Tüm alıştırma soruları

Soru 1561Soru →

If $n$ is a positive integer, is $n$ divisible by 18?

(1) $n^2$ is divisible by 54.
(2) $n^3$ is divisible by 108.

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

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

Cevap

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

Statement (1) establishes that

n^2

is divisible by

54 = 2^1 \times 3^3

. Because the exponent of 3 in

n^2

is

2b

, the condition

2b \geq 3

implies

b \geq 1.5

, which forces

b \geq 2

since

b

must be an integer. Similarly,

2a \geq 1 \implies a \geq 1

. Therefore,

n

must contain at least

2^1 \times 3^2 = 18

as a factor, guaranteeing that

n

is divisible by 18 (Definitive Yes). Statement (2) establishes that

n^3

is divisible by

108 = 2^2 \times 3^3

, which only forces

a \geq 1

and

b \geq 1

, so

n

must only be a multiple of 6. Since

n = 6

yields a 'No' and

n = 18

yields a 'Yes', Statement (2) is insufficient.

Adım Adım Çözüm

1

Rephrase the question target in terms of prime factorization

For a positive integer

n

to be divisible by

18 = 2^1 \times 3^2

, the prime factorization of

n

must contain at least one factor of 2 and at least two factors of 3.

Decomposing the target integer into prime factors establishes clear minimum exponent thresholds for evaluation.

2

Evaluate Statement (1):

n^2

is divisible by

54 = 2^1 \times 3^3

If

n = 2^a \times 3^b \times k

, then

n^2 = 2^{2a} \times 3^{2b} \times k^2

. Divisibility by

2^1 \times 3^3

requires

2a \geq 1 \implies a \geq 1

and

2b \geq 3 \implies b \geq 2

(since

a

and

b

are integers). Thus

n

must contain at least

2^1 \times 3^2 = 18

, giving a definitive YES.

Integer constraints on exponents force fractional lower bounds to round up to the next integer.

3

Evaluate Statement (2):

n^3

is divisible by

108 = 2^2 \times 3^3

If

n^3 = 2^{3a} \times 3^{3b} \times k^3

, then

3a \geq 2 \implies a \geq 1

and

3b \geq 3 \implies b \geq 1

. Thus

n

must be divisible by

2^1 \times 3^1 = 6

. Testing values: if

n = 6

,

6^3 = 216

(divisible by 108), but 6 is NOT divisible by 18 (NO). If

n = 18

,

18^3 = 5832

(divisible by 108), and 18 IS divisible by 18 (YES). Statement (2) is INSUFFICIENT.

Testing specific values demonstrates that Statement (2) allows both 'Yes' and 'No' outcomes.

Anahtar Kavram

Prime Factor Exponent Analysis under Integer Constraints in Data Sufficiency

Tahmini Süre:2m 0s

Soru 1562Soru →

If $x$ and $y$ are non-zero real numbers, is $\frac{x}{y} > 1$ ?

(1) $x^2 y > x y^2$
(2) $\frac{x - y}{x} > 0$

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

Cevap: Statements (1) and (2) TOGETHER are NOT sufficient.

Cevap

Statements (1) and (2) TOGETHER are NOT sufficient to determine whether

\frac{x}{y} > 1

.

The choice stating that statements (1) and (2) together are not sufficient is correct because combining both statements permits two valid cases: case 1 (

x=3, y=2

) yields a 'Yes' answer to the stem, while case 2 (

x=-1, y=2

) satisfies both statements but yields a 'No' answer to the stem.

Adım Adım Çözüm

1

Rephrase the target question

The condition

\frac{x}{y} > 1

is equivalent to

\frac{x - y}{y} > 0

, meaning

x - y

and

y

must have the same sign.

Simplifying the question target allows direct testing of signs.

2

Evaluate Statement (1) independently

Statement (1) states

x^2 y > x y^2 \iff x y (x - y) > 0

. If

x = 3, y = 2

, then

xy(x-y) = 6 > 0

and

\frac{x}{y} = 1.5 > 1

(Yes). If

x = -2, y = -3

, then

xy(x-y) = 6 > 0

and

\frac{x}{y} = \frac{2}{3} < 1

(No). Insufficient.

Testing positive and negative pairs shows Statement (1) alone yields both Yes and No.

3

Evaluate Statement (2) independently without carrying over Statement (1) information

Statement (2) states

\frac{x - y}{x} > 0

, meaning

x

and

x - y

have the same sign. If

x = 3, y = 2

,

\frac{1}{3} > 0

and

\frac{x}{y} = 1.5 > 1

(Yes). If

x = 2, y = -3

,

\frac{5}{2} > 0

and

\frac{x}{y} = -\frac{2}{3} < 1

(No). Insufficient.

Statement (2) evaluated strictly in isolation also yields both Yes and No.

4

Evaluate Statements (1) and (2) combined

From Statement (1),

xy(x-y) > 0

. From Statement (2),

\frac{x-y}{x} > 0 \implies x(x-y) > 0

. Combining these implies

y > 0

. Since

y > 0

, if

x > 0

, then

x - y > 0 \implies x > y > 0 \implies \frac{x}{y} > 1

(Yes). However, if

x < 0

, since

y > 0

,

x - y < 0

, satisfying

x(x-y) > 0

and

xy(x-y) > 0

. For example,

x = -1, y = 2

satisfies both statements but gives

\frac{x}{y} = -0.5 < 1

(No). Insufficient.

Even combined, two distinct cases exist (

x > y > 0

giving Yes, and

x < 0 < y

giving No).

Anahtar Kavram

Statement Independence Evaluation and Statement Combination with Real Number Sign Traps

Soru 1563Soru →

To bolster its regional commercial shipping sector, the port authority of City X recently instituted a substantial reduction in dockage fees for all international cargo vessels. Over the subsequent six months, the total volume of freight passing through the city's port increased by 25 percent. Based on this outcome, the port authority's director concluded that reducing dockage fees is a reliable strategy for any municipal port seeking to expand its international shipping volume.

The director's argument is most vulnerable to criticism on the grounds that it...

infers a general causal principle for all municipal ports based on evidence from a single case that may not be representative

mistakes an effect for a cause by assuming that the increase in shipping volume led to the reduction in dockage fees

confuses a condition that is necessary for increasing shipping volume with a condition that is sufficient to guarantee it

draws an invalid structural analogy between international cargo shipping and domestic commercial transport

concludes that lowering dockage fees reduces total municipal revenues despite data demonstrating the opposite effect

Cevabı ve açıklamayı göster

Cevap: infers a general causal principle for all municipal ports based on evidence from a single case that may not be representative

Cevap

The argument is most vulnerable to criticism because it infers a general causal principle for all municipal ports based on evidence from a single case that may not be representative.

