Tüm alıştırma soruları

Soru 1501Soru →

A financial advisory firm manages a portfolio of $90$ assets, each of which is classified as a Tech asset, a Biotech asset, or both. Exactly $50$ of the assets are Tech assets, and exactly $60$ of the assets are Biotech assets. Is the average (arithmetic mean) value of the Tech-only assets greater than the average value of the Biotech-only assets?

(1) The average value of all $50$ Tech assets is $\$12$ million, and the average value of all $60$ Biotech assets is $\$12$ million.
(2) The average value of the $20$ assets classified as both Tech and Biotech assets is $\$15$ million.

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 allows us to solve for the exact average value of the Tech-only assets (

10

million) and the Biotech-only assets (

10.5

million). Because we can answer the stem's question with a definitive 'No' (

10

is not greater than

10.5

), both statements together are sufficient.

Adım Adım Çözüm

1

Determine the number of assets in each non-overlapping subgroup using set theory.

Total assets

N = 90

, Tech assets

|T| = 50

, Biotech assets

|B| = 60

. Using

|T \cup B| = |T| + |B| - |T \cap B|

, we get

90 = 50 + 60 - |T \cap B| \implies |T \cap B| = 20

. Therefore, Tech-only assets

= 50 - 20 = 30

, Biotech-only assets

= 60 - 20 = 40

, and Both

= 20

.

Rephrasing the question stem into distinct, non-overlapping subset counts simplifies the algebraic system.

2

Evaluate Statement (1) independently.

Let

M_{T}

,

M_{B}

, and

M_{both}

represent the mean values of Tech-only, Biotech-only, and Both subsets respectively. From Statement (1), total value of Tech

= 30 M_T + 20 M_{both} = 50 \times 12 = 600

, and total value of Biotech

= 40 M_B + 20 M_{both} = 60 \times 12 = 720

. Subtracting the equations yields

40 M_B - 30 M_T = 120 \implies 4 M_B - 3 M_T = 12

.

Since

M_T

could be

16

(making

M_B = 15

, so

M_T > M_B

is Yes) or

M_T

could be

8

(making

M_B = 9

, so

M_T > M_B

is No), Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) independently.

Statement (2) gives

M_{both} = 15

. Without knowing the total asset values or subgroup means, we cannot compare

M_T

and

M_B

.

Statement (2) alone is NOT sufficient.

4

Evaluate Statements (1) and (2) together.

Substituting

M_{both} = 15

into Statement (1) equations:

30 M_T + 20(15) = 600 \implies 30 M_T = 300 \implies M_T = 10

. Similarly,

40 M_B + 20(15) = 720 \implies 40 M_B = 420 \implies M_B = 10.5

. Since

10 > 10.5

is definitively FALSE, we get a clear 'No' response.

In Yes/No Data Sufficiency questions, a definitive 'No' means the combined statements are sufficient.

Anahtar Kavram

Data Sufficiency decision logic for overlapping sets combined with weighted averages

Tahmini Süre:2m 0s

Soru 1502Soru →

For all positive real numbers $a$ and $b$ , the Data Sufficiency Yes/No target question "Is $\frac{a^2 + 3ab}{b^2 + 3ab} > 1$ ?" is algebraically equivalent to asking "Is $a > b$ ?"

Doğru

Yanlış

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True. The target question simplifies directly to "Is

a > b

?"

The statement is true because cross-multiplying the strictly positive denominator

b^2 + 3ab

and subtracting the shared term

3ab

reduces

\frac{a^2 + 3ab}{b^2 + 3ab} > 1

directly to

a^2 > b^2

. Since

a

and

b

are both positive,

a^2 > b^2

is logically equivalent to

a > b

.

Adım Adım Çözüm

1

Determine the sign of the denominator.

Since

a > 0

and

b > 0

,

b^2 + 3ab > 0

.

Knowing the denominator is strictly positive ensures we can cross-multiply without reversing the inequality sign.

2

Cross-multiply the inequality by the denominator.

a^2 + 3ab > b^2 + 3ab

Multiplying both sides of

\frac{a^2 + 3ab}{b^2 + 3ab} > 1

by

(b^2 + 3ab)

clears the fraction.

3

Subtract

3ab

from both sides.

a^2 > b^2

Eliminating the common linear term isolates the quadratic terms.

4

Take the square root of both sides.

a > b

Because

a

and

b

are positive,

a^2 > b^2

holds if and only if

a > b

.

