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Question 1321Question →

If xx and yy are non-zero real numbers, is xy>0\frac{x}{y} > 0?

(1) ∣x+y∣<∣x−y∣|x + y| < |x - y|
(2) x2y+xy2<0x^2 y + x y^2 < 0

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The option stating that Statement (1) alone is sufficient while Statement (2) alone is not sufficient is correct. Statement (1) simplifies to xy<0xy < 0, which proves conclusively that xy\frac{x}{y} is negative. Thus, the answer to the question 'Is xy>0\frac{x}{y} > 0?' is a definitive 'No', which makes Statement (1) sufficient. Statement (2) simplifies to xy(x+y)<0xy(x + y) < 0, which permits scenarios where xy>0xy > 0 as well as scenarios where xy<0xy < 0, rendering Statement (2) insufficient.

Step-by-Step Solution

1
Rephrase the question stem target.
The expression xy>0\frac{x}{y} > 0 is true if and only if xx and yy have the same sign, which means xy>0xy > 0. The question asks: Is xy>0xy > 0?
Converting division of signed variables into product sign simplifies algebraic evaluation.
2
Evaluate Statement (1): ∣x+y∣<∣x−y∣|x + y| < |x - y|.
Squaring both sides yields (x+y)2<(x−y)2  ⟹  x2+2xy+y2<x2−2xy+y2  ⟹  4xy<0  ⟹  xy<0(x + y)^2 < (x - y)^2 \implies x^2 + 2xy + y^2 < x^2 - 2xy + y^2 \implies 4xy < 0 \implies xy < 0.
Since xy<0xy < 0, xy\frac{x}{y} MUST be negative, so the answer to 'Is xy>0\frac{x}{y} > 0?' is a definitive 'NO'.
3
Apply Yes/No Data Sufficiency logic to Statement (1).
A statement that yields a definitive 'No' to a Yes/No question is SUFFICIENT.
Sufficiency in a Yes/No question requires a conclusive YES or a conclusive NO; ambiguity is the only cause for insufficiency.
4
Evaluate Statement (2): x2y+xy2<0x^2 y + x y^2 < 0.
Factor out xyxy to get xy(x+y)<0xy(x + y) < 0. Case A: If x=−2x = -2 and y=−3y = -3, then xy=6>0xy = 6 > 0 and x+y=−5<0x+y = -5 < 0, giving 6(−5)=−30<06(-5) = -30 < 0 (Answer: YES). Case B: If x=5x = 5 and y=−2y = -2, then xy=−10<0xy = -10 < 0 and x+y=3>0x+y = 3 > 0, giving −10(3)=−30<0-10(3) = -30 < 0 (Answer: NO).
Because Statement (2) allows both a YES and a NO response, Statement (2) alone is NOT sufficient.

Key Concept

Definitive Yes/No Decision Logic in Data Sufficiency
Estimated Time:2m 0s
Question 1322Question →

In a GMAT Data Sufficiency question asking whether the real number xx is positive, a statement that uniquely restricts xx to the set {−3,−1}\{-3, -1\} is sufficient to answer the question.

Show answer & explanation

Answer: True

Answer

True. In Yes/No Data Sufficiency questions, a statement is sufficient if it determines a conclusive 'Yes' or 'No'. Because all possible values of xx (−3-3 and −1-1) produce a definitive 'No' to whether xx is positive, the statement is sufficient.
The statement is true because in a Yes/No Data Sufficiency framework, sufficiency requires only a single definitive answer ('Yes' or 'No'). Since all candidate values in the set {−3,−1}\{-3, -1\} are strictly negative, the question 'Is xx positive?' receives a definitive 'No' answer in every case.

Step-by-Step Solution

1
Identify the decision structure of the question stem.
The target question stem asks 'Is x>0x > 0?', which is a Yes/No Data Sufficiency structure.
Determining whether a question stem requires a single numerical value (Value structure) or a definitive binary answer (Yes/No structure) dictates the criteria for sufficiency.
2
Evaluate the answer to the stem under all permissible values from the statement.
If x=−3x = -3, x>0x > 0 is False ('No'). If x=−1x = -1, x>0x > 0 is False ('No').
Check if every allowed case produces the exact same binary outcome.
3
Apply Data Sufficiency criteria for Yes/No questions.
Because every permissible value leads to a single, unambiguous answer of 'No', the statement provides sufficient information.
A definitive 'No' establishes sufficiency just as effectively as a definitive 'Yes'.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic
Question 1323Question →

A rare species of deep-sea sponge produces a chemical compound called sponzenol only when exposed to water temperatures below 4∘C4^\circ\text{C}. In ocean regions where the water temperature is 4∘C4^\circ\text{C} or higher, these sponges never produce sponzenol. Marine researchers recently discovered a thriving colony of this sponge species in an uncharted trench in the South Pacific and confirmed that the sponges were actively producing sponzenol.

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

Show answer & explanation

Answer: The water temperature in the uncharted trench where the sponges were discovered is below 4∘C4^\circ\text{C}.

Answer

The water temperature in the uncharted trench where the sponges were discovered is below 4∘C4^\circ\text{C}.
The stimulus establishes a strict condition: sponges produce sponzenol only when the water temperature is strictly below 4∘C4^\circ\text{C}. Because researchers confirmed that the sponges in the trench were producing sponzenol, it must be true that the water temperature in that trench is below 4∘C4^\circ\text{C}.