The correct answer accurately describes an unrepresentative sample flaw (hasty generalization). The director observes a positive outcome following a policy change in a single municipality over a brief six-month window and uses that limited evidence to endorse the policy as a universally reliable strategy for all municipal ports worldwide.

Adım Adım Çözüm

1

Analyze the Premise and Conclusion structure of the argument.

Premise: City X reduced dockage fees, and freight volume at City X's port increased by 25 percent over six months. Conclusion: Reducing dockage fees is a reliable strategy for ANY municipal port seeking to expand international shipping volume.

Identifying the gap between a specific premise (one port's six-month outcome) and a broad conclusion (all municipal ports) isolates the central reasoning vulnerability.

2

Evaluate the logical leap from a single case study to a universal rule.

The director assumes that what occurred in City X over a short period will hold true across all municipal ports, ignoring unique local economic conditions, geographic advantages, or concurrent macro-environmental factors.

Generalizing from an unrepresentative or single sample represents a classic inductive fallacy in Critical Reasoning.

3

Select the choice that accurately articulates this inductive sampling flaw.

The statement highlighting that a general principle is inferred from a single, potentially unrepresentative instance precisely matches the identified logical flaw.

Abstract descriptions of unrepresentative sample flaws are standard correct answers for GMAT argument evaluation items.

Anahtar Kavram

Identifying Hasty Generalization and Unrepresentative Sample Flaws

Tahmini Süre:2m 0s

Soru 1564Soru →

If $m$ and $n$ are positive real numbers, is $m + n$ an integer?

(1) $m^2 - n^2$ is a prime number.
(2) $m - n$ is a positive integer.

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

Cevap: Statements (1) and (2) TOGETHER are NOT sufficient.

Cevap

Statements (1) and (2) together are NOT sufficient.

The correct answer is that both statements combined are insufficient. A common high-level trap in GMAT Data Sufficiency is assuming variables must be integers when the stem specifies 'real numbers'. Combining

(m - n)(m + n) = p

(prime) with

m - n = k

(positive integer) gives

m + n = \frac{p}{k}

. If

m = 2.25

and

n = 0.25

, we get

m - n = 2

(integer) and

m^2 - n^2 = 5

(prime), but

m + n = 2.5

(not an integer). Conversely,

m = 2

and

n = 1

gives

m - n = 1

and

m^2 - n^2 = 3

(prime), where

m + n = 3

(an integer). Because both an affirmative and a negative answer are possible, the information remains insufficient.

Adım Adım Çözüm

1

Evaluate Statement (1) independently.

Statement (1) is NOT sufficient.

If

m^2 - n^2 = 2

(a prime number), we could have

m = 2

and

n = √2

, giving

m + n = 2 + √2

(not an integer). Alternatively,

m = 2

and

n = 1

gives

m^2 - n^2 = 3

(prime) and

m + n = 3

(an integer). Hence, Statement (1) alone is insufficient.

2

Evaluate Statement (2) independently.

Statement (2) is NOT sufficient.

If

m - n = 2

, we could have

m = 3.5

and

n = 1.5

, giving

m + n = 5

(an integer). Or we could have

m = 3.2

and

n = 1.2

, giving

m + n = 4.4

(not an integer). Hence, Statement (2) alone is insufficient.

3

Evaluate Statements (1) and (2) combined.

Test for consistency with both integer and non-integer outcomes for

m + n

.

We know

m^2 - n^2 = (m - n)(m + n) = p

, where

p

is prime and

m - n = k

is a positive integer. Thus

k(m + n) = p

, so

m + n = \frac{p}{k}

.

4

Construct concrete counterexamples under both combined statements.

Statements (1) and (2) together are NOT sufficient.

Case 1 (YES): Let

m = 2

and

n = 1

. Then

m^2 - n^2 = 3

(prime) and

m - n = 1

(positive integer). Here,

m + n = 3

, which IS an integer.
Case 2 (NO): Let

m = 2.25

and

n = 0.25

. Both are positive real numbers.

m - n = 2.25 - 0.25 = 2

(positive integer).

m^2 - n^2 = (2.25 - 0.25)(2.25 + 0.25) = 2 \times 2.5 = 5

(prime number). But

m + n = 2.25 + 0.25 = 2.5

, which is NOT an integer. Since

m + n

can be an integer or a non-integer, both statements together are not sufficient.

Anahtar Kavram

Implicit Integer Constraints vs. Real Number Definitions in Data Sufficiency

Soru 1565Soru →

The table below presents financial and operational metrics for seven portfolio companies evaluated by a venture capital firm:

Company	Sector	Revenue Growth (%)	Profitable	Employee Retention Rate (%)
Alpha Corp	Tech	35	Yes	88
Beta Health	Biotech	45	No	92
Gamma Power	CleanEnergy	28	Yes	85
Delta Pay	FinTech	50	No	78
Epsilon Bio	Biotech	40	Yes	94
Zeta Systems	Tech	60	No	82
Eta Dynamics	CleanEnergy	52	Yes	90

An investment committee will shortlist companies that satisfy at least two of the following three conditions:
1. Revenue Growth greater than $40\%$
2. Profitable (Status = Yes)
3. Employee Retention Rate of at least $90\%$

Which of the following companies meet the investment committee's criteria for shortlisting?

Geçerli olan tümünü seçin

Beta Health

Delta Pay

Epsilon Bio

Zeta Systems

Eta Dynamics

Cevabı ve açıklamayı göster

Cevap: Beta Health; Epsilon Bio; Eta Dynamics

Cevap

The companies that qualify for shortlisting are Beta Health, Epsilon Bio, and Eta Dynamics.

The correct selections are Beta Health, Epsilon Bio, and Eta Dynamics because each satisfies at least two of the three stated conditions. Beta Health achieves Revenue Growth above 40% (45%) and Retention at or above 90% (92%). Epsilon Bio is Profitable and achieves Retention of at least 90% (94%). Eta Dynamics satisfies all three requirements.

Adım Adım Çözüm

1

Define the three evaluation criteria explicitly

Criterion 1: Revenue Growth

> 40\%

; Criterion 2: Profitable = Yes; Criterion 3: Employee Retention Rate

\geq 90\%

.

Clear definitions prevent boundary errors when filtering multi-column data.

