group.
Showing that an identical well without transducers experienced scaling confirms that scaling conditions were present, establishing that the transducers were the critical difference-maker.
A control group isolates the causal variable and confirms that the outcome was not due to ambient environmental changes.

Key Concept

Strengthening Causal Arguments via Controlled Comparison
Question 397Question

To reduce traffic congestion during peak hours, a city council plans to eliminate free on-street parking in the financial district and implement hourly parking fees. Council members claim this policy will encourage commuters to switch to public transit, thereby decreasing the total number of cars entering the area each morning. Which of the following would be most useful to evaluate in order to determine whether the city council's plan will succeed?

Show answer & explanation

Answer: Whether public transit lines serving the financial district currently have sufficient unused capacity during peak morning hours to accommodate additional passengers.

Answer

Whether public transit lines serving the financial district currently have sufficient unused capacity during peak morning hours to accommodate additional passengers.
The plan relies on a crucial assumption: that commuters discouraged by parking fees actually have the practical option to switch to public transit. Evaluating transit capacity tests this assumption directly. If transit is already at peak capacity, commuters cannot switch, negating the plan's intended mechanism.

Step-by-Step Solution

1
Identify the plan and its explicit goal.
Plan: Eliminate free parking and charge hourly fees. Goal: Reduce traffic congestion by prompting commuters to switch to public transit.
Evaluating a plan requires focusing strictly on the link between the proposed mechanism and the intended goal.
2
Apply the Variance Test to evaluate the key assumption.
If transit has capacity: Drivers can switch, reducing congestion (plan succeeds). If transit lacks capacity: Drivers cannot switch, remaining in traffic or finding alternatives without reducing vehicle count effectively (plan fails).
Answering this question yields opposite outcomes for the success of the plan, proving its critical relevance.

Key Concept

Evaluating Plan Viability (Variance Test)
Question 398Question

How many integer values of xx satisfy the inequality x24x3x6|x^2 - 4x| \leq 3x - 6?

Show answer & explanation

Answer: 4

Answer

4 integer values satisfy the inequality.
The solution requires breaking the inequality into cases based on the sign of x24xx^2 - 4x while enforcing that the right-hand side 3x63x - 6 must be non-negative (meaning x2x \geq 2). Combining the valid sub-intervals 3x<43 \leq x < 4 and 4x64 \leq x \leq 6 yields 3x63 \leq x \leq 6. The integers satisfying this inequality are 3, 4, 5, and 6, giving a total of 4 integers.

Step-by-Step Solution

1
Establish the domain restriction based on non-negativity.
Since the left side x24x0|x^2 - 4x| \geq 0 for all real xx, the right side must also be non-negative: 3x60    x23x - 6 \geq 0 \implies x \geq 2.
An absolute value quantity can never be less than a negative number.
2
Analyze Case 1 where the expression inside the absolute value is non-negative (x24x0x^2 - 4x \geq 0).
For x2x \geq 2, x(x4)0x(x - 4) \geq 0 implies x4x \geq 4. The inequality becomes x24x3x6    x27x+60    (x1)(x6)0x^2 - 4x \leq 3x - 6 \implies x^2 - 7x + 6 \leq 0 \implies (x - 1)(x - 6) \leq 0, so 1x61 \leq x \leq 6. Intersecting with x4x \geq 4 yields 4x64 \leq x \leq 6.
When x4x \geq 4, x24x=x24x|x^2 - 4x| = x^2 - 4x.
3
Analyze Case 2 where the expression inside the absolute value is negative (x24x<0x^2 - 4x < 0).
For x2x \geq 2, x(x4)<0x(x - 4) < 0 implies 2x<42 \leq x < 4. The inequality becomes (x24x)3x6    x2+4x3x6    x2x60    (x3)(x+2)0-(x^2 - 4x) \leq 3x - 6 \implies -x^2 + 4x \leq 3x - 6 \implies x^2 - x - 6 \geq 0 \implies (x - 3)(x + 2) \geq 0, so x2x \leq -2 or x3x \geq 3. Intersecting with 2x<42 \leq x < 4 yields 3x<43 \leq x < 4.
When 2x<42 \leq x < 4, x24x=(x24x)|x^2 - 4x| = -(x^2 - 4x).
4
Combine the valid intervals from both cases and count the integer solutions.
Combining [3,4)[3, 4) and [4,6][4, 6] gives the interval [3,6][3, 6]. The integer values in this range are x=3,4,5,6x = 3, 4, 5, 6. Total count = 4.
The union of the solution intervals yields all real numbers between 3 and 6 inclusive.