Anahtar Kavram

Data Sufficiency Question Stem Simplification

Soru 1503Soru →

The table below presents operational metrics for six regional renewable energy facilities:

Facility	Energy Source	Capacity (MW)	Operational Efficiency (%)	Storage Available
Alpha	Solar	45	88%	Yes
Beta	Wind	60	75%	No
Gamma	Hydro	50	92%	Yes
Delta	Solar	30	82%	No
Epsilon	Wind	55	84%	Yes
Zeta	Hydro	70	78%	Yes

A plant manager needs to select facilities that satisfy at least one of the following criteria:
- Criterion 1: Energy Source is Wind AND Capacity is greater than 50 MW.
- Criterion 2: Storage Available is "Yes" AND Operational Efficiency is at least 85%.

Which of the following facilities meet the manager's criteria? Select all that apply.

Geçerli olan tümünü seçin

Alpha

Beta

Delta

Epsilon

Zeta

Cevabı ve açıklamayı göster

Cevap: Alpha; Beta; Epsilon

Cevap

The facilities that meet the criteria are Alpha, Beta, and Epsilon.

Alpha qualifies under Criterion 2 because it has storage available and an operational efficiency of 88% (>= 85%). Beta qualifies under Criterion 1 because its energy source is Wind and its capacity is 60 MW (> 50 MW). Epsilon qualifies under Criterion 1 because its energy source is Wind and its capacity is 55 MW (> 50 MW).

Adım Adım Çözüm

1

Evaluate each facility against Criterion 1 (Energy Source = Wind AND Capacity > 50 MW).

Beta (Wind, 60 MW) and Epsilon (Wind, 55 MW) satisfy Criterion 1.

Both facilities use Wind energy and have capacities strictly above 50 MW.

2

Evaluate remaining facilities against Criterion 2 (Storage Available = Yes AND Operational Efficiency >= 85%).

Alpha (Storage = Yes, 88% Efficiency) satisfies Criterion 2. Gamma also satisfies Criterion 2, while Delta and Zeta fail both criteria.

Alpha meets both required conditions of Criterion 2.

3

Combine the results for the options provided (Alpha, Beta, Delta, Epsilon, Zeta).

Alpha, Beta, and Epsilon satisfy at least one criterion.

Selection requires satisfying Criterion 1 OR Criterion 2.

Anahtar Kavram

Evaluating compound logical conditions (AND/OR conjunctions) across multiple table attributes.

Tahmini Süre:1m 15s

Soru 1504Soru →

If $m$ and $n$ are positive integers, is $m$ an even integer?

(1) $m + n$ is an odd integer.
(2) $n = 5$

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.

Neither statement alone determines the parity of

m

. However, combining Statement (1) (

m+n

is odd) and Statement (2) (

n=5

, an odd integer) proves that

m

must be an even integer. Therefore, both statements together are sufficient.

Adım Adım Çözüm

1

Analyze Statement (1) independently.

Statement (1) states that

m + n

is odd. For the sum of two integers to be odd, one integer must be even and the other must be odd. If

n

is odd,

m

is even (Yes). If

n

is even,

m

is odd (No). Since the parity of

n

is unknown, Statement (1) alone is NOT sufficient.

Determining sufficiency requires a unique Yes or No answer.

2

Analyze Statement (2) independently, ignoring Statement (1).

Statement (2) states that

n = 5

. This gives no information about

m

. Thus, Statement (2) alone is NOT sufficient.

Statement 2 must be evaluated strictly without carrying over information from Statement 1.

3

Combine Statement (1) and Statement (2).

From Statement (2),

n = 5

, which is an odd integer. Substituting

n = 5

into Statement (1),

m + 5

is odd. Since an odd integer added to an even integer yields an odd integer,

m

must be even. This provides a definitive 'Yes' answer.

Combining both statements provides enough information to uniquely answer the question.

Anahtar Kavram

Statement Independence and Combination in Data Sufficiency

Soru 1505Soru →

If $r$ is a positive real number, is $r$ an integer?

(1) $r^2 + 2r$ is an integer.
(2) $r^2 - 2r$ is an 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: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Cevap

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

Neither statement alone is sufficient because irrational numbers like

\sqrt{2}-1

and

\sqrt{2}+1

can satisfy statements (1) and (2) respectively. However, combining both statements proves that

4r

is an integer

k

, and substituting

r = k/4

into the quadratic equation shows that

k

must be a multiple of 4, forcing

r

to be a positive integer.

Adım Adım Çözüm

1

Evaluate Statement (1) independently.

Statement (1) is INSUFFICIENT.

If

r = 1

, then

r^2 + 2r = 3

(an integer), and

r

is an integer (YES). If

r = \sqrt{2} - 1

, then

r^2 + 2r = (3 - 2\sqrt{2}) + (2\sqrt{2} - 2) = 1

(an integer), but

r

is NOT an integer (NO). Since

r

can be an integer or a non-integer, Statement (1) alone is not sufficient.

