Examkin

All practice questions

2195 questions

All types2,195Multiple choice1,339Multiple select37True / False283Numeric387Matching111Ordering25Fill in the blank13
Question 1341Question →

If pp and qq are distinct non-zero real numbers, is p3−q3p−q>p2+q2\frac{p^3 - q^3}{p - q} > p^2 + q^2?

(1) pq+qp>2\frac{p}{q} + \frac{q}{p} > 2

(2) ∣p+q∣>∣p−q∣|p + q| > |p - q|

Show answer & explanation

Answer: EACH statement ALONE is sufficient.

Answer

EACH statement ALONE is sufficient.
Rephrasing the question stem is the key strategy. Factoring the numerator gives (p−q)(p2+pq+q2)p−q=p2+pq+q2\frac{(p - q)(p^2 + pq + q^2)}{p - q} = p^2 + pq + q^2. Subtracting p2+q2p^2 + q^2 from both sides simplifies the target question to 'Is pq>0pq > 0?'. Statement (1) simplifies to p2+q2pq>2\frac{p^2 + q^2}{pq} > 2; since p2+q2>0p^2 + q^2 > 0, this inequality requires pq>0pq > 0, answering 'Yes'. Statement (2) simplifies by squaring both sides to 4pq>0  ⟺  pq>04pq > 0 \iff pq > 0, also answering 'Yes'. Thus, each statement alone is sufficient.

Step-by-Step Solution

1
Rephrase the question stem using algebraic factoring.
Since p≠qp \neq q, factor p3−q3=(p−q)(p2+pq+q2)p^3 - q^3 = (p - q)(p^2 + pq + q^2). The target inequality (p−q)(p2+pq+q2)p−q>p2+q2\frac{(p - q)(p^2 + pq + q^2)}{p - q} > p^2 + q^2 simplifies directly to p2+pq+q2>p2+q2p^2 + pq + q^2 > p^2 + q^2, which further simplifies to 'Is pq>0pq > 0?'
Simplifying the target question stem upfront converts a complex cubic rational expression into a simple condition about whether pp and qq have the same sign.
2
Evaluate Statement (1): pq+qp>2\frac{p}{q} + \frac{q}{p} > 2.
Combine fractions over a common denominator: p2+q2pq>2\frac{p^2 + q^2}{pq} > 2. Since pp and qq are distinct non-zero real numbers, (p−q)2>0  ⟹  p2+q2>2pq(p - q)^2 > 0 \implies p^2 + q^2 > 2pq. For p2+q2pq>2\frac{p^2 + q^2}{pq} > 2 to hold, pqpq must be positive (if pq<0pq < 0, the fraction would be negative). Thus, pq>0pq > 0 must be true.
Statement (1) yields a definitive 'Yes' to the rephrased target question 'Is pq>0pq > 0?'. Therefore, Statement (1) alone is sufficient.
3
Evaluate Statement (2): ∣p+q∣>∣p−q∣|p + q| > |p - q|.
Square both non-negative sides: (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.
Statement (2) also yields a definitive 'Yes' to the target question 'Is pq>0pq > 0?'. Therefore, Statement (2) alone is sufficient.

Key Concept

Question Stem Simplification and Target Rephrasing
Question 1342Question →

A corporate governance protocol enforces the following rules regarding financial compliance:

1. Every department that incurs an annual operational deficit exceeding 10%10\% undergoes an automatic internal audit.
2. An internal audit takes place if and only if either the division vice president requests it or the central risk oversight committee flags the department's ledger.
3. Whenever the central risk oversight committee flags a department's ledger, that department is prohibited from submitting capital expansion proposals for the following fiscal year.

During the current fiscal year, the Logistics Department was not prohibited from submitting capital expansion proposals for the following fiscal year.

Evaluate the following statement based strictly on the information provided:

Statement: If the Logistics Department incurred an operational deficit exceeding 10%10\% during the current fiscal year, then its division vice president requested an internal audit.

Show answer & explanation

Answer: True

Answer

True
The conclusion is logically unavoidable. The fact that Logistics was not prohibited from submitting capital proposals guarantees that the risk committee did not flag its ledger. Therefore, if a deficit over 10%10\% triggered an audit, the audit could only have been requested by the division vice president.

Step-by-Step Solution

1
Formalize the conditional statements into symbolic logic terms.
Let DD = Deficit >10%>10\%, AA = Internal Audit, VV = Vice President requests audit, RR = Risk committee flags ledger, PP = Prohibited from capital proposals.
Premise 1: D→AD \rightarrow A
Premise 2: A↔(V∨R)A \leftrightarrow (V \lor R)
Premise 3: R→PR \rightarrow P
Symbolic representation clarifies the logical relationships and valid inferences.
2
Derive deductions from the given fact using contrapositive logic.
Fact: ¬P\neg P (Not prohibited from submitting proposals).
From R→PR \rightarrow P, taking the contrapositive (¬P→¬R\neg P \rightarrow \neg R) yields ¬R\neg R (The risk committee did not flag the ledger).
A conditional statement and its contrapositive are logically equivalent.
3
Evaluate the antecedent condition of the statement (DD).
Assume DD (Logistics incurred a deficit >10%>10\%). By Modus Ponens on Premise 1 (D→AD \rightarrow A), AA must be true (An internal audit took place).
If the sufficient condition of a valid conditional rule occurs, the necessary condition must also occur.
4
Combine the intermediate deductions to determine the truth of VV.
From Premise 2, A→(V∨R)A \rightarrow (V \lor R). Since AA is true, the disjunction (V∨R)(V \lor R) must be true. Since ¬R\neg R was established in Step 2, disjunctive syllogism forces VV to be true.
If a disjunction 'A or B' is true and 'B' is false, then 'A' must be true.

