Drawing Inferences and Valid Conclusions

8 questions

All types8 Multiple choice5 Multiple select3

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

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

Select all that apply

Terra Energy does not hold exclusive regional distribution rights in Nation X.

Solis Corp's acquisition of the stake in Terra Energy occurred after the 2022 regulatory amendment went into effect.

If Terra Energy holds exclusive regional distribution rights in Nation X, Solis Corp's acquisition must have occurred prior to the 2022 regulatory amendment.

Prior to 2022, state-backed entities acquiring more than a 15 percent stake in a domestic renewable energy producer in Nation X were exempt from mandatory federal antitrust review.

Prior to 2022, non-state-backed corporations acquiring a 12 percent stake in a domestic renewable energy producer in Nation X were required to undergo federal antitrust review.

Show answer & explanation

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

Answer

The correct statements are: 1) 'If Terra Energy holds exclusive regional distribution rights in Nation X, Solis Corp's acquisition must have occurred prior to the 2022 regulatory amendment' and 2) 'Prior to 2022, state-backed entities acquiring more than a 15 percent stake in a domestic renewable energy producer in Nation X were exempt from mandatory federal antitrust review.'

The conclusion regarding state-backed entities being exempt prior to 2022 follows directly from the exception clause ('unless the acquiring entity was a state-backed entity'). The conditional conclusion regarding exclusive regional distribution rights follows by contrapositive reasoning: post-2022 rules mandate reviews for any acquisition of a firm with exclusive distribution rights regardless of stake size; since Solis Corp's acquisition of a 12 percent stake was unreviewed, if Terra Energy possesses exclusive distribution rights, the transaction could not have occurred under the post-2022 rules and must have taken place prior to the amendment.

Step-by-Step Solution

Analyze the pre-2022 regulatory framework premises.

Before 2022, mandatory antitrust review applied ONLY IF (stake > 15%) AND (acquiring entity is NOT state-backed). State-backed entities were explicitly exempt.

Establishes the boundary conditions for acquisitions occurring prior to 2022.

Analyze the post-2022 regulatory framework premises.

After the 2022 amendment, mandatory review applies to ALL corporate acquisitions IF target holds exclusive regional distribution rights (regardless of state-backed status or stake percentage).

Establishes the strict conditional trigger for post-2022 transactions.

Apply formal logic (contrapositive) to the unreviewed acquisition of Terra Energy by Solis Corp.

Solis Corp (private) acquired 12% of Terra Energy (domestic renewable producer) with NO review. If Terra Energy has exclusive distribution rights, the transaction CANNOT be post-2022 (since post-2022 requires review for any stake if exclusive rights exist). Thus, if exclusive rights exist, the transaction MUST be pre-2022.

Synthesizes the specific factual scenario with the conditional rules to deduce valid conclusions.

Key Concept

Drawing Valid Conditional Inferences and Contrapositive Deduction

Question 2Question →

During a three-year conservation project in Park Z, field researchers tracked native animal populations. The researchers found that whenever the population of wild rabbits decreased below 1,000 individuals, the population of red foxes consistently declined in the following year. Conversely, in years when the rabbit population was at or above 1,000, the red fox population never declined in the following year. Throughout both the second and third years of the project, the red fox population in Park Z experienced a decline. If the statements above are true, which of the following must also be true?

The population of wild rabbits in Park Z was below 1,000 individuals in both the first and second years of the project.

The red fox population in Park Z declined primarily due to a lack of alternative prey species.

In the third year of the project, the population of wild rabbits in Park Z reached zero.

The population of wild rabbits in Park Z remained at or above 1,000 individuals during the first year of the project.

Red foxes in Park Z rely exclusively on wild rabbits as their sole source of food.

Show answer & explanation

Answer: The population of wild rabbits in Park Z was below 1,000 individuals in both the first and second years of the project.

Answer

The population of wild rabbits in Park Z was below 1,000 individuals in both the first and second years of the project.

The passage establishes that a red fox decline in a given year occurs if and only if the rabbit population was below 1,000 in the preceding year. Since the red fox population declined in both the second and third years of the project, the rabbit population must have been below 1,000 in both the first and second years.

Step-by-Step Solution

Analyze the conditional rules given in the passage.

Rabbit population < 1,000 in Year N leads to Red Fox decline in Year N+1. Rabbit population >= 1,000 in Year N prevents Red Fox decline in Year N+1.

This establishes a necessary and sufficient conditional link between the rabbit count in one year and the fox population trend in the following year.

Apply the observed outcomes for Years 2 and 3.

Red fox population declined in Year 2 (requiring Rabbit < 1,000 in Year 1) and declined in Year 3 (requiring Rabbit < 1,000 in Year 2).