2

Evaluate each company against all three criteria

Alpha Corp: C1 (No, 35%), C2 (Yes), C3 (No, 88%) -> Total: 1 criterion.
Beta Health: C1 (Yes, 45%), C2 (No), C3 (Yes, 92%) -> Total: 2 criteria.
Gamma Power: C1 (No, 28%), C2 (Yes), C3 (No, 85%) -> Total: 1 criterion.
Delta Pay: C1 (Yes, 50%), C2 (No), C3 (No, 78%) -> Total: 1 criterion.
Epsilon Bio: C1 (No, 40% is not > 40%), C2 (Yes), C3 (Yes, 94%) -> Total: 2 criteria.
Zeta Systems: C1 (Yes, 60%), C2 (No), C3 (No, 82%) -> Total: 1 criterion.
Eta Dynamics: C1 (Yes, 52%), C2 (Yes), C3 (Yes, 90%) -> Total: 3 criteria.

Systematic evaluation ensures no row or condition is miscounted.

3

Identify all companies meeting at least two conditions

Beta Health (2 criteria), Epsilon Bio (2 criteria), and Eta Dynamics (3 criteria) qualify.

Filtering for total criteria count

\geq 2

yields the correct subset.

Anahtar Kavram

Multi-condition compound filtering requires evaluating individual logical constraints across multiple columns and aggregating total satisfied criteria per row.

Soru 1566Soru →

To protect vulnerable alpine wildflowers from being trampled by foot traffic, park authorities plan to replace the ground-level soil path through a popular mountain meadow with an elevated wooden boardwalk. They reason that elevating the walking surface will prevent hikers from stepping on the surrounding vegetation, thereby allowing damaged plant populations to recover.

Which of the following, if true, most seriously weakens the argument above?

The broad wooden planks of the elevated boardwalk cast dense shade and redirect rainwater, suppressing the growth of delicate alpine plant species directly adjacent to the pathway.

Preliminary trials in a neighboring park demonstrated that elevated boardwalks successfully reduced soil erosion by over eighty percent.

A majority of park visitors surveyed indicated a strong preference for guided nature tours rather than unguided trail walks.

Other mountain meadows in distant alpine regions have experienced plant recovery following severe droughts without any trail modifications.

The high costs associated with transporting wooden planks to high altitudes will require the park authority to reallocate funds from seasonal ranger payrolls.

Cevabı ve açıklamayı göster

Cevap: The broad wooden planks of the elevated boardwalk cast dense shade and redirect rainwater, suppressing the growth of delicate alpine plant species directly adjacent to the pathway.

Cevap

The argument is most weakened by the finding that the broad wooden planks of the elevated boardwalk cast dense shade and redirect rainwater, suppressing the growth of delicate alpine plant species directly adjacent to the pathway.

The correct answer identifies an unforeseen side effect of the proposed plan. If the boardwalk blocks sunlight and redirects rainwater away from the adjacent soil, the plants will suffer from lack of vital nutrients regardless of whether foot traffic is removed. This directly undermines the argument's conclusion that the boardwalk will allow plant populations to recover.

Adım Adım Çözüm

1

Identify the conclusion and premises of the argument.

Premise: Replacing soil paths with elevated boardwalks keeps hikers' feet off the ground. Conclusion: This change will allow damaged alpine wildflower populations to recover.

Understanding the logic underlying the plan is necessary to locate unstated assumptions.

2

Identify the central assumption underlying the plan.

The author assumes that elevating the path will not create any alternative conditions that hinder or destroy the wildflower population.

Weakening a plan-to-goal argument typically requires identifying an unintended side effect or bottleneck that prevents goal achievement.

3

Evaluate the choices to find new information that invalidates the assumption.

Showing that the physical structure of the boardwalk blocks essential sunlight and rainfall demonstrates that the plan itself will harm the plants, preventing their recovery.

This directly counteracts the central claim that the boardwalk will enable vegetation recovery.

Anahtar Kavram

Weakening a Plan-to-Goal Argument via Unintended Side Effects

Soru 1567Soru →

### Tab 1: Innovation Grant Policy
The Green Tech Foundation awards annual research grants to clean-energy startups. To qualify for a grant, a startup must allocate at least $40\%$ of its annual operating budget to solar or wind energy research.

*Exception:* Startups headquartered in designated rural zones qualify for grant funding regardless of their research focus area, provided their total annual operating budget does not exceed $\$150,000$ .

### Tab 2: Applicant Profiles
- Helios Inc.: Headquartered in an urban zone; total annual operating budget of $\$200,000$ , with $\$90,000$ allocated to solar energy research.
- AeroWind Ltd.: Headquartered in a rural zone; total annual operating budget of $\$180,000$ , with $\$30,000$ allocated to wind energy research.
- BioTerra Co.: Headquartered in a rural zone; total annual operating budget of $\$120,000$ , with $\$20,000$ allocated to biomass energy research.

### Tab 3: Funding Allocation Rules
Approved applicants receive grant funding equal to $50\%$ of their total annual operating budget, up to a maximum cap of $\$100,000$ per startup.

Based on the information provided across the three tabs, which of the following choices correctly evaluates the truth value (True or False) of each statement below?

1. Helios Inc. qualifies for the innovation grant under the standard policy rules.
2. AeroWind Ltd. qualifies for the innovation grant under the rural zone policy exception.
3. If approved, BioTerra Co. will receive exactly $\$60,000$ in grant funding.

Statement 1: True; Statement 2: False; Statement 3: True

Statement 1: True; Statement 2: True; Statement 3: True

Statement 1: False; Statement 2: False; Statement 3: True

Statement 1: True; Statement 2: False; Statement 3: False

Statement 1: False; Statement 2: True; Statement 3: False

Cevabı ve açıklamayı göster

Cevap: Statement 1: True; Statement 2: False; Statement 3: True

Cevap

Statement 1 is True; Statement 2 is False; Statement 3 is True.

The correct combination is Statement 1: True, Statement 2: False, Statement 3: True. Helios Inc. satisfies standard rules with 45% spent on solar research. AeroWind Ltd. fails rural exception criteria because its

180,000 budget exceeds the

150,000 maximum limit. BioTerra Co. qualifies via the rural exception and receives 50% of

120,000, totaling

60,000.

Adım Adım Çözüm

1

Evaluate Statement 1: Helios Inc. qualification under Tab 1 standard rules.

Helios Inc. allocates

\frac{\$90,000}{\$200,000} = 45\%

of its budget to solar energy research, which exceeds the required

40\%

threshold. Therefore, Statement 1 is True.

Standard policy requires at least 40% allocation to solar or wind research.

2

Evaluate Statement 2: AeroWind Ltd. qualification under Tab 1 rural exception.