Key Concept

Multi-step Conditional Deduction via Contrapositive and Disjunctive Syllogism
Question 1343Question →

Is the real number pp negative?

(1) p2>0p^2 > 0
(2) p3<0p^3 < 0

Show answer & explanation

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

Answer

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (1) tells us that p2>0p^2 > 0, which means pp can be any real number except 0. Since pp could be positive (e.g., p=5p = 5) or negative (e.g., p=−5p = -5), Statement (1) alone cannot answer whether pp is negative.

Statement (2) tells us that p3<0p^3 < 0. Because taking an odd power of a real number preserves its sign, p3<0p^3 < 0 implies pp must be negative. This provides a definitive 'Yes' answer to the question stem, making Statement (2) sufficient alone.

Step-by-Step Solution

1
Evaluate Statement (1): p2>0p^2 > 0
pp can be any non-zero real number (e.g., p=2p = 2 or p=−2p = -2).
Squaring any non-zero real number yields a positive value. Thus, pp could be positive or negative, so Statement (1) is not sufficient.
2
Evaluate Statement (2): p3<0p^3 < 0
pp must be negative.
An odd exponent preserves the sign of the base. If p3<0p^3 < 0, then pp must be negative. This provides a definitive 'Yes' answer to whether pp is negative, so Statement (2) is sufficient.

Key Concept

Properties of real numbers under even and odd exponents
Estimated Time:1m 0s
Question 1344Question →

In an arid agricultural basin, the regional water board subsidized advanced drip-irrigation technology for 80 percent of commercial farms, cutting the volume of water required per crop growing cycle by 35 percent. Surprisingly, over the three years following the widespread adoption of this technology, overall agricultural groundwater extraction from the basin's primary aquifer rose by nearly 20 percent, even though total cultivated land area remained unchanged and seasonal precipitation matched historic averages. Which of the following, if true, most helps to resolve the apparent paradox described above?

Show answer & explanation

Answer: The drip-irrigation systems enabled farmers in the basin to replace single-season crops with multi-harvest perennial crops and execute double-cropping cycles on the same acreage throughout the year.

Answer

The apparent paradox is resolved by the option explaining that drip-irrigation enabled year-round double-cropping and perennial crop cultivation on the same acreage, raising total annual water consumption despite improved per-cycle efficiency.
The correct answer resolves the discrepancy by introducing a new factor: land use intensity. While each individual crop cycle requires 35 percent less water thanks to drip technology, the ability to farm year-round with double-cropping means farms are running multiple additional growing cycles each year. The cumulative water required for multiple annual harvests exceeds the savings gained per individual harvest, thereby explaining why total annual agricultural groundwater extraction rose.

Step-by-Step Solution

1
Identify the two conflicting facts presented in the passage.
Fact 1: Drip-irrigation reduces water needed per crop growing cycle by 35% across 80% of farms (with acreage and rainfall held constant). Fact 2: Total agricultural groundwater extraction increased by nearly 20%.
Resolving a paradox requires understanding both facts that appear mutually exclusive.
2
Formulate a hypothesis for how per-cycle water reduction can coexist with an overall increase in total annual water use.
An increase in total annual volume can occur if the total frequency of growing cycles per year increases or if crop selection changes drastically to offset the per-cycle savings.
Efficiency is measured per crop cycle, whereas total consumption depends on the overall annual intensity of land use.
3
Evaluate the options to find the scenario that reconciles both facts without contradicting either.
The option describing year-round double-cropping demonstrates that farmers utilized the efficiency gains to plant multiple harvests per year on the same land, driving up total annual water extraction.
This provides a direct causal mechanism for increased total volume while maintaining the premise of per-cycle efficiency.

Key Concept

Reconciling per-unit efficiency gains with aggregate consumption increases (Jevons paradox / Rebound effect)
Question 1345Question →

Many industry analysts predict that introducing AI-driven chatbots for routine inquiries will inevitably reduce customer support costs for retail banks. However, implementing these systems requires significant ongoing expenditures for software updates and specialized technical staff. Furthermore, automated interfaces often alienate customers seeking complex financial guidance, leading to higher customer attrition. Therefore, retail banks that rely heavily on AI chatbots to cut operational expenses will ultimately experience a net decline in overall profitability.

In the argument above, which of the following best describes the roles played by the two boldfaced portions?

Show answer & explanation

Answer: The first is evidence offered to support the author's main position; the second is the main conclusion of the argument.

Answer

The first boldfaced statement provides evidence introduced by the author to counter the analysts' view and support the author's position, while the second boldfaced statement expresses the main conclusion of the argument.
The first boldfaced portion presents empirical evidence regarding ongoing expenditures, introduced with the pivot 'However' to challenge the analysts' claim and support the author's point of view. The second boldfaced statement begins with 'Therefore' and presents the author's final recommendation/prediction, which is the main conclusion of the passage.

Step-by-Step Solution

1
Identify the main argument structure and author stance
The author contrasts a prediction made by industry analysts with counter-arguments leading to a final judgment.
Understanding the overall flow distinguishes author premises/conclusions from opposing views.
2
Analyze the role of the first boldface statement
The first boldface ('However, implementing these systems requires...') follows a structural pivot ('However') and provides a premise supporting the author's critique.
It acts as direct evidence showing why AI chatbots involve unexpected costs.
3
Analyze the role of the second boldface statement
The second boldface ('Therefore, retail banks...') follows the conclusion indicator ('Therefore') and expresses the overall claim supported by the premises.
It represents the author's ultimate takeaway regarding net profitability.

Key Concept

Identifying Boldface Statement Roles in Critical Reasoning
Question 1346Question →

To increase net profit from its flagship consumer electronics line, a device manufacturer plans to eliminate bundled accessories from standard product packaging and sell them as standalone items. Executive leadership reasons that smaller packaging will significantly decrease global freight expenses, while individual accessory sales will create a lucrative secondary revenue stream without increasing baseline production costs.