2

Evaluate Statement (2) independently.

Statement (2) is INSUFFICIENT.

If

r = 3

, then

r^2 - 2r = 3

(an integer), and

r

is an integer (YES). If

r = \sqrt{2} + 1

, then

r^2 - 2r = (3 + 2\sqrt{2}) - (2\sqrt{2} + 2) = 1

(an integer), but

r

is NOT an integer (NO). Since

r

can be an integer or a non-integer, Statement (2) alone is not sufficient.

3

Evaluate Statement (1) and Statement (2) together.

Statements (1) and (2) together are SUFFICIENT.

Let

r^2 + 2r = a

and

r^2 - 2r = b

, where

a

and

b

are integers. Subtracting Statement (2) from Statement (1) gives

(r^2 + 2r) - (r^2 - 2r) = a - b \implies 4r = a - b

. Since

a

and

b

are integers,

a - b = k

for some integer

k

. Thus,

r = \frac{k}{4}

. Now substitute

r = \frac{k}{4}

back into Statement (1):

\left(\frac{k}{4}\right)^2 + 2\left(\frac{k}{4}\right) = a \implies \frac{k^2}{16} + \frac{k}{2} = a \implies \frac{k^2 + 8k}{16} = a

. This means

16

must divide

k^2 + 8k = k(k+8)

. If

k

were odd,

k(k+8)

would be odd and thus not divisible by 16. So

k

must be even. Let

k = 2m

. Then

k(k+8) = 2m(2m+8) = 4m(m+4)

. For

16

to divide

4m(m+4)

,

4

must divide

m(m+4)

. If

m

were odd,

m(m+4)

would be odd, which is not divisible by 4. Thus,

m

must be even. Let

m = 2p

. Then

k = 2m = 4p

, which means

k

is a multiple of 4. Therefore,

r = \frac{k}{4} = \frac{4p}{4} = p

, an integer. Thus,

r

MUST be an integer.

Anahtar Kavram

Testing integer constraints in Data Sufficiency requires evaluating whether non-integer real numbers satisfy given equations, and combining equations to determine if rational and integer bounds strictly hold.

Soru 1506Soru →

If $a$ and $b$ are positive real numbers such that $ab$ is an integer, is $a$ an integer?

(1) $a + b$ is an integer.
(2) $a - b$ is an 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: 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 shows that

2a

and

2b

are integers. This restricts

a

to being either a whole integer or a half-integer. Evaluating the product of two half-integers reveals that their product has a denominator of 4 and can never be an integer. Since the question stem specifies that

ab

is an integer,

a

must be an integer.

Adım Adım Çözüm

1

Analyze the question stem and given constraints

a

and

b

are positive real numbers and

ab = N

, where

N

is an integer. We must determine whether

a

is guaranteed to be an integer.

The variables are defined as real numbers, so we cannot assume they are integers unless forced by the mathematical statements.

2

Evaluate Statement (1):

a + b

is an integer

Statement (1) is NOT sufficient.

Let

a = 2 + \sqrt{3}

and

b = 2 - \sqrt{3}

. Both are positive real numbers. Here

a + b = 4

(an integer) and

ab = (2+\sqrt{3})(2-\sqrt{3}) = 1

(an integer). However,

a = 2 + \sqrt{3}

is not an integer. Conversely, if

a = 3

and

b = 1

, then

a + b = 4

and

ab = 3

, and

a

is an integer. Thus, Statement (1) alone does not uniquely determine if

a

is an integer.

3

Evaluate Statement (2):

a - b

is an integer

Statement (2) is NOT sufficient.

Let

a = \frac{1 + \sqrt{5}}{2}

and

b = \frac{-1 + \sqrt{5}}{2}

. Both are positive real numbers. Here

a - b = 1

(an integer) and

ab = \frac{(\sqrt{5}+1)(\sqrt{5}-1)}{4} = 1

(an integer). However,

a

is not an integer. Conversely, if

a = 4

and

b = 1

, then

a - b = 3

and

ab = 4

, and

a

is an integer. Thus, Statement (2) alone is not sufficient.

4

Evaluate Statement (1) and Statement (2) combined

Both statements together are SUFFICIENT.