AeroWind Ltd. is in a rural zone, but its operating budget of

\$180,000

exceeds the maximum allowed budget limit of

\$150,000

for the rural exception. Furthermore, its wind research allocation is only

\frac{\$30,000}{\$180,000} \approx 16.7\%

, failing standard rules. Thus, Statement 2 is False.

The rural zone exception applies only if the total annual budget does not exceed $150,000.

3

Evaluate Statement 3: BioTerra Co. grant funding calculation using Tabs 1, 2, and 3.

BioTerra Co. is in a rural zone with a

\$120,000

budget (

\le \$150,000

), so it qualifies under the rural exception. According to Tab 3, funding is

50\%

of total budget:

0.50 \times \$120,000 = \$60,000

, which is below the

\$100,000

cap. Therefore, Statement 3 is True.

Qualifying startups receive 50% of their operating budget capped at $100,000.

Anahtar Kavram

Multi-Source Reasoning Dichotomous Choice Evaluation

Soru 1568Soru →

A green energy consultancy's report recommends that the city transition to biomass fuel, asserting that biomass is an organic power source and is therefore inherently sustainable for urban energy grids. To support this claim, the report notes that organic material naturally decomposes in nature without human intervention, guaranteeing that relying on biomass will not cause lasting environmental damage.

Which of the following best describes the logical flaw in the consultancy's reasoning?

It relies on an ambiguity in the word 'organic' to infer environmental safety from biological composition.

It assumes without justification that non-organic energy sources are inherently harmful to the environment.

It ignores potential counterarguments regarding the financial feasibility of transitioning to biomass energy.

It mistakes a condition necessary for natural decomposition for a condition that guarantees immediate sustainability.

It focuses on the chemical decomposition of biomass rather than evaluating the total carbon emissions produced during combustion.

Cevabı ve açıklamayı göster

Cevap: It relies on an ambiguity in the word 'organic' to infer environmental safety from biological composition.

Cevap

The argument relies on an ambiguity in the word 'organic' to infer environmental safety from biological composition.

The correct answer correctly identifies that the argument commits the flaw of equivocation. The author uses 'organic' in a technical, biological sense in the premises (referring to matter derived from living organisms that decomposes naturally) and then shifts to a broader, colloquial sense of 'organic' in the conclusion (implying eco-friendly or environmentally benign). Because biological decomposition does not guarantee environmental sustainability when used as fuel, the argument relies on an ambiguous term to draw an invalid conclusion.

Adım Adım Çözüm

1

Identify the premises and conclusion

Premise: Biomass is organic material because it naturally decomposes. Conclusion: Biomass is an organic power source and therefore inherently sustainable and harmless to the environment.

Deconstructing the argument reveals how the author connects the physical property of biomass to the conclusion about sustainability.

2

Analyze key terms across premises and conclusion

The word 'organic' is used in the premise to mean 'biological matter that decomposes naturally'. In the conclusion, 'organic' is used to imply 'eco-friendly, sustainable, and harmless'.

Identifying shifts in key term definitions exposes equivocation flaws.

3

Evaluate the logical leap

Just because material is biologically organic does not mean burning or processing it for fuel is environmentally sustainable or free of harm.

The author exploits two distinct meanings of 'organic' to make an invalid inference.

Anahtar Kavram

Equivocation and Shift in Term Meaning

Soru 1569Soru →

The table below displays the industry sector, annual revenue (in millions of dollars), and number of employees for 10 tech startups.

Startup Name	Industry Sector	Annual Revenue ($M)	Employees
Apex Systems	Software	14	45
Beacon Health	Healthcare	30	110
Crest Tech	Software	42	160
Dome Logistics	Logistics	20	80
Echo Labs	Software	35	140
Flux Interactive	Software	52	210
Grid Solutions	Energy	65	190
Horizon Soft	Software	24	95
Impulse Media	Software	18	65
Jade Bio	Healthcare	32	125

Based on the table, what is the median annual revenue, in millions of dollars, for the startups in the Software sector?

24.0

29.5

31.0

35.0

43.5

Cevabı ve açıklamayı göster

Cevap: 29.5

Cevap

29.5

Filtering the dataset for startups in the Software sector yields 6 revenue figures:

14M,

18M,

24M,

35M,

42M, and

52M. Sorting these values in ascending order gives: 14, 18, 24, 35, 42, 52. Since

N = 6

is an even number, the median is the arithmetic mean of the 3rd and 4th values:

\frac{24 + 35}{2} = 29.5

.

Adım Adım Çözüm

1

Filter the table for startups in the Software sector.

Identified 6 Software startups with revenues of

14M,

42M,

35M,

52M,

24M, and

18M.

The question specifies restricting calculations to startups in the Software sector.

2

Sort the filtered revenues in ascending numerical order.

Sorted list: 14, 18, 24, 35, 42, 52.

Determining the median requires ordering data from smallest to largest.

3

Calculate the median for the even dataset (

N = 6

).

The two central numbers are the 3rd value (24) and the 4th value (35). The median is

\frac{24 + 35}{2} = 29.5

.

When

N

is even, the median is the average of the two middle elements.

Anahtar Kavram

Descriptive Statistics Interpretation

Tahmini Süre:1m 30s

Soru 1570Soru →

A dataset consists of $15$ distinct positive integers. Is the median of the dataset greater than its arithmetic mean?

(1) The sum of the $7$ smallest integers in the dataset is $42$ , and the sum of the $7$ largest integers in the dataset is $140$ .
(2) The dataset forms an arithmetic progression.

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

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

Cevap

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

The option stating that Statement (2) alone is sufficient while Statement (1) alone is not sufficient is correct because Statement (2) establishes that the dataset is an arithmetic progression, where median always equals mean. This provides a definitive 'No' to the question of whether the median is strictly greater than the mean, satisfying sufficiency. Statement (1) allows values of the median both above and below

13

, yielding both 'Yes' and 'No' outcomes.

Adım Adım Çözüm

1

Rephrase the question stem mathematically.

Let the 15 distinct positive integers be ordered as

x_1 < x_2 < \dots < x_7 < x_8 < x_9 < \dots < x_{15}

. The median is

x_8

, and the arithmetic mean is

\mu = \frac{\sum_{i=1}^{15} x_i}{15}

. We need to determine whether

x_8 > \mu

.

Simplifying the question target clarifies what information is necessary for sufficiency.

2

Evaluate Statement (1) independently.