Which of the following would be most useful to know in evaluating whether the manufacturer’s plan will achieve its goal?

Show answer & explanation

Answer: Whether a substantial proportion of consumers who would have bought the flagship device will instead purchase rival products that include all necessary accessories at no extra cost.

Answer

Whether a substantial proportion of consumers who would have bought the flagship device will instead purchase rival products that include all necessary accessories at no extra cost.
The option assessing consumer switching behavior passes the variance test. If a substantial proportion of customers switch to competitors that include accessories, the lost revenue from flagship device sales will outweigh freight savings and accessory profits, causing the plan to fail. If very few customers switch, demand for the main device will hold steady, allowing freight savings and accessory sales to increase net profit.

Step-by-Step Solution

1
Identify the goal and the proposed plan.
Goal: Increase net profit from the flagship line. Plan: Unbundle accessories, selling them separately while reducing package size to cut freight costs.
Evaluating a plan requires understanding the intended outcome relative to its mechanisms.
2
Identify key assumptions and potential vulnerabilities of the plan.
The plan assumes that consumer demand for the flagship device will remain constant despite the reduced included value.
If core product demand drops significantly due to unbundling, loss of primary sales revenue could outweigh freight savings and accessory profits.
3
Apply the Variance Test to the answer choices.
Evaluating whether consumers switch to competitors who bundle accessories yields opposite outcomes: a 'yes' answer invalidates the plan by destroying primary revenue, while a 'no' answer confirms the plan's efficacy.
The correct useful-information option must produce opposite logical impacts on plan success depending on which way the evaluation falls.

Key Concept

Evaluating Plan Viability via the Variance Test
Question 1347Question →

If xx is a real number, is ∣x−3∣+∣x+2∣≤7|x - 3| + |x + 2| \le 7?

(1) x2−2x−8≤0x^2 - 2x - 8 \le 0
(2) x(x−5)≤0x(x - 5) \le 0

Show answer & explanation

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

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Rephrasing the question target ∣x−3∣+∣x+2∣≤7|x - 3| + |x + 2| \le 7 shows that it is satisfied if and only if −3≤x≤4-3 \le x \le 4. Statement (1) yields the interval [−2,4][-2, 4], which is completely contained within [−3,4][-3, 4], guaranteeing a definitive 'Yes'. Statement (2) yields [0,5][0, 5], which includes values like 4.54.5 that result in a 'No'. Thus, Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Step-by-Step Solution

1
Rephrase the question stem inequality ∣x−3∣+∣x+2∣≤7|x - 3| + |x + 2| \le 7.
The target inequality simplifies to −3≤x≤4-3 \le x \le 4.
Interpret ∣x−3∣+∣x+2∣|x - 3| + |x + 2| as the sum of distances from xx to 33 and −2-2 on the real number line. The distance between −2-2 and 33 is 55. For −2≤x≤3-2 \le x \le 3, the sum of distances is constantly 5≤75 \le 7. For x>3x > 3, the sum is 2x−1≤7  ⟹  x≤42x - 1 \le 7 \implies x \le 4. For x<−2x < -2, the sum is 1−2x≤7  ⟹  x≥−31 - 2x \le 7 \implies x \ge -3. Thus, the inequality holds if and only if x∈[−3,4]x \in [-3, 4].
2
Evaluate Statement (1): x2−2x−8≤0x^2 - 2x - 8 \le 0.
Statement (1) gives −2≤x≤4-2 \le x \le 4.
Factoring gives (x−4)(x+2)≤0(x - 4)(x + 2) \le 0, which holds when x∈[−2,4]x \in [-2, 4]. Since [−2,4]⊆[−3,4][-2, 4] \subseteq [-3, 4], every value of xx satisfying Statement (1) guarantees that ∣x−3∣+∣x+2∣≤7|x - 3| + |x + 2| \le 7 is true. This yields a definitive 'Yes'. Statement (1) alone is sufficient.
3
Evaluate Statement (2): x(x−5)≤0x(x - 5) \le 0.
Statement (2) gives 0≤x≤50 \le x \le 5.
The solution set is x∈[0,5]x \in [0, 5]. If x=1x = 1, −3≤1≤4-3 \le 1 \le 4 is true (Yes). If x=4.5x = 4.5, ∣4.5−3∣+∣4.5+2∣=1.5+6.5=8≤7|4.5 - 3| + |4.5 + 2| = 1.5 + 6.5 = 8 \le 7 is false (No). Since Statement (2) allows both 'Yes' and 'No' outcomes, Statement (2) alone is not sufficient.

Key Concept

Question stem rephrasing for distance-based absolute values and set-inclusion sufficiency evaluation
Question 1348Question →

If xx is a real number, is ∣x−3∣<2x|x - 3| < 2x?

(1) x2−4x+3>0x^2 - 4x + 3 > 0
(2) ∣x−2∣<1|x - 2| < 1

Which of the following choices 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.
Rephrasing the stem ∣x−3∣<2x|x - 3| < 2x shows it is equivalent to asking whether x>1x > 1. Statement (2) restricts xx to the range 1<x<31 < x < 3, where every value of xx satisfies x>1x > 1, providing a definitive YES answer. Statement (1) permits x<1x < 1 (giving a NO) and x>3x > 3 (giving a YES), making Statement (1) insufficient.