By applying the contrapositive logic, any year experiencing a fox decline must have been preceded by a year with fewer than 1,000 rabbits.

Synthesize the valid logical deduction.

The rabbit population must have been below 1,000 during both Year 1 and Year 2.

This is the only conclusion that strictly must be true based solely on the provided premises.

Key Concept

Conditional Logic Deductions

Question 3Question →

In the mid-twentieth century, manufacturing plants employing automated assembly lines recorded higher worker productivity per hour and lower unit production costs than plants using manual assembly methods. Nevertheless, among plants that operated profitably and sold 100 percent of their output, total operating profits were consistently higher at manual plants producing custom, low-volume goods than at automated plants producing standardized, high-volume goods.

If the statements above are true, which of the following must also be true regarding the manufacturing plants during the specified period?

The average selling price per unit of custom goods produced at manual plants was higher than the average selling price per unit of standardized goods produced at automated plants.

Manual plants generated higher total annual revenues than automated plants did.

Worker wages at automated plants were higher than worker wages at manual plants due to increased productivity per hour.

Automated assembly lines were less cost-effective overall than manual assembly methods for all types of manufactured goods.

If a manual plant producing custom goods adopted automated assembly lines without altering its product line, its total operating profits would decrease.

Show answer & explanation

Answer: The average selling price per unit of custom goods produced at manual plants was higher than the average selling price per unit of standardized goods produced at automated plants.

Answer

The average selling price per unit of custom goods produced at manual plants was higher than the average selling price per unit of standardized goods produced at automated plants.

The correct answer must be true based on the algebraic relationship between total profit, production volume, unit costs, and unit selling prices. Given that manual plants produced a lower volume of goods (

Q_M < Q_A

) with higher unit production costs (

C_M > C_A

) yet earned higher total operating profit (

Q_M \cdot Margin_M > Q_A \cdot Margin_A

), the profit margin per unit for custom goods (

Price_M - C_M

) had to be greater than that for standardized goods (

Price_A - C_A

). Combining

Price_M - C_M > Price_A - C_A

with

C_M > C_A

logically forces

Price_M > Price_A

Step-by-Step Solution

Analyze the mathematical relationship for total profit.

Total Profit = Quantity Sold × (Unit Selling Price - Unit Cost).

Establishing the core profit formula allows us to compare manual plants producing custom goods (

M

) and automated plants producing standardized goods (

A

Identify the given comparative premises.

1) Unit Cost for manual plants is greater than Unit Cost for automated plants (

C_M > C_A

). 2) Quantity sold for manual plants is lower than for automated plants (

Q_M < Q_A

). 3) Total Profit for manual plants is greater than for automated plants (

Profit_M > Profit_A > 0

Extracting the quantitative constraints provided in the passage sets up the logical inequality.

Evaluate the profit per unit constraint.

Since

Q_M \cdot (Price_M - C_M) > Q_A \cdot (Price_A - C_A)

and

0 < Q_M < Q_A

, it must hold that

(Price_M - C_M) > (Price_A - C_A)

For a smaller quantity of goods to yield a larger total profit than a larger quantity of goods, the profit margin per unit for the smaller-quantity goods must be strictly greater.

Deduce the relationship between selling prices.

Since

(Price_M - C_M) > (Price_A - C_A)

and

C_M > C_A

, adding

C_M

to both sides gives

Price_M > Price_A + (C_M - C_A) > Price_A

. Thus,

Price_M > Price_A

Because manual unit costs were higher, the unit selling price of custom goods produced at manual plants had to be higher than that of standardized goods to yield both a higher unit margin and higher overall profit.

Key Concept

Quantitative and Logical Deductions from Mathematical Constraints

Estimated Time:2m 0s

Question 4Question →

Prior to 2022, technology firm X generated over 80 percent of its annual revenue from software licensing, with the remainder derived from consulting services. In 2022, Firm X introduced a cloud platform, offering it exclusively via usage-based subscriptions. By 2025, Firm X's total annual revenue was twice that of its 2021 revenue. However, its 2025 software licensing revenue had dropped by exactly 50 percent relative to 2021, while its consulting revenue remained unchanged. All 2025 cloud platform subscription revenues were generated from clients who had never previously purchased software licenses or consulting services from Firm X.

If the statements above are true, which of the following must also be true about Firm X in 2025?

The average subscription fee paid per client for the cloud platform in 2025 was higher than the average fee paid per client for software licensing in 2021.

In 2025, revenue from consulting services represented a larger percentage of Firm X's total annual revenue than it did in 2021.

Clients who had never purchased products or services from Firm X prior to 2022 accounted for more than half of the firm's total annual revenue in 2025.