Statement (1) gives

\sum_{i=1}^7 x_i = 42

and

\sum_{i=9}^{15} x_i = 140

. The total sum is

42 + x_8 + 140 = 182 + x_8

, so the mean is

\mu = \frac{182 + x_8}{15}

. The inequality

x_8 > \frac{182 + x_8}{15}

simplifies to

14 x_8 > 182

, or

x_8 > 13

. If

x_8 = 10

(with

x_1 \dots x_7 = \{3,4,5,6,7,8,9\}

and

x_9 \dots x_{15} = \{11,12,13,14,15,16,59\}

), then

x_8 \le 13

yields 'No'. If

x_8 = 15

(with

x_1 \dots x_7 = \{1,2,3,4,5,13,14\}

and

x_9 \dots x_{15} = \{16,17,18,19,20,21,29\}

), then

x_8 > 13

yields 'Yes'.

Since Statement (1) allows for both 'Yes' and 'No' answers, it is NOT sufficient.

3

Evaluate Statement (2) independently.

Statement (2) states that the elements form an arithmetic progression. In any set of numbers that forms an arithmetic progression, the distribution is perfectly symmetric, so the arithmetic mean is exactly equal to the median (

x_8 = \mu

). Therefore,

x_8 > \mu

is false, giving a definitive answer of 'No'.

In Data Sufficiency Yes/No questions, a definitive 'No' answer establishes that the statement IS sufficient.

Anahtar Kavram

Data Sufficiency evaluation of data distributions, comparing median and arithmetic mean in symmetric versus asymmetric datasets.

Soru 1571Soru →

Passage: A telecommunications firm observed that remote software engineers who voluntarily completed an asynchronous time-management training module logged 30% fewer project delays over six months than remote software engineers who did not complete the module. The human resources department concluded that the time-management training module directly caused the reduction in project delays.

Statement: If software engineers who possessed pre-existing high levels of self-motivation and organizational skills were significantly more likely to voluntarily enroll in the module, this factor functions as a confounding variable that undermines the human resources department's causal conclusion.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

The statement is True. Pre-existing baseline traits (such as self-motivation and organizational skills) among voluntary enrollees act as a confounding third variable, providing an alternative explanation for the observed reduction in project delays.

The statement accurately identifies a classic confounding variable (self-selection bias). In causal reasoning, if the group choosing to undergo an intervention already possesses traits that foster the desired outcome, one cannot attribute the outcome solely to the intervention.

Adım Adım Çözüm

1

Identify the author's causal conclusion and supporting evidence.

Evidence: Engineers who voluntarily completed training had 30% fewer delays. Conclusion: The training module caused the reduction in delays.

Understanding the premise-to-conclusion structure is essential for isolating the assumed causal link.

2

Evaluate the impact of self-selection and alternative explanations.

Voluntary enrollment means engineers with higher inherent motivation chose to take the module.

A confounding variable (third variable) occurs when a distinct factor correlates with both participation and the positive outcome.

3

Determine whether this factor constitutes a confounding variable that undermines the conclusion.

Because inherent motivation alone could explain why those engineers logged fewer delays, the claim that the training caused the result is vulnerable.

An unaddressed third variable invalidates a strict claim of cause and effect.

Anahtar Kavram

Causal Flaws and Confounding Variables

Soru 1572Soru →

If $x$ and $y$ are real numbers, what is the value of $x - y$ ?

(1) $x^2 - y^2 = 12(x + y)$ and $x + y \neq 0$
(2) $x^2 + y^2 = 2xy + 144$

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

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

Cevap

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. Factoring Statement (1) gives

(x - y)(x + y) = 12(x + y)

. Because

x + y \neq 0

, dividing both sides by

(x + y)

establishes

x - y = 12

uniquely. In contrast, Statement (2) simplifies to

(x - y)^2 = 144

, yielding two possible values (

12

and

-12

), which makes Statement (2) insufficient on its own.

Adım Adım Çözüm

1

Evaluate Statement (1) independently

The statement gives

x^2 - y^2 = 12(x + y)

. Factoring the difference of squares gives

(x - y)(x + y) = 12(x + y)

. Since

x + y \neq 0

, divide both sides by

(x + y)

to get

x - y = 12

.

Because a unique numerical value for

x - y

is obtained, Statement (1) ALONE is sufficient.

2

Evaluate Statement (2) independently

Rearranging

x^2 + y^2 = 2xy + 144

yields

x^2 - 2xy + y^2 = 144

, which contracts to

(x - y)^2 = 144

. Taking the square root gives

x - y = 12

or

x - y = -12

.

Because there are two distinct potential values for

x - y

, Statement (2) ALONE is not sufficient.

3

Combine the evaluations

Statement (1) alone is sufficient, whereas Statement (2) alone is not sufficient.

No combination of statements is required since Statement (1) alone uniquely determines the target value.

Anahtar Kavram

Algebraic Stem Simplification and Degree Ambiguity in Data Sufficiency

Tahmini Süre:2m 0s

Soru 1573Soru →

In a GMAT Data Sufficiency Yes/No question asking whether $x > 0$ , if Statement (1) implies $x^3 - x = 0$ and Statement (2) implies $x^2 - 1 = 0$ , then combining both statements is sufficient to answer the question because combining them narrows the set of possible values of $x$ to a smaller set than either statement alone.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False

The correct evaluation is False. In GMAT Data Sufficiency Yes/No questions, combining statements is sufficient only if every remaining value in the combined solution set yields the exact same answer (either all 'Yes' or all 'No'). Here, the combined set

\{-1, 1\}

contains

x = -1

(which yields 'No') and

x = 1

(which yields 'Yes'), so the combined statements remain insufficient.

Adım Adım Çözüm

1

Analyze Statement (1) independently.

Solving

x^3 - x = 0

yields

x(x - 1)(x + 1) = 0

, so

x \in \{-1, 0, 1\}

. Testing these values against the question 'Is

x > 0

?':

x = -1

gives No,

x = 0

gives No, and

x = 1

gives Yes. Because both Yes and No are possible, Statement (1) alone is insufficient.

Each statement must first be evaluated independently by checking if all allowed values yield a uniform answer.

2

Analyze Statement (2) independently.

Solving

x^2 - 1 = 0

yields

x \in \{-1, 1\}

. Testing these values:

x = -1

gives No and

x = 1

gives Yes. Because both Yes and No are possible, Statement (2) alone is insufficient.

Statement (2) must be evaluated strictly without carrying over any information or restrictions from Statement (1).

3

Evaluate the combined statement information.

Taking the intersection of the solution sets from both statements gives

\{-1, 0, 1\} \cap \{-1, 1\} = \{-1, 1\}

.

Combining statements requires finding all values that satisfy both Statement (1) and Statement (2) simultaneously.

4

Determine sufficiency of the combined set for a Yes/No question.