Let

a + b = k

and

a - b = m

, where

k

and

m

are integers. Adding the two equations gives

2a = k + m \implies a = \frac{k+m}{2}

. Subtracting gives

2b = k - m \implies b = \frac{k-m}{2}

. Since

k

and

m

are integers,

k+m

and

k-m

are integers with the same parity. If

k+m

is even, both

a

and

b

are integers. If

k+m

is odd,

a = \frac{p}{2}

and

b = \frac{q}{2}

for odd integers

p

and

q

. But then

ab = \frac{pq}{4}

, which cannot be an integer because the product of two odd integers is odd and thus not divisible by 4. This contradicts the stem constraint that

ab

is an integer. Therefore,

k+m

must be even, forcing

a

to be an integer.

Anahtar Kavram

Real number vs. integer constraints and parity properties in quadratic system equations

Soru 1507Soru →

If $k$ is a positive integer, is $\frac{k^3 - 4k}{k + 2}$ an odd integer?

(1) $k^2 + 3k$ is an even integer.
(2) $3k + 1$ is an odd 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: 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.

Rephrasing the target question

\frac{k^3 - 4k}{k + 2}

by factoring the numerator gives

\frac{k(k-2)(k+2)}{k+2} = k(k-2)

. Because

k

and

k-2

share the same parity, their product

k(k-2)

is odd if and only if

k

is odd. Thus, the question simplifies to: 'Is

k

an odd integer?' Statement (1) tells us

k^2 + 3k = k(k+3)

is even, which is true for all integers

k

, so it provides no information about whether

k

is odd or even (NOT sufficient). Statement (2) tells us

3k + 1

is odd, which implies

3k

is even, and therefore

k

must be even. Since

k

is definitively even, the answer to 'Is

k

an odd integer?' is a definitive 'No'. Therefore, Statement (2) alone is sufficient.

Adım Adım Çözüm

1

Rephrase and simplify the question stem algebraically.

Since

k

is a positive integer,

k + 2 > 0

. Factoring the numerator gives

k^3 - 4k = k(k^2 - 4) = k(k - 2)(k + 2)

. Dividing by

k + 2

yields

\frac{k(k - 2)(k + 2)}{k + 2} = k(k - 2)

.

Simplifying the target expression reduces cognitive complexity before evaluating statements.

2

Determine the parity condition for

k(k - 2)

to be an odd integer.

The factors

k

and

k - 2

differ by 2, so they have the same parity. If

k

is even,

k(k - 2)

is (even)(even) = even. If

k

is odd,

k(k - 2)

is (odd)(odd) = odd. Thus, the target question 'Is

k(k - 2)

an odd integer?' simplifies to 'Is

k

an odd integer?'

Rephrasing the target question to 'Is

k

odd?' establishes a clear, minimal sufficiency criterion.

3

Evaluate Statement (1):

k^2 + 3k

is an even integer.

Factor

k^2 + 3k

as

k(k + 3)

. The terms

k

and

k + 3

differ by 3, meaning one is always even and the other is odd. Their product is ALWAYS even regardless of whether

k

is odd or even. Therefore, Statement (1) provides no information about whether

k

is odd. NOT sufficient.

A statement that holds true for all integers provides no distinguishing information about

k

.

4

Evaluate Statement (2):

3k + 1

is an odd integer.

If

3k + 1

is odd, then

3k

must be even. Since 3 is odd,

3k

is even if and only if

k

is even. Hence,

k

is definitely even. This gives a definitive 'No' to the rephrased question 'Is

k

an odd integer?'. A definitive 'No' means the statement IS sufficient.

In Data Sufficiency Yes/No questions, a statement that yields a conclusive 'No' is sufficient.

Anahtar Kavram

Data Sufficiency Question Stem Simplification and Parity Analysis

Tahmini Süre:1m 30s

Soru 1508Soru →

Although proponents of urban vertical farming emphasize its potential to eliminate long-distance food transportation emissions, critics correctly point out that the energy required for artificial lighting and climate control often far exceeds the carbon savings achieved during transport. Nevertheless, evaluating vertical farming solely through its current energy grid footprint is shortsighted. As municipal energy grids transition toward renewable energy, the operational carbon overhead of vertical farms will decline dramatically, whereas urban land constraints and rural transportation logistics remain permanently fixed. Therefore, vertical farming will ultimately prove to be an essential component of sustainable urban food supply systems.

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

The carbon emissions generated by lighting and climate control in vertical farms currently exceed the emissions saved from shorter transit distances.

Evaluating vertical farming strictly by its present-day energy grid footprint is an inadequate approach.

Urban vertical farming will ultimately become an indispensable element of sustainable municipal food networks.

Transitioning urban power grids to renewable energy sources will completely remove all environmental drawbacks of vertical farming.

Long-distance rural transportation logistics represent the single greatest environmental challenge in modern agricultural supply chains.

Cevabı ve açıklamayı göster

Cevap: Urban vertical farming will ultimately become an indispensable element of sustainable municipal food networks.