Step-by-Step Solution

1
Rephrase the target question stem algebraically.
The target inequality is ∣x−3∣<2x|x - 3| < 2x. Since absolute values are non-negative (∣x−3∣≥0|x - 3| \ge 0), 2x2x must be strictly positive, so x>0x > 0.
- If x≥3x \ge 3, ∣x−3∣=x−3<2x  ⟹  x>−3|x - 3| = x - 3 < 2x \implies x > -3, which holds for all x≥3x \ge 3.
- If 0<x<30 < x < 3, ∣x−3∣=3−x<2x  ⟹  3x>3  ⟹  x>1|x - 3| = 3 - x < 2x \implies 3x > 3 \implies x > 1.
Thus, the inequality ∣x−3∣<2x|x - 3| < 2x holds if and only if x>1x > 1. The target question simplifies to: 'Is x>1x > 1?'
Simplifying the question stem before analyzing statements prevents misinterpreting the range of valid solutions.
2
Evaluate Statement (1): x2−4x+3>0x^2 - 4x + 3 > 0.
Factoring the quadratic yields (x−1)(x−3)>0(x - 1)(x - 3) > 0, so x<1x < 1 or x>3x > 3.
- If x=0x = 0 (which is <1< 1), ∣0−3∣=3|0 - 3| = 3 and 2(0)=02(0) = 0. Is 3<03 < 0? NO.
- If x=4x = 4 (which is >3> 3), ∣4−3∣=1|4 - 3| = 1 and 2(4)=82(4) = 8. Is 1<81 < 8? YES.
Since Statement (1) allows for both YES and NO outcomes, it is NOT sufficient.
Testing specific values from the disjoint solution set demonstrates that a single definitive answer cannot be reached.
3
Evaluate Statement (2): ∣x−2∣<1|x - 2| < 1.
Solving the absolute value inequality gives −1<x−2<1  ⟹  1<x<3-1 < x - 2 < 1 \implies 1 < x < 3.
For every value of xx in the interval (1,3)(1, 3), xx is strictly greater than 11. Therefore, the answer to 'Is x>1x > 1?' is a definitive YES for all possible values of xx in this statement.
A statement is sufficient if every allowed value of xx yields a consistent YES answer to the rephrased question stem.

Key Concept

Question Stem Rephrasing for Absolute Value Inequalities
Estimated Time:2m 0s
Question 1349Question →

Municipal planners in City X recently replaced traditional asphalt in high-density commercial zones with permeable interlocking concrete pavers to reduce storm runoff and mitigate the urban heat island effect. Although the pavers successfully absorbed rainfall and lowered surface temperatures, routine road maintenance costs rose significantly because traditional mechanical rotary sweepers dislodged the stabilizing joint sand between the pavers, requiring frequent re-sanding. To eliminate these extra maintenance expenses while preserving the environmental benefits, the city plans to replace its mechanical sweepers with high-pressure suction vacuum sweepers. However, this plan is unlikely to achieve its intended cost-saving goal because __________

Which of the following most logically completes the passage?

Show answer & explanation

Answer: high-pressure suction sweepers pull joint sand from between interlocking pavers at a rate equal to or greater than mechanical rotary sweepers do

Answer

The passage is most logically completed by the statement that high-pressure suction sweepers pull joint sand from between interlocking pavers at a rate equal to or greater than mechanical rotary sweepers do.
The correct answer completes the logical chain of the passage. The passage identifies the root cause of increased maintenance costs as the dislodgement of joint sand by sweeping equipment. If high-pressure suction sweepers dislodge or extract joint sand at an equal or higher rate than mechanical rotary sweepers, switching to suction sweepers will not resolve the sand loss issue, thus failing to lower maintenance costs.

Step-by-Step Solution

1
Analyze the premises and identify the core argument structure
Goal: Reduce road maintenance costs caused by lost joint sand while preserving environmental benefits of permeable pavers. Plan: Replace mechanical rotary sweepers with high-pressure suction vacuum sweepers.
The conclusion begins with 'However, this plan is unlikely to achieve its intended cost-saving goal because...', which requires a premise that explains why the new sweepers will fail to reduce joint sand maintenance costs.
2
Evaluate the mechanism of failure needed to complete the argument
The problem with the old sweepers was that they dislodged joint sand. For the new sweepers to fail at reducing costs, they must also dislodge joint sand to a similar or greater extent.
Completing a passage logically requires closing the gap between the proposed intervention and its stated failure mechanism.
3
Match against the option choices
The option stating that suction sweepers extract joint sand at an equal or greater rate directly demonstrates why switching equipment will not reduce re-sanding maintenance expenses.
This is the only choice that strictly builds upon the explicit premises without introducing unstated external factors.

Key Concept

Completing the Passage Logically
Estimated Time:1m 45s
Question 1350Question →

Conservators at a national museum suspect that a famous seventeenth-century oil painting suffered discolored fading primarily due to historical exposure to trace hydrogen sulfide gas released by nineteenth-century coal heating systems. To prevent further chemical degradation, the museum plans to install specialized ambient air filtration units designed to absorb hydrogen sulfide gas from the gallery. The head curator concludes that installing these units will effectively halt the ongoing chemical discoloration of the painting.

Which of the following, if true, provides the strongest support for the head curator's conclusion?

Show answer & explanation

Answer: Air quality sensors in the gallery have recently measured continuous trace levels of hydrogen sulfide entering the building from outside vehicle exhaust.

Answer

The argument is most strongly supported by the statement indicating that air quality sensors in the gallery have recently measured continuous trace levels of hydrogen sulfide entering the building from outside vehicle exhaust.
The curator concludes that filtering hydrogen sulfide will halt ongoing discoloration. For this plan to succeed, hydrogen sulfide must currently be present in the gallery environment. Demonstrating that modern vehicle exhaust introduces continuous trace levels of hydrogen sulfide into the gallery confirms that an active threat exists for the filters to neutralize, directly supporting the conclusion.