Within the combined set

\{-1, 1\}

,

x = -1

yields 'No' (

x \ngtr 0

) while

x = 1

yields 'Yes' (

x > 0

). Since a definitive Yes or No answer cannot be reached, the statements together remain insufficient.

For a Yes/No Data Sufficiency question, sufficiency requires that EVERY value in the combined solution set leads to the exact same answer.

Anahtar Kavram

Data Sufficiency Statement Combination for Yes/No Questions

Soru 1574Soru →

Consider the following corporate IT compliance guidelines:

1. Every software module deployed to the primary server must undergo automated security scanning prior to deployment.
2. Any software module that fails the automated security scan is immediately flagged for manual review and is never deployed directly to the primary server.
3. During yesterday's system release, Software Module X was deployed directly to the primary server.

Statement: Based strictly on the guidelines above, Software Module X must have successfully passed the automated security scan prior to its deployment.

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

The statement is True. The given premises logically entail that Software Module X underwent and successfully passed the automated security scan prior to its direct deployment.

The statement is logically valid and True. Premise 1 requires that all modules deployed to the primary server undergo automated security scanning. Premise 2 states that failing the scan prevents direct deployment. By contrapositive logic, any module deployed directly to the primary server cannot have failed the scan. Since Module X was deployed directly, it must have undergone and passed the automated security scan.

Adım Adım Çözüm

1

Analyze Premise 1 regarding deployment requirements.

Deployment to the primary server necessitates undergoing automated security scanning.

Establishes a mandatory prerequisite for any module deployed to the primary server.

2

Formulate the contrapositive of Premise 2.

If a module is deployed directly to the primary server, then it did not fail the automated security scan.

Premise 2 establishes that Fails Scan → Not Directly Deployed. The contrapositive (Directly Deployed → Did Not Fail Scan) is logically equivalent and valid.

3

Apply the factual premise about Software Module X to the derived logic.

Software Module X was deployed directly to the primary server, so it underwent scanning (Premise 1) and did not fail (Premise 2 contrapositive). Therefore, it passed.

Synthesizing the premises produces a 100% guaranteed deduction.

Anahtar Kavram

Identifying Must-Be-True Statements using Conditional Logic and Contrapositives

Soru 1575Soru →

If $x$ and $y$ are real numbers such that $x + y \neq 0$ , what is the value of the product $xy$ ?

(1) $x^3 + y^3 = 28(x + y)$
(2) $x^2 + y^2 = 20 - xy$

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

Cevap: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Cevap

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Combining both statements provides two independent linear equations in terms of

(x+y)^2

and

xy

. Subtracting Statement (1) from Statement (2) eliminates the squared sum term

(x+y)^2

and yields a unique value of

-4

for the product

xy

, with real solutions existing for

x

and

y

. Therefore, both statements together are sufficient.

Adım Adım Çözüm

1

Analyze Statement (1) algebraically.

(x + y)^2 - 3xy = 28

Factor

x^3 + y^3

as

(x + y)(x^2 - xy + y^2)

. Since

x + y \neq 0

, divide both sides by

(x + y)

to obtain

x^2 - xy + y^2 = 28

. Express

x^2 + y^2

as

(x + y)^2 - 2xy

, yielding

(x + y)^2 - 3xy = 28

. Because

(x + y)^2

is unknown,

xy

can take multiple real values (e.g., if

(x+y)^2 = 16

,

xy = -4

; if

(x+y)^2 = 36

,

xy = 8/3

). Thus, Statement (1) alone is insufficient.

2

Analyze Statement (2) algebraically.

(x + y)^2 - xy = 20

Rearrange

x^2 + y^2 = 20 - xy

to

x^2 + xy + y^2 = 20

. Express

x^2 + y^2

as

(x + y)^2 - 2xy

, yielding

(x + y)^2 - xy = 20

. Again, since

(x + y)^2

is unknown,

xy

is not uniquely determined (e.g., if

(x+y)^2 = 16

,

xy = -4

; if

(x+y)^2 = 4

,

xy = -16

). Thus, Statement (2) alone is insufficient.

3

Combine both statements and solve the system of equations.

xy = -4

Let

u = (x + y)^2

and

v = xy

. Statement (1) gives

u - 3v = 28

and Statement (2) gives

u - v = 20

. Subtracting the first equation from the second yields

(u - v) - (u - 3v) = 20 - 28 \implies 2v = -8 \implies v = -4

. Hence,

xy = -4

uniquely.

4

Verify existence of real solutions for

x

and

y

.

Real solutions exist because the discriminant is positive.

With

u = 16

, we have

x + y = 4

or

x + y = -4

. For

x + y = 4

and

xy = -4

,

x

and

y

are roots of

t^2 - 4t - 4 = 0

, which has discriminant

16 - 4(1)(-4) = 32 > 0

. Thus real values of

x

and

y

exist.

Anahtar Kavram

System rephrasing in Data Sufficiency by substituting composite variables like

(x+y)^2

and

xy

.

Soru 1576Soru →

### Tab 1: Commercialization Policy (Policy 404)
Under University Policy 404, technologies developed by university faculty using internal funds are owned by the university. Faculty creators are entitled to a 40% share of net licensing revenues, defined as gross licensing royalties minus direct legal protection costs and patent maintenance fees. However, if external commercialization funding exceeding $100,000 is received prior to patent application filing, the university's royalty share increases by 10 percentage points (reducing the faculty creator's share to 30%), unless an explicit exemption is granted by the Vice President of Research (VPR).

### Tab 2: Project Chronology & Financial Audit (Project Helios)
Project Helios, developed by Dr. Vance, received a $25,000 university seed grant in 2023. In January 2024, Dr. Vance secured a$ 150,000 research grant from an industry partner for prototype development. The patent application for Project Helios was filed in August 2024. Direct legal expenses incurred for patent protection totaled $30,000, and initial maintenance fees were$ 10,000. In 2025, Project Helios generated $500,000 in gross licensing royalties. No individual VPR exemption documentation for Project Helios exists in the project registry.

### Tab 3: Executive Memorandum (Office of the VPR)
In July 2024, the VPR issued a policy memorandum clarifying that all industry research grants awarded under the university's Sustainable Energy Initiative are exempt from the 10 percentage point royalty adjustment specified in Policy 404, regardless of award size, provided the grant agreement was executed prior to June 2024. University records confirm Project Helios was formally designated under the Sustainable Energy Initiative upon its initial seed funding in 2023, and Dr. Vance's industry grant agreement was executed in January 2024.

Based on the information provided in the three tabs, what is the total monetary amount Dr. Vance is entitled to receive as creator share from the 2025 licensing royalties of Project Helios?