Cevap

Urban vertical farming will ultimately become an indispensable element of sustainable municipal food networks.

The main conclusion of the argument is stated in the final sentence: vertical farming will ultimately prove to be an essential component of sustainable urban food supply systems. The option stating that urban vertical farming will ultimately become an indispensable element of sustainable municipal food networks provides an exact paraphrase of this claim without altering its scope or tone.

Adım Adım Çözüm

1

Analyze the structural components and indicators in the passage.

Identified background context, a concession to critics ('critics correctly point out...'), an intermediate conclusion ('evaluating vertical farming solely... is shortsighted'), premises regarding renewable grid transitions, and a main conclusion indicator ('Therefore').

Structural indicators help distinguish premises and subsidiary claims from the author's primary thesis.

2

Isolate the final claim supported by the entire reasoning chain.

The final sentence ('Therefore, vertical farming will ultimately prove to be an essential component of sustainable urban food supply systems') is supported by all preceding claims and supports no further claim.

The main conclusion of a Critical Reasoning argument is the ultimate claim for which all other statements serve as evidence or context.

3

Match the isolated final claim to the correct paraphrase among the answer choices.

The statement expressing that vertical farming will ultimately become an indispensable element of sustainable municipal food networks directly matches the final claim in meaning.

An accurate main conclusion option must preserve the scope, tone, and specific assertion of the author's main claim without introducing unstated extrapolations.

Anahtar Kavram

Identifying Main Conclusion in Arguments with Counterarguments and Intermediate Claims

Soru 1509Soru →

To combat declining commuter usage of its central passenger rail system, a metropolitan transit authority plans to introduce free high-speed Wi-Fi service on all trains. Municipal officials reason that providing internet access will allow passengers to work productively during travel, thereby persuading individuals who currently drive to work to switch to commuting by train. Which of the following would be most useful to determine in evaluating the likelihood that the transit authority's plan will succeed?

Whether a substantial proportion of automobile commuters refrain from using the rail system primarily because they cannot work while commuting.

Whether the municipal transit authority will need to raise passenger fares slightly to offset the installation costs of the Wi-Fi equipment.

Whether automobile commuters in the metropolitan area routinely commute during peak traffic hours.

Whether installing Wi-Fi service on trains will cause current rail passengers to lengthen their overall daily travel time.

Whether private intercity coach services operating outside the metropolitan area offer free Wi-Fi to their passengers.

Cevabı ve açıklamayı göster

Cevap: Whether a substantial proportion of automobile commuters refrain from using the rail system primarily because they cannot work while commuting.

Cevap

Determining whether a substantial proportion of automobile commuters refrain from using the rail system primarily because they cannot work while commuting is most useful for evaluating the plan.

The correct answer evaluates the primary mechanism of the plan. The transit authority's goal is to convert automobile commuters into train passengers by allowing them to work on board. For this plan to succeed, the inability to work while traveling must be a key reason drivers currently choose cars over trains. Evaluating this factor directly tests the validity of the authority's core strategy.

Adım Adım Çözüm

1

Identify the plan and its stated goal.

Plan: Install free high-speed Wi-Fi on trains. Goal: Persuade automobile commuters to switch to rail transit by enabling them to work during their commute.

Evaluating a plan requires understanding the causal link between the proposed action and the intended outcome.

2

Identify the key unstated assumption connecting the plan to the goal.

The plan assumes that a lack of Wi-Fi / inability to work during travel is a primary reason drivers currently avoid taking the train.

If the targeted audience does not value working during travel or drives for unrelated reasons, the incentive will fail to change their behavior.

3

Apply the Variance Test to the correct option.

If YES (drivers avoid trains due to inability to work), the plan removes the main barrier and succeeds. If NO (drivers avoid trains due to schedules, cost, or location), Wi-Fi will not persuade them and the plan fails.

Answering this question in opposite directions yields opposite conclusions regarding the plan's success, confirming its utility.

Anahtar Kavram

Evaluating Plans and Useful Information

Tahmini Süre:1m 45s

Soru 1510Soru →

To earn the Global Eco-Standard certification, a textile manufacturer is required to source at least 80 percent of its organic cotton from certified sustainable farms. Apex Apparels recently completed a comprehensive audit establishing that over 85 percent of the organic cotton used in its manufacturing line originates from certified sustainable farms. Therefore, Apex Apparels will definitely be awarded the Global Eco-Standard certification this year.

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

It relies on an unrepresentative sample of apparel manufacturers to draw a broad conclusion about industry-wide certification standards.

It assumes without justification that achieving the certification will automatically result in an increase in Apex Apparels' market share.