Step-by-Step Solution

1
Deconstruct the argument into premise and conclusion.
Premise: The painting suffered past damage from hydrogen sulfide gas, and the museum plans to install units that filter hydrogen sulfide from gallery air. Conclusion: The filtration units will halt the painting's ongoing discoloration.
Identifying the logical leap helps isolate unstated assumptions.
2
Identify the critical gap in reasoning.
The argument assumes that hydrogen sulfide is currently present in the gallery air and actively contributing to ongoing discoloration. If no hydrogen sulfide is present today, filtering it will have no effect on current discoloration.
A strengthening option must bridge this gap by confirming that hydrogen sulfide remains an active threat in the gallery.
3
Evaluate the choices against the logical gap.
The option establishing that sensors currently detect hydrogen sulfide from vehicle exhaust confirms that the gas is actively present today, making the filtration units effective at halting the ongoing damage.
Supplying missing evidence of a current hazard directly validates the curator's prediction.

Key Concept

Strengthening Causal Plans by Confirming Present-Day Hazard
Estimated Time:2m 0s
Question 1351Question →

In a GMAT Data Sufficiency 'Yes/No' question, a statement that restricts a variable to a domain of values for which the condition in the question stem is false for every value in that domain is insufficient to answer the question.

Show answer & explanation

Answer: False

Answer

False. A statement that consistently yields a 'No' answer for all permissible values provides a definitive answer and is therefore sufficient.
The correct evaluation is False. In GMAT Data Sufficiency 'Yes/No' decision logic, a statement provides sufficient information if it yields a single, conclusive answer to the question stem. If a statement restricts a variable such that the stem condition is false for every possible value, the answer to the question is conclusively 'No'. Because the question is answered with certainty, the statement is sufficient.

Step-by-Step Solution

1
Define the criterion for sufficiency in GMAT 'Yes/No' Data Sufficiency questions.
A statement is sufficient if it allows the question in the stem to be answered with certainty—either always 'Yes' or always 'No'.
Sufficiency depends on determinism, not on receiving an affirmative result.
2
Analyze the scenario where the stem condition is false for every value in the statement's restricted domain.
Because every permissible value makes the condition false, the answer to the stem's question is guaranteed to be 'No'.
There is no ambiguity or variation in outcome across the allowed values.
3
Evaluate the statement's claim of insufficiency.
The claim that such a statement is 'insufficient' is false because a deterministic 'No' satisfies all requirements for data sufficiency.
Insufficiency only occurs when a statement permits both 'Yes' and 'No' answers under different allowed values.

Key Concept

Definitive Answer Criterion in Yes/No Data Sufficiency Logic
Question 1352Question →

A marine biology survey cataloged deep-sea coral reefs off the coast of Peninsula Y. The survey established that every reef located below a depth of 500 meters contains bioluminescent coral species. Furthermore, all coral reefs containing bioluminescent species in this region also host distinct populations of deep-sea shrimp. However, during the survey, several reefs located above a depth of 500 meters were found to host these same deep-sea shrimp populations.

Based on the survey results described above, which of the following statements must be true? (Select all that apply.)

Select all that apply

Show answer & explanation

Answer: Every coral reef off Peninsula Y located below a depth of 500 meters hosts deep-sea shrimp populations.; Any coral reef off Peninsula Y that lacks deep-sea shrimp populations is located at a depth of 500 meters or less.

Answer

The statements establishing that every reef located below a depth of 500 meters hosts deep-sea shrimp populations, and that any reef lacking deep-sea shrimp populations must be located at a depth of 500 meters or less, are both valid deductions that must be true.
The passage establishes two linked conditional rules: any reef deeper than 500 meters contains bioluminescent coral, and any reef with bioluminescent coral hosts deep-sea shrimp. Combining these yields the direct deduction that every reef below 500 meters hosts deep-sea shrimp. Furthermore, taking the contrapositive of this combined rule shows that any reef lacking deep-sea shrimp cannot be below 500 meters, meaning it must be located at a depth of 500 meters or less. Both of these statements are logically necessary conclusions.

Step-by-Step Solution

1
Identify and map explicit conditional premises
Premise 1: Reef Depth > 500m → Bioluminescent Coral. Premise 2: Bioluminescent Coral → Deep-Sea Shrimp. Premise 3: Some Reefs Depth ≤ 500m → Deep-Sea Shrimp.
Mapping the statements into formal conditional logic clarifies valid inferential paths.
2
Synthesize the conditional premises into a transitive chain
Transitive chain: Reef Depth > 500m → Bioluminescent Coral → Deep-Sea Shrimp. Thus, Reef Depth > 500m → Deep-Sea Shrimp.
Combining the first two premises establishes that all reefs deeper than 500 meters necessarily host deep-sea shrimp.
3
Formulate the logically equivalent contrapositive of the transitive chain
Contrapositive: No Deep-Sea Shrimp → Reef Depth ≤ 500m.
If a conditional statement 'If X then Y' is true, its contrapositive 'If not Y then not X' is guaranteed to be true.

Key Concept

Conditional Logic & Valid Deductive Inferences
Question 1353Question →

If xx is a real number, is x2−4x+3<0x^2 - 4x + 3 < 0?

(1) (x−4)2≤0(x - 4)^2 \le 0
(2) ∣x−2∣<2|x - 2| < 2

Which of the following statements correctly describes the sufficiency of the given statements to answer the question?

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 choice stating that Statement (1) alone is sufficient, but Statement (2) alone is not sufficient is correct. Statement (1) forces x=4x = 4. Evaluating x=4x = 4 against the condition x2−4x+3<0x^2 - 4x + 3 < 0 gives 42−4(4)+3=3<04^2 - 4(4) + 3 = 3 < 0, which is conclusively false. A statement that yields a definitive 'No' to a Yes/No question is sufficient. Statement (2) yields the range 0<x<40 < x < 4, which contains values of xx that make x2−4x+3<0x^2 - 4x + 3 < 0 true (such as x=2x = 2) and false (such as x=3.5x = 3.5), making Statement (2) insufficient.