$184,000

$138,000

$200,000

$150,000

$124,000

Cevabı ve açıklamayı göster

Cevap: $184,000

Cevap

Dr. Vance is entitled to receive $184,000.

Synthesizing all three tabs demonstrates that net revenues equal

460,000 (

500,000 gross minus

30,000 legal costs and

10,000 maintenance fees). While external funding exceeded

100,000 before patent filing, the blanket VPR policy in Tab 3 exempts Sustainable Energy Initiative grants executed before June 2024. Since Project Helios satisfies these criteria, Dr. Vance receives the full 40% creator share of

460,000, which equals $184,000.

Adım Adım Çözüm

1

Calculate Net Licensing Revenue

500,000 - (

30,000 +

10,000) =

460,000

Tab 1 defines net licensing revenue as gross royalties minus direct legal protection costs and patent maintenance fees. Data from Tab 2 gives gross royalties of

500,000, legal costs of

30,000, and maintenance fees of $10,000.

2

Determine Applicable Royalty Share Percentage across Tabs

40% Creator Share applies

Tab 1 states that external commercialization funding over

100,000 prior to filing reduces creator share to 30% unless an exemption is granted. Tab 2 shows

150,000 external funding before filing and notes no individual exemption in the registry. However, Tab 3 establishes a blanket VPR exemption for Sustainable Energy Initiative grants executed before June 2024. Tab 3 confirms Project Helios was designated in 2023 and the grant was executed in January 2024, so the exemption applies and preserves the 40% rate.

3

Compute Final Creator Share

40% of

460,000 =

184,000

Multiply the net licensing revenue by the creator share percentage.

Anahtar Kavram

Multi-Source Policy Exception Synthesis and Net Revenue Calculation

Tahmini Süre:2m 30s

Soru 1577Soru →

If $r$ and $s$ are non-zero real numbers, what is the value of $\frac{r^2 + 2s^2}{rs}$ ?

(1) $r^2 - 3rs + 2s^2 = 0$
(2) $r + s = 6$

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

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

Cevap

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

The correct option states that Statement (1) alone is sufficient while Statement (2) is not. Rephrasing the target expression

\frac{r^2 + 2s^2}{rs}

as

\frac{r}{s} + 2\left(\frac{s}{r}\right)

shows that the target value depends exclusively on the ratio

t = \frac{r}{s}

. Statement (1) factors into

(r - s)(r - 2s) = 0

, giving

t = 1

or

t = 2

. Testing

t = 1

yields

1 + 2 = 3

, and testing

t = 2

yields

2 + 1 = 3

. Because both possible values of

t

evaluate to the same constant result (

3

), Statement (1) alone uniquely determines the target value and is sufficient. Statement (2) allows infinitely many ratios for

r/s

, giving different outcomes, and is therefore insufficient.

Adım Adım Çözüm

1

Rephrase the target expression algebraically.

Dividing each term in the numerator by the denominator gives

\frac{r^2 + 2s^2}{rs} = \frac{r}{s} + 2\left(\frac{s}{r}\right)

. Letting

t = \frac{r}{s}

, the target expression is

t + \frac{2}{t}

.

Simplifying the question stem reveals that we only need to know the ratio

\frac{r}{s}

.

2

Evaluate Statement (1):

r^2 - 3rs + 2s^2 = 0

.

Divide the entire equation by

s^2

(since

s \neq 0

) to get

\left(\frac{r}{s}\right)^2 - 3\left(\frac{r}{s}\right) + 2 = 0

, or

t^2 - 3t + 2 = 0

. Factoring yields

(t - 1)(t - 2) = 0

, so

t = 1

or

t = 2

.
If

t = 1

,

t + \frac{2}{t} = 1 + 2 = 3

.
If

t = 2

,

t + \frac{2}{t} = 2 + \frac{2}{2} = 3

.
In both cases, the target expression equals

3

.

Although there are two solutions for the ratio

t

, both lead to the identical value of

3

for the target expression. Thus, Statement (1) alone is sufficient.

3

Evaluate Statement (2):

r + s = 6

.

If

r = 2

and

s = 4

, then

\frac{r}{s} = \frac{1}{2}

, giving a target value of

\frac{1}{2} + 4 = 4.5

.
If

r = 3

and

s = 3

, then

\frac{r}{s} = 1

, giving a target value of

1 + 2 = 3

.
Since different pairs of

r

and

s

yield different values for the expression, Statement (2) alone is not sufficient.

Knowing only the linear sum of two variables does not uniquely fix their ratio.

Anahtar Kavram

Question Stem Rephrasing and Symmetry in Homogeneous Quadratic Expressions

Soru 1578Soru →

A logistics center processes packages using two sorting machines, Machine X and Machine Y, each operating continuously at its own constant hourly rate. On a given operational shift, Machine X processed packages for $t_x$ hours and Machine Y processed packages for $t_y$ hours. What percentage of the total number of packages processed by both machines combined during the shift was processed by Machine X?

(1) If Machine X had operated for $20\%$ more time and Machine Y had operated for $20\%$ less time, Machine X would have processed $50\%$ more packages than Machine Y.

(2) The ratio of the hourly processing rate of Machine X to the hourly processing rate of Machine Y was $3:2$ , and the total operating time of both machines combined was $10$ hours.

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

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Cevabı ve açıklamayı göster

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

Cevap

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

Statement (1) alone is sufficient because translating the percentage modifications into an equation gives

1.2 P_x = 1.5 \times (0.8 P_y)

, which simplifies to

1.2 P_x = 1.2 P_y

, or

P_x = P_y

. This proves Machine X processed exactly

50\%

of the total packages. Statement (2) alone is not sufficient because knowing

t_x + t_y = 10

and

r_x / r_y = 3/2

allows infinitely many different package output ratios depending on how the

10

hours are split between the two machines.

Adım Adım Çözüm

1

Define target variable algebraically from question stem

Let

r_x

and

r_y

be the constant hourly processing rates of Machine X and Machine Y, respectively. The total packages processed by Machine X is

P_x = r_x t_x

, and by Machine Y is

P_y = r_y t_y

. The target percentage processed by Machine X is

\frac{P_x}{P_x + P_y} \times 100\% = \frac{1}{1 + \frac{P_y}{P_x}} \times 100\%

. Finding the ratio

\frac{P_x}{P_y}

is necessary and sufficient.

Rephrasing the question stem shows that finding the single ratio of total packages

P_x / P_y

is sufficient to answer the question.