It treats a requirement that must be satisfied to obtain the certification as a condition that guarantees the certification will be granted.

It mistakes a correlation between sustainable cotton sourcing and corporate profitability for a direct cause-and-effect relationship.

It infers that failing to meet the cotton sourcing threshold would have no negative impact on Apex Apparels' overall brand reputation.

Cevabı ve açıklamayı göster

Cevap: It treats a requirement that must be satisfied to obtain the certification as a condition that guarantees the certification will be granted.

Cevap

The argument treats a condition that is necessary for obtaining the certification as though it were sufficient to guarantee receiving the certification.

The argument establishes that sourcing at least 80 percent certified organic cotton is a necessary requirement ('is required to') for obtaining the Global Eco-Standard certification. Fulfilling a single necessary prerequisite does not guarantee that the certification will be granted, because Apex Apparels may fail to satisfy other unmentioned requirements (such as environmental compliance or waste management). The reasoning incorrectly treats this necessary prerequisite as a sufficient condition.

Adım Adım Çözüm

1

Identify the premises and main conclusion of the argument.

Premise 1: Sourcing at least 80% organic cotton from sustainable farms is required for certification. Premise 2: Apex Apparels sources 85%. Conclusion: Apex Apparels will definitely be awarded the certification.

Deconstructing the argument into premises and conclusion is essential for identifying logical leaps.

2

Analyze the conditional logic in the premise.

The phrase 'is required to' introduces a necessary condition (Certification → ≥80% Sustainable Cotton). Meeting the necessary condition (≥80% Sustainable Cotton) does not logically establish that the condition is sufficient to trigger the conclusion.

Differentiating between necessary prerequisites and sufficient guarantees tests validity.

3

Evaluate the choices to find the statement that accurately reflects this logical error.

The statement asserting that the argument treats a mandatory requirement as a guarantee precisely captures the confusion between necessary and sufficient conditions.

The correct option must describe the specific structural flaw without introducing out-of-scope concepts.

Anahtar Kavram

Confusing Necessary and Sufficient Conditions

Tahmini Süre:2m 0s

Soru 1511Soru →

If $p$ and $q$ are real numbers, what is the value of $p + q$ ?

(1) $p^2 q + p q^2 = 36$ and $p^2 + 2pq + q^2 = 9$
(2) $p^2 - q^2 = 15$

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 simplifying

(p+q)^2 = 9

yields two potential values for the sum:

p+q = 3

or

p+q = -3

. Combining each sum with

pq(p+q) = 36

gives corresponding products

pq = 12

and

pq = -12

. For real numbers

p

and

q

, the discriminant

S^2 - 4P

must be non-negative. The sum

p+q = 3

gives a negative discriminant

3^2 - 4(12) = -39

, which yields no real solutions for

p

and

q

. The sum

p+q = -3

gives a positive discriminant

(-3)^2 - 4(-12) = 57

, which yields valid real numbers. Thus,

p+q

uniquely equals

-3

.

Statement (2) alone is not sufficient because

p^2 - q^2 = (p-q)(p+q) = 15

allows infinitely many different values for

p+q

depending on

p-q

. Hence, the correct statement selection is that Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Adım Adım Çözüm

1

Rephrase and analyze Statement (1) algebraically.

From

p^2 + 2pq + q^2 = 9

, we have

(p + q)^2 = 9

, which implies

p + q = 3

or

p + q = -3

. Factor the second equation:

p^2 q + p q^2 = pq(p + q) = 36

.

Factoring exposes the sum

S = p + q

and product

P = pq

structure of the algebraic system.

2

Evaluate the real number constraint for Case 1 (

p + q = 3

) in Statement (1).

If

p + q = 3

, then

pq(3) = 36 \implies pq = 12

. For real numbers

p

and

q

with sum

3

and product

12

, they must be real roots of

t^2 - 3t + 12 = 0

. The discriminant is

\Delta = (-3)^2 - 4(1)(12) = 9 - 48 = -39 < 0

.

A negative discriminant means no real numbers

p

and

q

exist for which

p + q = 3

and

pq = 12

. Thus,

p + q = 3

is impossible.

3

Evaluate the real number constraint for Case 2 (

p + q = -3

) in Statement (1).

If

p + q = -3

, then

pq(-3) = 36 \implies pq = -12

. The corresponding quadratic equation for

p

and

q

is

t^2 + 3t - 12 = 0

, with discriminant

\Delta = 3^2 - 4(1)(-12) = 57 > 0

. Real solutions exist.

Since a positive discriminant guarantees real solutions for

p

and

q

,

p + q

must uniquely equal

-3

. Therefore, Statement (1) alone is sufficient.