Step-by-Step Solution

1
Rephrase the question stem target inequality.
The inequality x2−4x+3<0x^2 - 4x + 3 < 0 factors into (x−1)(x−3)<0(x - 1)(x - 3) < 0, which holds true if and only if 1<x<31 < x < 3. Thus, the question asks: 'Is 1<x<31 < x < 3?'
Simplifying the question stem establishes the exact criteria needed for a 'Yes' vs. 'No' response.
2
Evaluate Statement (1): (x−4)2≤0(x - 4)^2 \le 0.
Since any square of a real number is non-negative, (x−4)2≥0(x - 4)^2 \ge 0. The only way (x−4)2≤0(x - 4)^2 \le 0 can hold is if (x−4)2=0(x - 4)^2 = 0, which means x=4x = 4. Substituting x=4x = 4 into 1<x<31 < x < 3 gives 1<4<31 < 4 < 3, which is false. Therefore, the answer to the stem's question is a definitive 'NO'. In Yes/No Data Sufficiency logic, a definitive 'No' means the statement IS SUFFICIENT.
A statement that yields a consistent and definitive answer—whether 'Yes' or 'No'—provides sufficient information.
3
Evaluate Statement (2): ∣x−2∣<2|x - 2| < 2.
The absolute value inequality ∣x−2∣<2|x - 2| < 2 unravels to −2<x−2<2-2 < x - 2 < 2, or 0<x<40 < x < 4.
- If x=2x = 2 (which is in 0<x<40 < x < 4), then 1<2<31 < 2 < 3 is true ('YES').
- If x=0.5x = 0.5 (which is in 0<x<40 < x < 4), then 1<0.5<31 < 0.5 < 3 is false ('NO').
Since Statement (2) allows both 'Yes' and 'No' answers depending on the value chosen for xx, Statement (2) is NOT SUFFICIENT.
If a statement leads to contradictory answers ('Yes' under some conditions, 'No' under others), it is insufficient.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic
Estimated Time:2m 0s
Question 1354Question →

Over a three-year period, a logistics firm monitored two regional fulfillment centers: Center X, which implemented an ergonomic workspace redesign featuring adjustable assembly stations and specialized fatigue-reducing flooring, and Center Y, which maintained its standard physical layout. During this period, Center X reported 40 percent fewer worker compensation claims for musculoskeletal exertion than Center Y. Management concluded that the ergonomic workspace redesign was directly responsible for the lower rate of exertion-related claims at Center X.

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

Show answer & explanation

Answer: At the start of the three-year period, Center X replaced its manual heavy-lifting operations with an automated conveyor system, significantly reducing physical exertion for its workers.

Answer

The argument is most seriously weakened by revealing that Center X implemented automated conveyor systems at the start of the study, introducing a major confounding variable that offers an alternative explanation for the drop in injury claims.
The correct answer weakens the argument by introducing a major confounding variable. If Center X introduced an automated conveyor system that eliminated heavy manual lifting around the same time as the workspace redesign, this automation provides an independent, highly plausible alternative cause for the 40 percent reduction in musculoskeletal injury claims. Consequently, management cannot attribute the improvement specifically to the ergonomic assembly stations and flooring.

Step-by-Step Solution

1
Deconstruct the argument core
Premise: Center X (ergonomic redesign) had 40% fewer exertion claims than Center Y (no redesign). Conclusion: Ergonomic redesign caused the reduction in exertion claims.
Identifying the author's leap from correlation/observed difference to direct causation is necessary to locate the logical vulnerability.
2
Identify the causal flaw
The argument assumes no other factor differentiated Center X from Center Y during the three-year monitoring period.
Causal conclusions based on comparative observations are vulnerable to third-variable confounders or alternative causes.
3
Evaluate the choices for a confounding variable
The statement regarding the implementation of automated conveyor systems at Center X introduces a concurrent operational change that directly reduces worker physical strain, rendering it impossible to attribute the outcome solely to ergonomic furniture.
An alternative cause that accounts for the observed effect shatters the author's exclusive causal attribution.

Key Concept

Causal Reasoning and Confounding Variables
Question 1355Question →

Many city planners argue that constructing additional highway lanes is the most effective way to reduce urban traffic congestion. However, recent urban planning studies demonstrate that expanding highway capacity consistently attracts more vehicles onto the road, a phenomenon known as induced demand. Consequently, expanding highway lanes fails to deliver lasting congestion relief. Cities seeking sustainable traffic management should therefore shift their capital investments toward high-capacity public transit infrastructure.

Which of the following best expresses the main conclusion of the argument?

Show answer & explanation

Answer: Cities aiming for sustainable traffic management ought to direct their capital investments toward high-capacity public transit.

Answer

Cities aiming for sustainable traffic management ought to direct their capital investments toward high-capacity public transit.
The author's primary goal is to advocate for a specific policy change: shifting traffic management investments toward high-capacity public transit. The final sentence uses the conclusion indicator 'therefore' to signal that this recommendation is the ultimate claim supported by the evidence regarding induced demand and the failure of highway expansion.

Step-by-Step Solution

1
Analyze the structural role of each sentence in the passage.
Sentence 1 provides background context/opposing view; Sentence 2 provides empirical evidence (premise); Sentence 3 draws an intermediate conclusion; Sentence 4 presents the author's main recommendation.
Identifying structural roles helps isolate the final claim from supporting evidence and background information.
2
Locate conclusion keywords and pivot markers.
The word 'therefore' in the final sentence signals the author's main logical destination.
Conclusion indicators explicitly mark the primary claim supported by preceding premises.
3
Match the identified main claim with the paraphrased option.
The option advocating a shift in capital investments toward public transit precisely matches the final sentence's recommendation.
The correct option must accurately restate the author's final claim without altering its scope or tone.