Step-by-Step Solution

1
Identify the given conditional premise
Sponzenol production implies water temperature is below 4∘C4^\circ\text{C} (Production →\rightarrow Temperature <4∘C< 4^\circ\text{C}).
The stimulus specifies that sponges produce sponzenol ONLY WHEN exposed to temperatures below 4∘C4^\circ\text{C}.
2
Apply the factual premise from the stimulus
The sponges in the newly discovered trench are actively producing sponzenol.
This fact triggers the condition required for sponzenol production.
3
Deduce the necessary conclusion
The water in the trench must be below 4∘C4^\circ\text{C}.
Since active production requires a temperature below 4∘C4^\circ\text{C}, this condition must be met.

Key Concept

Identifying Must-Be-True Statements and Valid Deductions
Question 1324Question →

If rr and ss are real numbers, is r∣s∣<s∣r∣r|s| < s|r|?

(1) rs<0rs < 0
(2) r+s>∣r−s∣r + s > |r - s|

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

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 while Statement (1) alone is not sufficient is correct. Rephrased, r∣s∣<s∣r∣r|s| < s|r| is true only when r<0r < 0 and s>0s > 0. Statement (1) allows rr to be positive while ss is negative, yielding a 'No', as well as rr negative while ss is positive, yielding a 'Yes', so it is insufficient. Statement (2) simplifies algebraically to rs>0rs > 0 and r+s>0r + s > 0, which guarantees both numbers are positive. When both numbers are positive, r∣s∣<s∣r∣r|s| < s|r| reduces to rs<rsrs < rs, which is false. Because Statement (2) yields a definitive 'No', it is sufficient on its own.

Step-by-Step Solution

1
Rephrase the question stem target
The inequality r∣s∣<s∣r∣r|s| < s|r| holds if and only if r<0r < 0 and s>0s > 0.
If rr and ss have the same sign or either is zero, r∣s∣=s∣r∣r|s| = s|r|, making the strict inequality false. If r>0r > 0 and s<0s < 0, r∣s∣=−rsr|s| = -rs and s∣r∣=−rss|r| = -rs, making both sides equal. Only when r<0r < 0 and s>0s > 0 does r∣s∣=rs<0r|s| = rs < 0 and s∣r∣=−rs>0s|r| = -rs > 0, which makes the inequality true.
2
Evaluate Statement (1): rs<0rs < 0
Statement (1) is NOT sufficient.
This condition means rr and ss have opposite signs. Case 1: If r=−2r = -2 and s=3s = 3, then r<0r < 0 and s>0s > 0, so the answer is YES. Case 2: If r=3r = 3 and s=−2s = -2, then r>0r > 0 and s<0s < 0, so the answer is NO. Since both YES and NO are possible, Statement (1) is insufficient.
3
Evaluate Statement (2): r+s>∣r−s∣r + s > |r - s|
Statement (2) ALONE is sufficient.
Since ∣r−s∣≥0|r - s| \ge 0, we have r+s>0r + s > 0. Squaring both positive sides gives (r+s)2>(r−s)2  ⟹  r2+2rs+s2>r2−2rs+s2  ⟹  4rs>0  ⟹  rs>0(r + s)^2 > (r - s)^2 \implies r^2 + 2rs + s^2 > r^2 - 2rs + s^2 \implies 4rs > 0 \implies rs > 0. Since rs>0rs > 0 and r+s>0r + s > 0, both rr and ss must be positive. If r>0r > 0 and s>0s > 0, then r∣s∣=rsr|s| = rs and s∣r∣=rss|r| = rs, so r∣s∣<s∣r∣r|s| < s|r| simplifies to rs<rsrs < rs, which is FALSE. This gives a definitive NO to the question, making Statement (2) sufficient.

Key Concept

Data Sufficiency Yes/No Decision Logic with Absolute Value Inequalities
Question 1325Question →

In an effort to increase agricultural production, an agricultural board in a drought-prone province advised tomato growers to replace conventional overhead sprinkler systems with subsurface drip irrigation, which delivers water directly below the soil surface to root zones. The board claimed that adopting subsurface drip irrigation will significantly increase average tomato yields per acre across farms in the province. The board reasoned that because subsurface drip irrigation minimizes surface evaporation, it ensures consistent moisture levels near the plant roots, which is crucial for healthy fruit development.

Which of the following, if true, provides the strongest support for the agricultural board's claim regarding tomato yields?

Show answer & explanation

Answer: Consistently stable moisture levels in the root zone prevent a soil-borne fungal infection common to the province that severely reduces tomato plant yields.

Answer

The statement that consistently stable moisture levels in the root zone prevent a soil-borne fungal infection common to the province that severely reduces tomato yields provides the strongest support for the argument.
The argument concludes that subsurface drip irrigation will increase tomato yields per acre because it maintains consistent root-zone moisture by preventing evaporation. The option stating that stable root-zone moisture prevents a common local fungal infection that severely reduces yields provides a concrete biological mechanism explaining WHY consistent moisture will result in higher yields, thus strongly reinforcing the conclusion.