At least some clients who purchased software licenses from Firm X in 2021 canceled their licenses to switch to competitor software by 2025.

Every client who purchased consulting services from Firm X in 2025 had also purchased software licenses from Firm X in 2021.

Show answer & explanation

Answer: Clients who had never purchased products or services from Firm X prior to 2022 accounted for more than half of the firm's total annual revenue in 2025.

Answer

In 2025, clients who had never purchased products or services from Firm X prior to 2022 accounted for more than half of the firm's total annual revenue.

The correct choice must strictly follow from combining the mathematical premises. In 2021, licensing was over 80% of revenue and consulting was under 20%. In 2025, total revenue doubled (

2R

). Licensing revenue fell to half its 2021 level (under 40% of

R

, or under 20% of

2R

), while consulting revenue remained unchanged (under 20% of

R

, or under 10% of

2R

). Thus, all non-cloud revenue combined accounted for under 30% of 2025 total revenue (

2R

). Since all cloud platform revenue came from new clients who had never purchased from Firm X prior to 2022, these new clients generated over 70% of 2025 total revenue, which is strictly greater than half.

Step-by-Step Solution

Express the 2021 revenue breakdown algebraically.

Let

R

be the total revenue in 2021. Software licensing revenue

L_{2021} > 0.80R

and consulting revenue

C_{2021} < 0.20R

, with

L_{2021} + C_{2021} = R

Establishing 2021 baseline figures allows precise comparison with 2025 figures.

Calculate the maximum revenue generated in 2025 from clients who purchased products prior to 2022.

In 2025, total revenue is

2R

. Licensing revenue

L_{2025} = 0.50 \times L_{2021} < 0.40R

. Consulting revenue

C_{2025} = C_{2021} < 0.20R

. Total revenue from returning client streams is

L_{2025} + C_{2025} < 0.40R + 0.20R = 0.60R

Since cloud subscription clients are strictly new clients, returning client revenue consists solely of licensing and consulting.

Calculate the minimum contribution of new cloud platform clients to 2025 total revenue.

Cloud platform subscription revenue

P_{2025} = 2R - (L_{2025} + C_{2025}) > 2R - 0.60R = 1.40R

. As a fraction of 2025 total revenue (

2R

), cloud revenue is

\frac{P_{2025}}{2R} > \frac{1.40R}{2R} = 70\%

Comparing new client revenue to the 2025 total (

2R

) proves that new clients accounted for over 70% of total revenue, which is strictly greater than 50%.

Key Concept

Quantitative and Proportional Deductions in Logical Arguments

Question 5Question →

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

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.

Any coral reef off Peninsula Y that hosts deep-sea shrimp populations must also contain bioluminescent coral species.

Reefs located above a depth of 500 meters contain a larger total population of deep-sea shrimp than reefs located below 500 meters.

Water temperature variations between depth zones explain why deep-sea shrimp inhabit certain reefs located above 500 meters.

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

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.

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.

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 6Question →

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?

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

In 2024, farms cultivating high-yield cash crops consumed less total water than farms growing low-yield staple crops.

Any farm in Region K that reduced its synthetic fertilizer usage by more than 30 percent in 2024 cultivated high-yield cash crops.

In 2025, farms growing low-yield staple crops will receive lower total water allocations than farms cultivating high-yield cash crops.

Reducing synthetic fertilizer usage is the most effective method for farms in Region K to increase their overall crop yields.

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

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.

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.

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 7Question →

Between 2018 and 2024, all commercial solar farms in Country X that integrated lithium-iron-phosphate (LFP) battery storage systems achieved continuous grid synchronization during peak demand hours. Conversely, no solar farm relying exclusively on nickel-manganese-cobalt (NMC) storage maintained uninterrupted grid connectivity throughout those same peak periods. During this six-year period, any solar farm in Country X that failed to maintain continuous grid synchronization during peak demand hours was assessed a regulatory surcharge. Furthermore, every commercial solar farm built in Country X after 2020 integrated either LFP or NMC storage systems, but never both.

Based on the information provided, which of the following statements must be logically true? Select all that apply.

Select all that apply

Every commercial solar farm in Country X relying exclusively on NMC battery storage between 2018 and 2024 was assessed a regulatory surcharge.

Commercial solar farms using NMC battery storage generated less total electricity than those using LFP battery storage.

Any commercial solar farm built in Country X in 2022 that integrated LFP storage achieved continuous grid synchronization during peak demand hours.

Integrating LFP battery storage was the sole method available for solar farms in Country X to avoid regulatory surcharges.

Any solar farm in Country X assessed a regulatory surcharge between 2018 and 2024 must have utilized an NMC battery storage system.