Key Concept

Identifying Main Conclusions and Final Claims
Question 1356Question →

Agricultural firms operating large commercial orchards recently replaced periodic manual inspections by agronomists with autonomous drone swarms equipped with hyperspectral cameras to detect fungal infections. Although the drone swarms identify fungal outbreaks several days earlier than human agronomists can, farms employing the drones ultimately suffered higher seasonal crop losses from fungal disease. This unexpected result is largely explained by the fact that manual agronomists routinely pruned infected branches immediately upon detection during their walkthroughs, whereas drone detection relies on scheduled follow-up spraying teams, so...

Which of the following most logically completes the passage above?

Show answer & explanation

Answer: the delay between drone detection and the arrival of spraying teams allowed fungal spores to spread to adjacent healthy trees before any corrective action took place.

Answer

The passage is logically completed by explaining that the delay between drone detection and the deployment of spraying teams allowed fungal spores to spread to adjacent healthy trees before any corrective action took place.
The correct option provides the missing causal link that bridges the premise gap: manual inspectors contained the disease instantly via immediate pruning, whereas the delay inherent in scheduling spraying teams after drone detection allowed fungal spores to spread to nearby healthy trees before treatment occurred. This directly explains why earlier detection by drones still resulted in higher overall crop loss.

Step-by-Step Solution

1
Analyze the core paradox presented in the stimulus premises.
Drones detect infection earlier than humans, yet drone-monitored farms suffer higher total crop losses.
Completing the passage requires resolving why earlier detection failed to yield better crop protection.
2
Examine the differentiating factor provided right before the blank.
Human inspectors performed immediate physical removal (pruning) upon detection, whereas drones trigger delayed follow-up treatments (spraying teams).
The sentence ending in 'so...' must connect this operational contrast to the negative outcome.
3
Synthesize the contrast to deduce the logical conclusion.
The lapse of time between automated drone detection and actual treatment allows the disease to spread further than it did under immediate manual pruning.
This provides a complete, self-contained causal explanation without introducing extraneous assumptions.

Key Concept

Completing the Passage Logically
Question 1357Question →

If xx is a real number, is x2<4x^2 < 4?

(1) ∣x−1∣<2|x - 1| < 2
(2) ∣x+1∣<3|x + 1| < 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.
Rephrasing the target question x2<4x^2 < 4 shows that we need to determine if −2<x<2-2 < x < 2. Statement (1) gives −1<x<3-1 < x < 3, which allows values outside (−2,2)(-2, 2) like x=2.5x = 2.5, so it is insufficient alone. Statement (2) gives −4<x<2-4 < x < 2, which allows values outside (−2,2)(-2, 2) like x=−3x = -3, so it is insufficient alone. Taking the intersection of both statements gives −1<x<2-1 < x < 2. Since every number in (−1,2)(-1, 2) satisfies −2<x<2-2 < x < 2, the combined statements definitively answer YES.

Step-by-Step Solution

1
Rephrase the target question
The target question asking whether x2<4x^2 < 4 is equivalent to asking whether −2<x<2-2 < x < 2.
Taking the square root of both sides of x2<4x^2 < 4 yields ∣x∣<2|x| < 2, which expands to −2<x<2-2 < x < 2.
2
Evaluate Statement (1) independently
Statement (1) states ∣x−1∣<2|x - 1| < 2, which expands to −2<x−1<2-2 < x - 1 < 2, or −1<x<3-1 < x < 3.
If x=0x = 0, then −1<0<3-1 < 0 < 3 is true and 02<40^2 < 4 (Yes). If x=2.5x = 2.5, then −1<2.5<3-1 < 2.5 < 3 is true, but 2.52=6.25≮42.5^2 = 6.25 \not< 4 (No). Because we get both Yes and No answers, Statement (1) alone is insufficient.
3
Evaluate Statement (2) independently
Statement (2) states ∣x+1∣<3|x + 1| < 3, which expands to −3<x+1<3-3 < x + 1 < 3, or −4<x<2-4 < x < 2.
If x=0x = 0, then −4<0<2-4 < 0 < 2 is true and 02<40^2 < 4 (Yes). If x=−3x = -3, then −4<−3<2-4 < -3 < 2 is true, but (−3)2=9≮4(-3)^2 = 9 \not< 4 (No). Because we get both Yes and No answers, Statement (2) alone is insufficient.
4
Evaluate Statements (1) and (2) together
Combining −1<x<3-1 < x < 3 and −4<x<2-4 < x < 2 requires xx to satisfy both inequalities simultaneously, yielding the intersection −1<x<2-1 < x < 2.
Every value of xx in the interval (−1,2)(-1, 2) lies strictly inside the required target interval (−2,2)(-2, 2). Thus, x2<4x^2 < 4 is definitively YES. Both statements together are sufficient.

Key Concept

Inequality range intersection and absolute value distance expansion in Data Sufficiency
Estimated Time:2m 0s
Question 1358Question →

In Region K, agricultural water permits are issued annually based on historical crop yield metrics. In 2024, farms growing low-yield staple crops received 40 percent lower base water allocations than farms cultivating high-yield cash crops. However, regional environmental regulations dictate that any farm reducing its overall synthetic fertilizer usage by at least 25 percent in a given year is automatically granted a 30 percent bonus to its base water allocation for the subsequent year. In 2024, every farm cultivating high-yield cash crops reduced its synthetic fertilizer usage by more than 30 percent.

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

Show answer & explanation

Answer: In 2025, every farm that cultivated high-yield cash crops in 2024 will qualify for a 30 percent bonus to its base water allocation.