Step-by-Step Solution

1
Identify the main conclusion and core premise of the argument.
Premise: Subsurface drip irrigation minimizes evaporation and keeps root zone moisture levels consistent. Conclusion: Adopting subsurface drip irrigation will significantly increase average tomato yields per acre in the province.
Understanding the precise logical gap between consistent root zone moisture and increased crop yield is necessary to evaluate potential strengtheners.
2
Evaluate how an additional fact can bridge the gap between premise and conclusion.
If consistent root zone moisture directly prevents a prevalent local disease that normally cuts yields, then maintaining that moisture level will logically cause overall yields to increase.
A valid strengthening statement establishes a direct causal connection between the operational mechanism and the desired outcome.
3
Eliminate choices that weaken the argument, focus on cost/water savings, or introduce out-of-scope details.
Options raising concerns about system clogging weaken the claim; options discussing electricity or total water savings address collateral benefits rather than yield per acre; options discussing greenhouse farming in other regions are out of scope.
Only facts directly bolstering the mechanism driving higher crop yield per acre serve as valid strengthening evidence.

Key Concept

Strengthening Arguments
Question 1326Question →

A recent municipal proposal suggests replacing all diesel-powered harbor tugboats with fully electric alternatives in order to reduce port emissions. Proponents claim that this transition will immediately lower overall harbor operational costs because electric motors require less maintenance. However, this argument overlooks the major electrical grid upgrades needed to charge high-capacity batteries during peak operating hours. The capital expense of installing these dedicated charging stations will far exceed any short-term savings in motor maintenance. Therefore, implementing the proposal as currently structured is unlikely to achieve a net reduction in port operating costs.

In the argument given, the two boldfaced portions play which of the following roles?

Show answer & explanation

Answer: The first is a claim put forward by proponents of a proposal that the argument as a whole opposes; the second is a premise offered to support the author's main conclusion.

Answer

The first statement is a claim put forward by proponents of a proposal that the argument as a whole opposes; the second is a premise offered to support the author's main conclusion.
The argument opens by mentioning a proposal and then states what proponents claim in the first boldfaced portion. The pivot word 'However' introduces the author's rebuttal, establishing that the author opposes this claim. The second boldfaced statement provides evidence (capital expense of charging stations) supporting the author's conclusion at the end. Thus, the correct choice accurately describes the first as a claim of proponents opposed by the argument, and the second as a supporting premise for the main conclusion.

Step-by-Step Solution

1
Analyze the main argument structure and identify the main conclusion.
The main conclusion is the final sentence: implementing the proposal as currently structured is unlikely to reduce net port operating costs.
The conclusion represents the primary point the author is advocating for, introduced by the conclusion indicator 'Therefore'.
2
Determine the role of the first boldface statement.
It presents the argument of the proponents ('Proponents claim...'), which the author proceeds to counter after the transition word 'However'.
The author opposes the idea that operational costs will be lowered immediately.
3
Determine the role of the second boldface statement.
It provides factual evidence regarding capital expenses of charging infrastructure to explain why net costs will not decrease.
This serves as a premise that directly supports the author's main conclusion.

Key Concept

Analyzing structural roles of boldface statements relative to the author's conclusion.
Question 1327Question →

Over a five-year period in a coastal agricultural district, local fruit orchards gradually replaced synthetic chemical pesticides with natural predatory insects to control pest populations. During the exact same period, nearby estuarine populations of a threatened wild salmon species increased by over 30 percent. Environmental analysts concluded that the reduction in synthetic pesticide runoff was the direct cause of the recovery in the wild salmon population.

Which of the following would it be most useful to establish in order to evaluate the validity of the environmental analysts' conclusion?

Show answer & explanation

Answer: Whether regional commercial fishing quotas for salmon were significantly reduced during the same five-year period

Answer

The correct option is the one inquiring whether regional commercial fishing quotas for salmon were significantly reduced during the same five-year period.
The argument concludes that reduced pesticide runoff caused the 30 percent increase in wild salmon based solely on the fact that both changes occurred over the same five-year period. To evaluate a causal argument of this structure, one must test for alternative explanations that could account for the observed increase in salmon. Finding out whether regional commercial fishing quotas for salmon were significantly tightened during this period provides critical information: if quotas were reduced, fewer salmon were caught, offering a direct alternative explanation for the population rise. If quotas remained unchanged, alternative causes are minimized, strengthening the analysts' conclusion.

Step-by-Step Solution

1
Deconstruct the core argument and identify premises and conclusion
Premise: Orchards replaced synthetic pesticides with natural predators. Premise: Salmon populations increased by 30% over the same 5-year period. Conclusion: The reduction in pesticide runoff directly caused the increase in wild salmon populations.
Understanding the precise causal leap from observed correlation (pesticide change + salmon increase) to cause is necessary to evaluate the argument.
2
Identify the central assumption and vulnerabilities of the causal claim
The author assumes that no other co-occurring factor (confounding variable or alternative explanation) was responsible for the increase in salmon numbers.
Causal claims based on co-occurring events are vulnerable to alternative explanations that occurred during the same timeframe.
3
Assess the answer choices for a factor that tests for alternative causes
Checking whether commercial fishing quotas were reduced tests an alternative cause. If quotas were significantly reduced, the salmon population increase may be due to reduced harvesting rather than cleaner water.
Evaluating a prominent alternative explanation directly determines whether the stated cause or an unstated external factor produced the observed effect.