4

Evaluate Statement (2) independently.

p^2 - q^2 = 15 \implies (p - q)(p + q) = 15

. For example, if

p = 4, q = 1

, then

p + q = 5

. If

p = 8, q = 7

, then

p + q = 15

.

Without knowing

p - q

, infinitely many pairs of real numbers satisfy

p^2 - q^2 = 15

with different sums

p + q

. Statement (2) alone is not sufficient.

Anahtar Kavram

Evaluating non-linear algebraic systems in Data Sufficiency using real variable discriminant constraints

Soru 1512Soru →

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

(1) $m - n$ is an integer.
(2) $m^2 - n^2$ is an 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.

Evaluating Statement (1) alone: If

m = \sqrt{2}

and

n = \sqrt{2}

, then

m - n = 0

(an integer), but

m + n = 2\sqrt{2}

is not an integer. If

m = 2

and

n = 1

, then

m - n = 1

(an integer) and

m + n = 3

is an integer. Thus, Statement (1) alone is not sufficient.

Evaluating Statement (2) alone: If

m = \sqrt{2}

and

n = 1

, then

m^2 - n^2 = 1

(an integer), but

m + n = \sqrt{2} + 1

is not an integer. If

m = 2

and

n = 1

, then

m^2 - n^2 = 3

(an integer) and

m + n = 3

is an integer. Thus, Statement (2) alone is not sufficient.

Evaluating Statements (1) and (2) together: Factoring gives

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

. If

m - n = k \neq 0

and

m^2 - n^2 = p

for integers

k

and

p

, then

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

. This establishes that

m + n

must be rational, but a rational number is not necessarily an integer. For example, if

m = \frac{5}{4}

and

n = -\frac{3}{4}

, then

m - n = 2

(an integer) and

m^2 - n^2 = 1

(an integer), but

m + n = \frac{1}{2}

is not an integer. If

m = 2

and

n = 0

, both statements hold and

m + n = 2

is an integer. Since

m + n

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

Adım Adım Çözüm

1

Analyze the question stem and identify variable constraints.

The variables

m

and

n

are defined as real numbers, NOT necessarily integers.

Failing to account for non-integer real values is a primary trap in GMAT Data Sufficiency number property questions.

2

Evaluate Statement (1) independently.

Statement (1) states

m - n = k

for some integer

k

.
If

m = 2

and

n = 1

,

m - n = 1

(integer) and

m + n = 3

(integer).
If

m = \sqrt{2}

and

n = \sqrt{2}

,

m - n = 0

(integer) and

m + n = 2\sqrt{2}

(not an integer).
Since

m + n

can be an integer or non-integer, Statement (1) is NOT sufficient.

Testing both integer and irrational values reveals that a difference being an integer does not constrain the sum to be an integer.

3

Evaluate Statement (2) independently.

Statement (2) states

m^2 - n^2 = p

for some integer

p

.
If

m = 2

and

n = 1

,

m^2 - n^2 = 3

(integer) and

m + n = 3

(integer).
If

m = \sqrt{2}

and

n = 1

,

m^2 - n^2 = 1

(integer) and

m + n = \sqrt{2} + 1

(not an integer).
Since

m + n

can be an integer or non-integer, Statement (2) is NOT sufficient.

Testing non-integer values shows that the difference of squares being an integer does not guarantee that the sum is an integer.

4

Evaluate Statements (1) and (2) together.

We have

m - n = k

and

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

for integers

k

and

p

.
If

k = 0

,

m = n

, so

m - n = 0

and

m^2 - n^2 = 0

. In this case

m + n = 2m

, which can be non-integer if

m = \sqrt{2}

.
If

k \neq 0

, then

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

. This proves that

m + n

is a rational number, but not necessarily an integer.
For instance, let

m = \frac{5}{4}

and

n = -\frac{3}{4}

:
-

m - n = \frac{5}{4} - \left(-\frac{3}{4}\right) = 2

(integer)
-

m^2 - n^2 = \frac{25}{16} - \frac{9}{16} = 1

(integer)
-

m + n = \frac{5}{4} + \left(-\frac{3}{4}\right) = \frac{1}{2}

(not an integer).
Conversely, if

m = 2

and

n = 0

,

m - n = 2

(integer),

m^2 - n^2 = 4

(integer), and

m + n = 2

(integer).
Because

m + n

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

Algebraic division demonstrates that the sum is guaranteed to be rational, but rational numbers include non-integer fractions.