Answer

In 2025, every farm that cultivated high-yield cash crops in 2024 will qualify for a 30 percent bonus to its base water allocation.
The passage explicitly defines a rule: any farm reducing synthetic fertilizer usage by at least 25 percent in one year receives a 30 percent bonus to its base water allocation the next year. Since every farm cultivating high-yield cash crops reduced fertilizer usage by more than 30 percent in 2024, every such farm met the condition and must qualify for the 30 percent allocation bonus in 2025.

Step-by-Step Solution

1
Identify the rule governing water allocation bonuses.
A farm qualifies for a 30% water allocation bonus in year N+1 if it reduces synthetic fertilizer usage by at least 25% in year N.
This sets up the conditional requirement for earning the bonus.
2
Apply the 2024 performance facts to the rule.
In 2024, every high-yield cash crop farm reduced fertilizer usage by more than 30%, which satisfies the 'at least 25%' threshold.
Because all high-yield cash crop farms met the necessary requirement, all of them must receive the specified bonus in 2025.
3
Evaluate option choices to find the statement that must be true without external assumptions.
The statement asserting that every high-yield cash crop farm from 2024 qualifies for the 30 percent bonus in 2025 is mathematically and logically sound.
It is a direct deduction requiring no outside information.

Key Concept

Combining conditional rules and factual premises to derive a logically necessary conclusion.
Estimated Time:1m 30s
Question 1359Question →

Consider the following passage:

A study of corporate executives found that every executive who completed an advanced management program recorded a minimum 15 percent increase in team productivity over the following year. Additionally, all executives in the study who received a performance bonus had completed the program.

Evaluate the following statement: Based strictly on the passage, the claim 'Completing the advanced management program guarantees that an executive will receive a performance bonus' is a valid logical inference.

Show answer & explanation

Answer: False

Answer

False. The claim represents an unwarranted speculation based on a conditional reversal, not a valid inference that must be true.
The claim is false because a valid inference in Critical Reasoning must strictly follow from the explicit facts given. The passage states that all bonus recipients completed the program, meaning program completion was a necessary requirement for getting a bonus. However, it does not state that completing the program automatically guarantees receiving a bonus. Inferring a guaranteed bonus reverses the conditional logic, making it an unwarranted speculation rather than a valid inference.

Step-by-Step Solution

1
Analyze the explicit facts provided in the passage premises.
Premise 1: Program Completion leads to Productivity Increase of 15% or more. Premise 2: Receiving a Performance Bonus requires Program Completion (Bonus implies Program Completion).
A valid inference must strictly follow from the established premises without requiring external assumptions.
2
Analyze the logic of the claim being evaluated.
The claim states that Program Completion guarantees a Performance Bonus (Program Completion implies Bonus).
To determine whether the statement is a valid inference, we must check if the claim is guaranteed by the premises.
3
Compare the claim's conditional direction with the passage premise.
The passage states that completing the program is necessary for a bonus, but does not state that it is sufficient to receive one. Reversing this relationship is a speculative error, not a valid deduction.
An unstated premise or reversed condition cannot be treated as a valid inference.

Key Concept

Distinguishing valid inferences (must be true) from unwarranted assumptions and conditional reversals
Question 1360Question →

Consider the following argument regarding urban economic policy:

"While some economists argue that capping rent prices in urban centers protects low-income residents from displacement, empirical data indicates that strict price controls invariably suppress private investment in residential construction. This suppression of capital over time restricts total housing supply, thereby driving up shadow prices in unregulated market sectors. Consequently, although rent control provides immediate relief to current tenants, its overall long-term effect is a net decline in housing accessibility for future residents. Therefore, municipal leaders seeking to broaden housing affordability should implement direct tenant income subsidies rather than statutory price caps."

Match each claim from the passage on the left to its exact structural role and relationship within the overall argument flow on the right.

Click a left item, then click its matching right item

Items

Strict price controls invariably suppress private investment in residential construction.
Rent control provides immediate relief to current tenants.
Its overall long-term effect is a net decline in housing accessibility for future residents.
Municipal leaders seeking to broaden housing affordability should implement direct tenant income subsidies rather than statutory price caps.

Matches

Show answer & explanation

Answer

Each claim matches its corresponding structural role: the investment suppression claim matches the foundational premise regarding supply restriction; the immediate relief claim matches the conceded counter-point; the long-term decline claim matches the intermediate conclusion; and the income subsidy recommendation matches the author's main conclusion.
The argument builds from empirical evidence (suppression of investment) to an intermediate logical consequence (restricted supply leading to long-term decline in accessibility), while explicitly acknowledging a short-term benefit as a concession, all of which culminate in supporting the main policy recommendation to favor income subsidies over price caps.

Step-by-Step Solution

1
Analyze the main argument structure and identify the final conclusion.
The final sentence beginning with 'Therefore' presents the author's overall recommendation (use income subsidies instead of price caps), establishing it as the main conclusion.
Identifying the main conclusion provides the reference point for evaluating all supporting claims.
2
Determine the role of premises and intermediate steps leading to the main conclusion.
The claim that strict price controls suppress private investment acts as an empirical premise. This leads to restricted supply and higher shadow prices, establishing an intermediate conclusion that the overall long-term effect is a net decline in housing accessibility.
Evaluating how premises build logically upon each other reveals the intermediate conclusion that bridges evidence to the main conclusion.
3
Evaluate transitional indicators and concessions.
The clause introduced by 'although' ('although rent control provides immediate relief to current tenants') acknowledges a localized benefit without undermining the overall argument, identifying it as a concession.
Recognizing concessive transitions clarifies how counter-evidence is integrated into the author's reasoning flow.

Key Concept

Evaluating Inter-Claim Relationships and Argument Flow
PreviousPage 68 / 110Next
All practice questions — GMAT | Examkin