Key Concept

Evaluating Causal Arguments via Confounding Variables / Alternative Explanations
Estimated Time:2m 0s
Question 1328Question →

In pharmaceutical research, many analysts maintain that scaling up high-throughput automated synthesis in early-stage drug discovery will invariably reduce overall development timelines for breakthrough therapies. However, this reliance on automated high-throughput screening frequently leads researchers to prioritize easily synthesized, minor variations of existing compounds over structurally novel molecules. Because high-throughput platforms struggle to characterize complex biological interactions early on, promising drug candidates that require intricate synthesis pathways are routinely discarded prematurely. Consequently, laboratories that depend heavily on these automated systems ultimately spend more time troubleshooting late-stage clinical failures than those employing traditional, targeted research methodologies.

In the argument given, which of the following best describes the structural roles played by the two bolded statements?

Show answer & explanation

Answer: The first is a position that the argument aims to refute; the second is a premise offered in support of the author's overall conclusion.

Answer

The first bolded statement is a position that the argument aims to refute, and the second is a premise offered in support of the author's overall conclusion.
The argument opens with a position held by many analysts regarding automated synthesis. The author uses the transition 'However' to challenge this view, establishing that the first bolded statement is a claim the argument seeks to refute. The second bolded statement explains why automated platforms fail (promising candidates are discarded prematurely), serving as an supporting premise for the author's final conclusion that laboratories using these systems waste more time in the long run.

Step-by-Step Solution

1
Identify the author's main stance and structural pivots in the passage.
The word 'However' after the first bolded phrase indicates that the author disagrees with the analysts' view that automated synthesis reduces overall timelines.
Tracking structural pivot words helps establish whether the author agrees or disagrees with cited positions.
2
Determine the role of the first bolded statement.
The first bolded statement is the analysts' opinion, which the author argues against. Thus, it is a position the argument seeks to refute.
The author builds an argument showing that heavy reliance on this automated synthesis actually lengthens development timelines due to late-stage failures.
3
Determine the role of the second bolded statement.
The second bolded statement follows the premise indicator 'Because' and describes how promising drug candidates are discarded prematurely. This acts as evidence supporting the author's final conclusion.
Premises explain why automated platforms lead to late-stage clinical failures, supporting the author's ultimate claim.
4
Match the identified roles to the correct choice.
The option stating that the first is a position the argument aims to refute and the second is a premise supporting the author's overall conclusion accurately describes both roles.
This choice correctly captures the structural relationship between the opposing view, the author's evidence, and the main conclusion.

Key Concept

Evaluating structural roles of bolded statements in Critical Reasoning arguments.
Estimated Time:2m 0s
Question 1329Question →

If pp and qq are non-zero real numbers, is ∣p+q∣>∣p−q∣|p + q| > |p - q|?

(1) ∣p+2q∣<∣p−2q∣|p + 2q| < |p - 2q|
(2) p−q>0p - q > 0

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The correct response identifies Statement (1) as sufficient and Statement (2) as insufficient. Rephrasing the question stem by squaring both sides of ∣p+q∣>∣p−q∣|p + q| > |p - q| yields 4pq>04pq > 0, or pq>0pq > 0. Statement (1) expands and simplifies to 8pq<08pq < 0, meaning pq<0pq < 0. This provides a definitive 'No' answer to the question 'Is pq>0pq > 0?', which constitutes full sufficiency. Statement (2) merely tells us p>qp > q, which permits pp and qq to both be positive (pq>0pq > 0) or to have opposite signs (pq<0pq < 0), rendering Statement (2) insufficient.

Step-by-Step Solution

1
Rephrase the question stem target geometrically or algebraically.
Squaring both non-negative sides of ∣p+q∣>∣p−q∣|p + q| > |p - q| gives (p+q)2>(p−q)2  ⟹  p2+2pq+q2>p2−2pq+q2  ⟹  4pq>0  ⟹  pq>0(p + q)^2 > (p - q)^2 \implies p^2 + 2pq + q^2 > p^2 - 2pq + q^2 \implies 4pq > 0 \implies pq > 0. The question asks: Is pq>0pq > 0?
Simplifying the question stem simplifies evaluation of both statements by focusing on whether pp and qq have the same sign.
2
Evaluate Statement (1): ∣p+2q∣<∣p−2q∣|p + 2q| < |p - 2q|.
Squaring both non-negative sides gives (p+2q)2<(p−2q)2  ⟹  p2+4pq+4q2<p2−4pq+4q2  ⟹  8pq<0  ⟹  pq<0(p + 2q)^2 < (p - 2q)^2 \implies p^2 + 4pq + 4q^2 < p^2 - 4pq + 4q^2 \implies 8pq < 0 \implies pq < 0.
Since pq<0pq < 0, we can answer the rephrased target question ('Is pq>0pq > 0?') with a definitive 'NO'. In Data Sufficiency, a definitive 'No' means the statement is sufficient.
3
Evaluate Statement (2): p−q>0p - q > 0.
If p=3p = 3 and q=1q = 1, then p−q=2>0p - q = 2 > 0 and pq=3>0pq = 3 > 0 (Yes). If p=1p = 1 and q=−2q = -2, then p−q=3>0p - q = 3 > 0 and pq=−2<0pq = -2 < 0 (No).
Because Statement (2) allows both 'Yes' and 'No' outcomes, it is not sufficient.