2

Evaluate Statement (1)

Under the hypothetical scenario in Statement (1), the new operating time for Machine X is

1.2 t_x

and for Machine Y is

0.8 t_y

. The new package totals are

r_x (1.2 t_x) = 1.2 P_x

and

r_y (0.8 t_y) = 0.8 P_y

. The statement specifies that

1.2 P_x = 1.5 \times (0.8 P_y)

. Simplifying the right-hand side:

1.5 \times 0.8 = 1.2

, so

1.2 P_x = 1.2 P_y \implies P_x = P_y

. Thus,

\frac{P_x}{P_y} = 1

, which means Machine X processed

\frac{P_x}{P_x + P_x} = 50\%

of the total packages.

Algebraic simplification yields a unique value for the target percentage, making Statement (1) sufficient.

3

Evaluate Statement (2)

Statement (2) gives

\frac{r_x}{r_y} = \frac{3}{2}

and

t_x + t_y = 10

. The ratio of total packages processed is

\frac{P_x}{P_y} = \left(\frac{r_x}{r_y}\right) \left(\frac{t_x}{t_y}\right) = \frac{3}{2} \left(\frac{t_x}{t_y}\right)

. Since

t_x

and

t_y

can take any positive real values summing to

10

(e.g.,

t_x = 2, t_y = 8 \implies \frac{P_x}{P_y} = \frac{3}{8}

vs.

t_x = 6, t_y = 4 \implies \frac{P_x}{P_y} = \frac{9}{4}

), the percentage varies.

Without individual values for

t_x

and

t_y

, multiple target percentages are possible, so Statement (2) is not sufficient.

Anahtar Kavram

Question Stem Rephrasing and Algebraic Simplification of Combined Rates

Tahmini Süre:2m 30s

Soru 1579Soru →

To increase the proportion of borrowed books returned on or before their due date, the Metro Central Library system plans to eliminate all monetary overdue fines and instead send automated daily text reminders starting three days prior to each book's due date. Library administrators reason that monetary fines create anxiety that deters patrons from returning late books promptly, whereas text notifications directly address the primary reason for late returns: patrons simply forgetting the due date. Which of the following, if true, provides the strongest ground for doubting that the library system's plan will achieve its goal?

A survey of library patrons revealed that most late returns are driven by the physical inconvenience of visiting a branch rather than forgetfulness, and patrons are even less motivated to make prompt return trips when monetary penalties are absent.

Patrons who opt in to text messaging services from commercial retailers return overdue rental items significantly faster than those who do not receive digital alerts.

The automated text reminder system requires an initial software license purchase that will consume a notable portion of the library's annual technology budget.

Many library patrons who regularly return books on time also utilize digital e-books, which automatically expire without requiring physical return.

While text notifications increase patron engagement with library announcements, digital reminders cannot be delivered to patrons who do not provide a valid cell phone number.

Cevabı ve açıklamayı göster

Cevap: A survey of library patrons revealed that most late returns are driven by the physical inconvenience of visiting a branch rather than forgetfulness, and patrons are even less motivated to make prompt return trips when monetary penalties are absent.

Cevap

The plan is most weakened by evidence showing that late returns are primarily caused by the inconvenience of visiting a branch rather than forgetfulness, and that eliminating fines decreases patrons' motivation to return books on time.

The correct answer undermines the fundamental assumption of the plan. The library assumes that forgetfulness is the main cause of late returns and that fines are counterproductive. If late returns are actually caused by the inconvenience of visiting a branch, text reminders will not solve the underlying problem. Furthermore, if eliminating fines removes patrons' motivation to make the trip, the plan will actively decrease on-time returns.

Adım Adım Çözüm

1

Identify the conclusion and main premise of the argument.

Conclusion: Replacing monetary overdue fines with text reminders will increase on-time book returns. Main Premise: Late returns occur primarily because patrons forget due dates, and fines cause anxiety.

Understanding the central assumption—that forgetfulness causes late returns—is essential to evaluating how to weaken the conclusion.

2

Evaluate the underlying assumption.

The argument assumes that text reminders will fix the main cause of late returns (forgetfulness) and that eliminating fines will not decrease on-time returns.

To weaken a plan-to-goal argument, one must show that the plan fails to address the real problem or introduces counterproductive incentives.

3

Select the choice that directly attacks the core assumption.

The option showing that convenience, not forgetfulness, drives late returns and that removing fines reduces motivation directly undermines the plan's feasibility.

This shows both that the text reminders address a non-primary factor and that removing fines makes the goal harder to achieve.

Anahtar Kavram

Weakening a Plan-to-Goal Argument

Soru 1580Soru →

Executives at a luxury hotel chain noted that properties featuring a newly installed organic tea station in the main lobby achieved significantly higher overall guest satisfaction scores than properties without such a station. Based on this observation, the executives concluded that providing free organic tea to guests directly improves overall guest satisfaction.

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

The hotel properties selected to receive organic tea stations were also those that had recently completed major room renovations and staff retraining.

Guests who visited the lobby tea station reported feeling significantly more relaxed during check-in than guests who did not visit the station.

Operating an organic tea station requires less daily maintenance than managing a complimentary breakfast buffet.

Guest satisfaction ratings at properties with tea stations began rising immediately following the installation of the stations.

The executive team implemented the tea stations as an intermediate trial phase prior to reviewing overall guest service amenities.

Cevabı ve açıklamayı göster

Cevap: The hotel properties selected to receive organic tea stations were also those that had recently completed major room renovations and staff retraining.

Cevap

The argument is most seriously weakened by revealing that the hotel properties featuring tea stations had also undergone major room renovations and staff retraining, introducing a confounding variable.

The correct answer weakens the argument by introducing a classic confounding variable (third variable). If the hotels that received tea stations were also renovated and had their staff retrained, those improvements—rather than the tea station—could fully account for the higher guest satisfaction scores.

Adım Adım Çözüm

1

Identify the premise and conclusion of the causal argument.

Premise: Hotel properties with organic tea stations have higher satisfaction scores than those without. Conclusion: Offering organic tea directly causes higher guest satisfaction.

Understanding the precise gap between observed correlation and claimed causality is necessary to evaluate the argument.

2

Analyze the logical flaw in the conclusion.

The argument commits a causal flaw by assuming that because the tea stations and high satisfaction ratings occurred together, the tea station must be the cause.

Causal conclusions based on simple correlations are vulnerable to alternative explanations, such as third-variable confounders.

3

Evaluate the choices for a third variable or alternate cause.

The option noting that properties with tea stations also received major room renovations and staff retraining introduces confounding factors that easily explain the higher satisfaction scores independently of the tea.

Showing that another major positive change co-occurred at the exact same properties severely undermines the claim that the tea station specifically caused the increase.

Anahtar Kavram

Causal Flaws and Confounding Variables

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