Key Concept

Solving Absolute Value Inequalities with Variable RHS
Estimated Time:2m 30s
Question 399Question

If xx is a real number, is x>0x > 0?

(1) x=x|x| = -x
(2) x+x>0x + |x| > 0

Which of the following choices correctly describes the sufficiency of the statements?

Show answer & explanation

Answer: EACH statement ALONE is sufficient.

Answer

EACH statement ALONE is sufficient.
The option stating that each statement alone is sufficient is correct. Statement (1) shows that x0x \le 0, which gives a definitive 'No' to whether x>0x > 0. Statement (2) shows that x>0x > 0, which gives a definitive 'Yes' to whether x>0x > 0. Because both statements yield a clear, conclusive answer independently, each statement alone is sufficient.

Step-by-Step Solution

1
Analyze Statement (1): x=x|x| = -x
By definition of absolute value, x=x|x| = -x holds true if and only if x0x \le 0.
If x0x \le 0, then xx is not strictly positive, so the answer to 'Is x>0x > 0?' is a definitive 'No'.
2
Evaluate sufficiency of Statement (1)
Statement (1) provides a definitive 'No' answer to the question stem.
In Data Sufficiency, a statement that consistently yields a definitive 'No' is sufficient.
3
Analyze Statement (2): x+x>0x + |x| > 0
If x0x \le 0, then x=x|x| = -x, so x+x=xx=0x + |x| = x - x = 0, which is not greater than 00. If x>0x > 0, then x=x|x| = x, so x+x=2x>0x + |x| = 2x > 0.
The inequality x+x>0x + |x| > 0 is satisfied if and only if x>0x > 0.
4
Evaluate sufficiency of Statement (2)
Statement (2) provides a definitive 'Yes' answer to the question stem.
Since Statement (2) guarantees x>0x > 0, it is sufficient on its own.
5
Combine evaluations
Each statement alone provides a definitive answer to the question stem.
Therefore, EACH statement ALONE is sufficient.

Key Concept

Absolute Value Definition and Yes/No Data Sufficiency Decision Logic
Estimated Time:1m 0s
Question 400Question

In a GMAT Data Sufficiency 'Value' question asking for the numerical value of the expression xyxy, a statement that permits xx to be either 22 or 2-2 while establishing that y=8xy = \frac{8}{x} is insufficient to answer the question because xx itself is not uniquely determined.

Show answer & explanation

Answer: False

Answer

False. In Data Sufficiency 'Value' questions, sufficiency depends solely on whether the target expression can be uniquely determined. Because xy=8xy = 8 under all permitted conditions, the statement is sufficient regardless of whether xx has multiple values.
The claim presented in the stem is false. In GMAT Data Sufficiency 'Value' questions, a statement is sufficient if it yields a single, unambiguous numerical value for the requested target expression. It is not necessary for individual variables within the expression to be uniquely determined. Given y=8xy = \frac{8}{x}, multiplying both sides by xx yields xy=8xy = 8. Whether x=2x = 2 or x=2x = -2, the product xyxy remains constant at 88. Thus, the statement is sufficient to answer the question, rendering the claim of insufficiency false.

Step-by-Step Solution

1
Identify the precise target of the question stem.
The target quantity is the expression xyxy, not the individual variable xx or yy.
Evaluating Data Sufficiency requires focusing on the target expression as a single entity.
2
Test all cases allowed by the statement.
Case 1: If x=2x = 2, then y=82=4y = \frac{8}{2} = 4, so xy=(2)(4)=8xy = (2)(4) = 8.
Case 2: If x=2x = -2, then y=82=4y = \frac{8}{-2} = -4, so xy=(2)(4)=8xy = (-2)(-4) = 8.
Both permissible values of xx must be tested alongside their corresponding yy values.
3
Determine sufficiency based on target uniqueness.
Both cases yield the exact same value (xy=8xy = 8). The statement provides a unique numerical answer to the question.
Because the value of the target expression is uniquely determined, the statement is sufficient, making the claim in the stem false.

Key Concept

Target Expression Uniqueness vs. Variable Uniqueness in Value Questions
Estimated Time:2m 0s
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