Key Concept

Rephrasing absolute value distance inequalities and recognizing that a definitive 'No' response in Yes/No Data Sufficiency constitutes sufficiency.
Question 1330Question →

Passage:
In 2022, a municipal public health board enacted a regulatory mandate stipulating that any water treatment facility constructed after the mandate's passage must incorporate advanced ultraviolet disinfection units. Official compliance reports confirm that every facility incorporating advanced ultraviolet disinfection units successfully reduced bacterial counts below threshold levels. Furthermore, municipal records indicate that total administrative overhead costs dropped in every municipality where a water treatment facility was constructed between 2022 and 2025.

Statement: Based on the passage above, it MUST BE TRUE that at least one water treatment facility incorporating advanced ultraviolet disinfection units was constructed between 2022 and 2025 in a municipality where total administrative overhead costs dropped.

Show answer & explanation

Answer: False

Answer

The statement is False because the passage provides conditional mandates and observations, but does not state or guarantee that any water treatment facility was actually constructed after 2022.
The correct answer is False because the passage sets forth conditional requirements (what occurs IF a facility is built) without establishing that any facility was built between 2022 and 2025. Without proof of actual construction, the statement is merely a 'could be true' scenario rather than a strictly required deduction.

Step-by-Step Solution

1
Analyze the logical structure of the passage premises.
Premise 1: Facility constructed post-2022 → Must incorporate UV units (Conditional Rule). Premise 2: UV units → Reduced bacterial counts. Premise 3: Facility constructed between 2022 and 2025 → Administrative overhead dropped in that municipality.
Distinguish between conditional rules and existential facts in the stimulus.
2
Check whether the antecedent condition (that a facility was actually constructed post-2022) is established as fact.
The passage contains no premise asserting that any construction project actually took place after 2022.
Determine if the existence of at least one constructed facility is logically guaranteed.
3
Evaluate the truth value of the 'Must Be True' statement.
If zero facilities were constructed, all conditional rules remain uncontradicted, yet no such facility exists. Thus, the statement COULD be true (if construction occurred), but it DOES NOT MUST BE TRUE. Therefore, the assertion that it MUST be true is False.
Avoid the classic GMAT trap of confusing 'could be true' scenarios with 'must be true' deductions.

Key Concept

Avoiding 'Could Be True' and Existential Assumptions in Conditional Deduction
Question 1331Question →

To boost regional farm earnings during droughts, a state agricultural agency plans to subsidize half the cost of a new drought-resistant wheat seed for local farmers. Because this new strain yields 25 percent more grain per acre during dry spells than traditional strains, agency officials claim the subsidy program will increase net agricultural revenue across the region during drought years. Which of the following would be most useful to determine in evaluating the likelihood that the agency's plan will achieve its intended goal?

Show answer & explanation

Answer: Whether the market price per bushel of wheat declines disproportionately when regional supply increases during drought years.

Answer

Determining whether the market price per bushel drops disproportionately when supply rises provides the necessary test of variance to evaluate whether increased yield translates into increased net agricultural revenue.
The plan relies on the mathematical assumption that a 25 percent increase in grain volume will increase total revenue. However, Total Revenue = Price × Quantity. If increasing local output causes the market price per bushel to drop significantly, total revenue could decrease despite the higher yield. Determining the price behavior under increased supply is therefore critical for evaluating the plan.

Step-by-Step Solution

1
Identify the plan and its explicit objective.
Plan: Subsidize 50% of the cost of a high-yielding drought-resistant wheat seed. Objective: Increase net agricultural revenue during drought years based on a 25% yield increase per acre.
Evaluating a plan requires checking whether the proposed mechanism directly leads to the desired objective.
2
Apply the Variance Test to evaluate the plan's core financial assumption.
Revenue is calculated as Quantity Sold multiplied by Price per Unit, minus Costs. If total quantity produced increases due to higher yields, but the market price per unit drops at a faster rate due to oversupply, total gross revenue (and thus net revenue) will fall.
Knowing price elasticity reveals whether higher crop volume actually yields higher revenue or causes a market price crash that undermines net earnings.
3
Select the choice that directly measures this price-yield relationship.
The option assessing whether price per bushel declines disproportionately directly impacts the success or failure of the goal.
An affirmative answer undermines the plan's objective, while a negative answer validates it.

Key Concept

Evaluating Plan Efficacy via Test of Variance
Question 1332Question →

For any non-zero real numbers xx and yy, the Data Sufficiency target question 'Is xy>0\frac{x}{y} > 0?' is algebraically equivalent to the rephrased target question 'Do xx and yy have the same sign?'

Show answer & explanation

Answer: True

Answer

True. The target question simplifies directly to asking whether xx and yy share the same sign.
The target question asks if the ratio xy\frac{x}{y} is positive. In arithmetic, the quotient of two real numbers is positive if and only if both numbers have the same sign (both positive or both negative). Thus, rephrasing the target to 'Do xx and yy have the same sign?' is a completely equivalent simplification.

Step-by-Step Solution

1
Analyze the condition for a fraction to be positive
For xy>0\frac{x}{y} > 0, either (x>0x > 0 and y>0y > 0) or (x<0x < 0 and y<0y < 0).
Dividing two numbers with identical signs yields a positive quotient, while dividing numbers with opposite signs yields a negative quotient.
2
Compare the condition to the proposed rephrased question
The condition 'both positive or both negative' is the definition of xx and yy having the same sign.
Rephrasing a Data Sufficiency stem requires finding a target condition that is true under the exact same conditions as the original question.