Show answer & explanation

Answer: Every commercial solar farm in Country X relying exclusively on NMC battery storage between 2018 and 2024 was assessed a regulatory surcharge.; Any commercial solar farm built in Country X in 2022 that integrated LFP storage achieved continuous grid synchronization during peak demand hours.

Answer

The correct statements are that every commercial solar farm relying exclusively on NMC battery storage between 2018 and 2024 was assessed a regulatory surcharge, and that any commercial solar farm built in 2022 that integrated LFP storage achieved continuous grid synchronization during peak demand hours.

The statement regarding exclusive NMC storage farms being assessed a regulatory surcharge directly synthesizes two explicit passage facts: exclusive NMC farms failed to maintain continuous connectivity during peak hours, and failing continuous connectivity resulted in a regulatory surcharge. The statement regarding 2022 LFP-integrated farms directly applies the universal premise about LFP farms operating between 2018 and 2024.

Step-by-Step Solution

Analyze the premise regarding NMC storage and regulatory surcharges.

No exclusive NMC farm maintained uninterrupted grid connectivity, and failing uninterrupted connectivity triggered a surcharge. Synthesizing these two premises proves that all exclusive NMC farms incurred surcharges.

Direct deduction from linked conditional premises.

Analyze the premise regarding LFP storage for farms built in 2022.

The year 2022 is within 2018–2024. All LFP farms in this period achieved continuous grid synchronization during peak demand hours.

Direct application of a general premise to a specific year within the defined timeframe.

Evaluate the incorrect choices for logical leaps or scope errors.

Statements introducing unmentioned metrics (total electricity generation), necessary/sufficient confusions (sole method), or formal conditional reversals are invalid inferences.

Valid inferences on the GMAT must be strictly supported without external assumptions or formal fallacies.

Key Concept

Drawing Valid Inferences via Premise Synthesis

Question 8Question →

From 2015 to 2023, all municipal transit authorities in Region M derived their annual operational funding exclusively from passenger fares and regional tax subsidies. In 2019, a regional ordinance mandated that any transit authority receiving more than 40 percent of its operational funding from passenger fares must provide discounted passes to senior citizens. Furthermore, under the ordinance, no transit authority could receive regional tax subsidies if passenger fares accounted for more than 50 percent of its operational funding.

If the statements above are true, which of the following must also be true about municipal transit authorities in Region M after the 2019 ordinance took effect?

Municipal transit authorities that provided discounted passes to senior citizens experienced a net decrease in total operational funding after 2019.

Any municipal transit authority that provided discounted passes to senior citizens derived at least 40 percent of its operational funding from passenger fares.

Any municipal transit authority whose passenger fares accounted for more than 50 percent of its operational funding was required to provide discounted passes to senior citizens.

Most municipal transit authorities in Region M altered their fare structures after 2019 in order to remain eligible for regional tax subsidies.

A municipal transit authority that received regional tax subsidies was prohibited from offering discounted passes to senior citizens.

Show answer & explanation

Answer: Any municipal transit authority whose passenger fares accounted for more than 50 percent of its operational funding was required to provide discounted passes to senior citizens.

Answer

Any municipal transit authority whose passenger fares accounted for more than 50 percent of its operational funding was required to provide discounted passes to senior citizens.

The correct response logically follows by synthesizing the rules given in the stem. If passenger fares exceeded 50 percent of operational funding, the authority could receive no regional tax subsidies. Because operational funding came exclusively from fares and subsidies, an authority receiving no subsidies derived 100 percent of its funding from fares. Because 100 percent is greater than 40 percent, the authority was required under the 2019 ordinance to provide discounted passes to senior citizens.

Step-by-Step Solution

Identify the strict constraints provided in the premises.

Constraint 1: Total Funding = Passenger Fares + Tax Subsidies (exclusively).
Constraint 2: If Fares > 40%, Senior Discounts are mandatory.
Constraint 3: If Fares > 50%, Tax Subsidies = 0.

Establishing the exact formal logic parameters allows synthesizing multi-sentence premises.

Analyze the condition where Fares > 50%.

By Constraint 3, Tax Subsidies must equal 0%. Combined with Constraint 1, Fares must account for 100% of total operational funding.

Synthesizing the exclusive funding sources with the subsidy restriction reveals the precise percentage of funding coming from fares.

Apply Constraint 2 to the calculated result.

Since 100% is greater than 40%, the condition for mandatory senior discounts is satisfied.

Deducing that Fares = 100% guarantees that the > 40% threshold is met, making the requirement inescapable.

Key Concept

Drawing Deductive Inferences from Synthesized Constraints

Estimated Time:2m 0s

Drawing Inferences and Valid Conclusions

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Common Mistakes