Key Concept

Question Stem Rephrasing for Quotient Inequalities
Question 1333Question →

If kk is a real number, is ∣k2−4∣<3k|k^2 - 4| < 3k?

(1) k2−5k+4<0k^2 - 5k + 4 < 0
(2) ∣k−1∣<2|k - 1| < 2

Which statement(s) provide sufficient information to determine whether the inequality holds?

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The stem inequality ∣k2−4∣<3k|k^2 - 4| < 3k simplifies to 1<k<41 < k < 4. Statement (1) directly yields 1<k<41 < k < 4, providing a definitive Yes answer. Statement (2) yields −1<k<3-1 < k < 3, which includes values inside (1,4)(1, 4) such as k=2k = 2 (Yes) and values outside (1,4)(1, 4) such as k=0.5k = 0.5 (No), making Statement (2) insufficient.

Step-by-Step Solution

1
Rephrase the target question stem algebraically.
The target inequality ∣k2−4∣<3k|k^2 - 4| < 3k requires 3k>03k > 0 (so k>0k > 0) and translates to −3k<k2−4<3k-3k < k^2 - 4 < 3k. Solving k2−4<3kk^2 - 4 < 3k yields (k−4)(k+1)<0  ⟹  −1<k<4(k - 4)(k + 1) < 0 \implies -1 < k < 4. Solving −3k<k2−4-3k < k^2 - 4 for k>0k > 0 yields k2+3k−4>0  ⟹  (k+4)(k−1)>0  ⟹  k>1k^2 + 3k - 4 > 0 \implies (k + 4)(k - 1) > 0 \implies k > 1. Combining these gives the rephrased question: 'Is 1<k<41 < k < 4?'
Simplifying the question stem before evaluating the statements prevents misinterpretation of absolute value boundary conditions.
2
Evaluate Statement (1): k2−5k+4<0k^2 - 5k + 4 < 0.
Factoring the quadratic gives (k−1)(k−4)<0(k - 1)(k - 4) < 0, which means 1<k<41 < k < 4.
Since Statement (1) guarantees that kk lies strictly between 11 and 44, the answer to the rephrased question is a definitive Yes. Statement (1) ALONE is sufficient.
3
Evaluate Statement (2): ∣k−1∣<2|k - 1| < 2.
Removing the absolute value gives −2<k−1<2-2 < k - 1 < 2, or −1<k<3-1 < k < 3.
If k=2k = 2, then 1<2<41 < 2 < 4, giving a Yes answer. If k=0.5k = 0.5, then 0.50.5 is in (−1,3)(-1, 3) but not in (1,4)(1, 4), giving a No answer (since ∣0.52−4∣=3.75>3(0.5)=1.5|0.5^2 - 4| = 3.75 > 3(0.5) = 1.5). Because Statement (2) allows both Yes and No outcomes, it is NOT sufficient.

Key Concept

Absolute Value Inequalities and Question Stem Rephrasing

Alternative Method

Instead of solving the quadratic inequality −3k<k2−4<3k-3k < k^2 - 4 < 3k algebraically, test the boundary points k=1k = 1 and k=4k = 4 in ∣k2−4∣=3k|k^2 - 4| = 3k: at k=1k = 1, ∣1−4∣=3=3(1)|1 - 4| = 3 = 3(1); at k=4k = 4, ∣16−4∣=12=3(4)|16 - 4| = 12 = 3(4). Since 3k3k grows linearly while k2−4k^2 - 4 grows quadratically, the inequality holds strictly between these two positive roots 1<k<41 < k < 4.
Estimated Time:2m 0s
Question 1334Question →

If kk is a positive integer, is kk divisible by 6?

(1) kk is a multiple of 2.
(2) kk is a multiple of 3.

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.
To determine whether an integer is divisible by 6, it must be divisible by both prime factors of 6, which are 2 and 3. Statement (1) indicates kk is divisible by 2, and Statement (2) indicates kk is divisible by 3. Neither statement alone is sufficient because a number can be a multiple of 2 without being a multiple of 3 (e.g., 2, 4) or a multiple of 3 without being a multiple of 2 (e.g., 3, 9). Taking both statements together ensures kk is a multiple of both 2 and 3, which means kk is a multiple of 6. Therefore, both statements together are sufficient.

Step-by-Step Solution

1
Rephrase the question target.
For a positive integer kk to be divisible by 6, it must be divisible by both 2 and 3 because lcm(2,3)=6\text{lcm}(2,3) = 6.
6 is the product of the prime numbers 2 and 3.
2
Evaluate Statement (1) independently.
If k=2k = 2, it is divisible by 2 but not by 6 (No). If k=6k = 6, it is divisible by 2 and by 6 (Yes). Insufficient.
Statement (1) alone allows multiple outcomes for divisibility by 6.
3
Evaluate Statement (2) independently.
If k=3k = 3, it is divisible by 3 but not by 6 (No). If k=6k = 6, it is divisible by 3 and by 6 (Yes). Insufficient.
Statement (2) alone allows multiple outcomes for divisibility by 6.
4
Combine Statement (1) and Statement (2).
Since kk is divisible by 2 and divisible by 3, kk must be a multiple of lcm(2,3)=6\text{lcm}(2,3) = 6. Thus, kk is definitely divisible by 6 (Definitive Yes).
Both conditions combined uniquely answer the question with a definitive Yes.

Key Concept

Divisibility Rules and Prime Factorization
Question 1335Question →

A recent survey of urban professionals revealed that individuals who drink green tea every day report significantly lower stress levels than those who do not drink green tea. Based on this correlation, the researchers concluded that daily green tea consumption directly causes a reduction in psychological stress. Which of the following, if true, most seriously weakens the researchers' conclusion?

Show answer & explanation

Answer: Individuals who drink green tea daily are far more likely to engage in regular physical exercise, which independently lowers stress levels.

Answer

The argument is most seriously weakened by pointing out that green tea drinkers are also more likely to engage in regular physical exercise, introducing an alternate factor that accounts for the lower stress levels.
The correct answer identifies a classic confounding variable flaw. By pointing out that daily green tea drinkers are also significantly more likely to engage in regular exercise—a habit known to independently lower stress—it demonstrates that the observed lower stress levels could be caused by exercise rather than green tea, thereby severely undermining the researchers' causal conclusion.

Step-by-Step Solution

1
Identify the premise and conclusion of the argument.
Premise: Daily green tea drinkers report lower stress levels than non-drinkers. Conclusion: Daily green tea consumption directly causes a reduction in stress.
Understanding the logic structure reveals that the author assumes correlation implies direct causation without accounting for potential confounding variables.
2
Determine the weak point in the causal reasoning.
The argument commits a causal flaw by failing to rule out third-variable confounders that could cause the reduced stress instead of the green tea itself.
To weaken a causal conclusion based on correlation, look for an option showing an alternate cause for the effect.
3
Evaluate the answer choices for a confounding variable.
The choice noting that daily green tea drinkers also participate in regular exercise identifies a confounding factor that independently causes stress reduction.
If exercise is responsible for lower stress levels among green tea drinkers, the green tea itself may have no direct causal effect on stress.

Key Concept

Causal Reasoning and Confounding Variables
Question 1336Question →

If nn is a real number, is n>5n > 5?

(1) n2+6n+9=0n^2 + 6n + 9 = 0
(2) n2=36n^2 = 36

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1) yields n=−3n = -3, which definitively answers 'No' to the question of whether n>5n > 5. In GMAT Data Sufficiency Yes/No questions, a single conclusive 'No' answer makes a statement sufficient. Statement (2) gives n=6n = 6 or n=−6n = -6, leading to both 'Yes' and 'No' answers, making it insufficient. Thus, Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Step-by-Step Solution

1
Rephrase the question stem target.
The target is a Yes/No question: 'Is n>5n > 5?' A statement is sufficient if it allows us to answer either a conclusive 'Yes' for all valid values or a conclusive 'No' for all valid values.
In Data Sufficiency Yes/No questions, both a definitive 'Yes' and a definitive 'No' constitute sufficiency.
2
Evaluate Statement (1) independently.
n2+6n+9=0⇒(n+3)2=0⇒n=−3n^2 + 6n + 9 = 0 \Rightarrow (n + 3)^2 = 0 \Rightarrow n = -3. Testing n=−3n = -3 against n>5n > 5 gives a definitive 'No'. Therefore, Statement (1) ALONE is sufficient.
Since n=−3n = -3 produces a unique answer ('No') to the question stem, Statement (1) is sufficient.
3
Evaluate Statement (2) independently.
n2=36⇒n=6n^2 = 36 \Rightarrow n = 6 or n=−6n = -6. If n=6n = 6, 6>56 > 5 ('Yes'). If n=−6n = -6, −6≯5-6 \ngtr 5 ('No'). Since we get both 'Yes' and 'No', Statement (2) ALONE is not sufficient.
Multiple conflicting answers to a Yes/No question mean the statement cannot conclusively answer the question.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic
Question 1337Question →

Many macroeconomists contend that Central Bank interventions to suppress short-term interest rates during economic downturns inevitably create asset price bubbles. However, a recent retrospective analysis of mid-century industrial expansion demonstrates that monetary easing in that era consistently stimulated capital reinvestment without distorting asset valuations. This finding suggests that liquidity injections do not inherently inflate asset values; rather, the modern tendency toward asset bubbles stems primarily from financial deregulation that allows banks to leverage cheap credit for speculative trading.

In the argument given, the two boldfaced portions play which of the following roles?

Show answer & explanation

Answer: The first is empirical evidence presented to challenge a claim opposed by the author; the second is the author's main conclusion.

Answer

The first bolded statement is empirical evidence presented to challenge a claim opposed by the author; the second is the author's main conclusion.
The correct option accurately identifies that the first bolded statement serves as factual evidence introduced to refute the opposing viewpoint held by many macroeconomists. Furthermore, it correctly identifies the second bolded statement as the author's primary conclusion, which proposes an alternative cause for modern asset price bubbles.

Step-by-Step Solution

1
Analyze the overall argument structure and identify the main conclusion.
The author opposes the macroeconomists' view that interest rate suppression inevitably leads to asset bubbles, concluding instead that financial deregulation is the primary cause.
Determining the author's main point establishes the logical framework of the passage.
2
Evaluate the role of the first bolded statement.
The first bolded statement introduces historical data showing monetary easing without asset distortion, which directly counters the macroeconomists' contention.
This serves as empirical evidence supporting the author's rebuttal.
3
Evaluate the role of the second bolded statement.
The second bolded statement expresses the author's definitive claim regarding the real cause of asset bubbles (financial deregulation).
It follows the contrast transition ('rather') and represents the central takeaway/main conclusion of the argument.

Key Concept

Analyzing Bolded Statement Roles
Question 1338Question →

Consider the following argument: A study observed that technology companies offering complimentary daily lunches to employees reported 20% higher project completion rates than technology companies without free lunch programs. The researcher concluded that providing complimentary lunches directly causes an increase in employee productivity. In this argument, the possibility that overall company funding is a third factor influencing both the ability to offer perks and the ability to hire top-performing talent acts as a confounding variable.

Show answer & explanation

Answer: True

Answer

The statement is True. Overall company funding represents a classic third-variable confounder that accounts for both the perk (complimentary lunches) and the outcome (higher productivity), undermining the claim of a direct causal relationship.
The claim is accurate because a confounding variable is a third factor that systematically correlates with both the presumed cause and effect. In this scenario, well-funded firms have the budget for employee perks like free lunch and also have the capital to hire more effective teams or build better infrastructure, which explains the higher completion rates without requiring free lunch to be the direct cause.

Step-by-Step Solution

1
Identify the author's causal conclusion and evidence
The author infers that free lunches (Cause) directly increase employee productivity (Effect) based solely on an observed correlation between the two.
Establishing the claimed cause-and-effect relationship is necessary before assessing logical vulnerabilities.
2
Evaluate the proposed potential confounding variable
Company funding level can plausibly cause both the presence of free lunches and higher productivity (by attracting top talent or providing better equipment).
A confounding variable (third variable) provides an alternative explanation for the correlation without a direct causal link between the two observed phenomena.
3
Determine the truth value of the statement
Since company funding fits the precise definition of a confounding variable that weakens the causal conclusion, the evaluation statement is True.
Validating whether the identified factor acts as a confounder directly answers the question.

Key Concept

Causal Reasoning: Third-Variable Confounders
Question 1339Question →

In 2025, Apex Motors produced 10,000 electric vehicles, all of which were manufactured at its main manufacturing plant in City X. In that same year, 30 percent of the electric vehicles produced by Apex Motors were exported to international markets, while the remainder were sold domestically.

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

Show answer & explanation

Answer: Apex Motors sold exactly 7,000 electric vehicles domestically in 2025.

Answer

Apex Motors sold exactly 7,000 electric vehicles domestically in 2025.
The passage establishes that Apex Motors produced 10,000 electric vehicles, 30 percent of which were exported and the remainder (70 percent) were sold domestically. Calculating 70 percent of 10,000 yields exactly 7,000 vehicles sold domestically. Therefore, this statement must be strictly true based solely on the provided premises.

Step-by-Step Solution

1
Identify the given facts in the passage
Total production = 10,000 vehicles. Exported percentage = 30%. Domestic percentage = remainder (100% - 30% = 70%).
Inference questions require deductions based strictly on the provided factual premises.
2
Calculate the domestic sales quantity
70% of 10,000 = 7,000 vehicles.
Mathematical certainty derived directly from the explicit facts.
3
Evaluate options against strict 'Must Be True' criterion
The statement calculating 7,000 domestic vehicle sales is guaranteed to be true, while all other options introduce unstated assumptions or speculative claims.
A valid GMAT inference must follow logically from the premises without external assumptions.

Key Concept

Distinguishing mathematical/deductive inferences from unstated assumptions and speculative claims
Question 1340Question →

A hospital recently introduced an automated ultraviolet-light room sanitation system intended to lower patient infection rates. During the six months following the system's installation, the hospital reported a 30 percent drop in patient infection rates compared to the previous six-month period. Hospital administrators concluded that the ultraviolet sanitation system was directly responsible for the reduction in patient infections. Which of the following, if true, most seriously weakens the hospital administrators' conclusion?

Show answer & explanation

Answer: Three months prior to installing the system, the hospital implemented a strict hand-hygiene protocol and staff training program that significantly reduced bacterial transmission.

Answer

The statement regarding the implementation of a strict hand-hygiene protocol and staff training program three months prior to the installation of the ultraviolet system most seriously weakens the argument.
The correct answer provides an alternative explanation for the observed 30 percent decline in patient infections. If a comprehensive hand-hygiene protocol was instituted three months before the UV system was installed, that hygiene initiative could be the real reason infection rates decreased, thereby undermining the conclusion that the UV system was the primary cause.

Step-by-Step Solution

1
Identify the conclusion and premises
Premise: Infections dropped by 30% after installing a UV sanitation system. Conclusion: The UV system caused the reduction in infections.
Understanding the precise causal claim is essential for evaluating argument weakness.
2
Analyze the logical gap
The argument assumes no other factor caused the infection rate decline during the relevant timeframe.
Causal conclusions rely on the assumption that alternative causes have been ruled out.
3
Evaluate the choices for alternative explanations
The option introducing a newly enforced hand-hygiene protocol provides a competing explanation for the drop in infection rates.
Introducing a viable alternative cause directly undermines the claim that the UV system was responsible.

Key Concept

Weakening Causal Arguments via Alternative Causes
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