Anahtar Kavram

Real Number Constraints vs. Integer Constraints in Data Sufficiency

Tahmini Süre:2m 0s

Soru 1513Soru →

To reduce cargo loss from food spoilage during long-distance transport, a logistics firm plans to equip all its refrigerated trucks with automated high-precision humidity sensors. The firm argues that because elevated humidity is the primary catalyst for mold proliferation in boxed produce, real-time sensor alerts allowing drivers to manually open external air vents whenever humidity spikes will significantly lower the rate of produce spoilage. Which of the following, if true, most undermines the reasoning behind the logistics firm's plan?

Opening external air vents during highway transit introduces ambient outdoor moisture and road dust into the cargo bay, creating optimal conditions for rapid mold spore activation inside the produce packaging.

Automated high-precision humidity sensors require higher annual calibration costs and driver training expenditures than the standard mechanical gauges currently installed in the fleet.

Real-time environmental alerts increase driver vigilance and dramatically decrease the average time required for fleet operators to detect refrigeration unit power failures.

Refrigerated shipments passing through arid geographical regions experience lower overall spoilage rates than shipments traveling along humid coastal transit corridors.

Mold proliferation is not the sole factor responsible for cargo degradation during multi-day commercial agricultural transport.

Cevabı ve açıklamayı göster

Cevap: Opening external air vents during highway transit introduces ambient outdoor moisture and road dust into the cargo bay, creating optimal conditions for rapid mold spore activation inside the produce packaging.

Cevap

The statement that opening external air vents during highway transit introduces ambient outdoor moisture and road dust into the cargo bay, creating optimal conditions for rapid mold spore activation inside produce packaging.

The correct answer identifies a fatal flaw in the plan's execution mechanism. The author assumes that opening external vents when humidity spikes will lower spoilage. However, if opening those vents introduces outside moisture and dust that actively accelerates mold spore activation inside the packaging, taking the planned action will actually increase or exacerbate produce spoilage rather than reduce it.

Adım Adım Çözüm

1

Deconstruct the argument into premise, plan, and central assumption.

Premise: Elevated humidity causes mold proliferation in boxed produce. Plan: Install real-time humidity sensors so drivers can open external air vents when humidity spikes. Conclusion: This plan will significantly lower produce spoilage.

Identifying the unstated assumption is essential for evaluating argument validity.

2

Identify the core underlying assumption of the plan.

The argument assumes that opening external air vents when humidity spikes will successfully lower internal humidity without introducing new factors that promote mold growth.

Weakening questions targeting plans typically break the connection between the action taken and the desired goal.

3

Evaluate the impact of introducing new evidence on the central assumption.

If opening the vents introduces ambient moisture and dust that activates mold spores inside the packaging, the proposed action directly causes the exact harm it was designed to prevent.

Showing that an action produces a counterproductive side effect directly undermines the feasibility of achieving the stated goal.

Anahtar Kavram

Plan-to-Goal Causal Breakdown and Counterproductive Side Effects

Soru 1514Soru →

In a commercial survey of $120$ retail stores, each store sells products from Brand P, Brand Q, or both. The average (arithmetic mean) monthly revenue of the stores that sell Brand P is $\$40,000$ , and the average monthly revenue of the stores that sell Brand Q is $\$50,000$ . What is the average monthly revenue of all $120$ stores combined?

(1) Exactly $30$ stores sell both Brand P and Brand Q, and their average monthly revenue is $\$60,000$ .
(2) Exactly $40$ stores sell only Brand P.

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.

The correct response identifies that neither statement alone provides enough information to determine both the exact store counts in each category and the overlap revenue sum, but combining both statements gives a unique system of linear equations that yields an exact combined average revenue of

\frac{\$5,000,000}{120} \approx \$41,666.67

.

Adım Adım Çözüm

1

Formulate the total revenue expression in terms of overlapping sets and subgroup means.

Let

n(P)

be the number of stores selling Brand P and

n(Q)

be the number of stores selling Brand Q. Total stores

N = n(P \text{ only}) + n(Q \text{ only}) + n(P \cap Q) = 120

. Total revenue

S_{total} = S(P) + S(Q) - S(P \cap Q) = 40,000 n(P) + 50,000 n(Q) - S(P \cap Q)

.

Stores selling both brands are counted twice when summing

S(P)

and

S(Q)

, so their revenue sum

S(P \cap Q)

must be subtracted once.

2

Evaluate Statement (1) alone.

Statement (1) gives

n(P \cap Q) = 30

and average overlap revenue

= \$60,000 \implies S(P \cap Q) = 30 \times 60,000 = 1,800,000

. Also

n(P) + n(Q) = 120 + 30 = 150

.

Since

n(P)

and

n(Q)

can still vary while their sum is

150

(e.g.,

n(P)=70, n(Q)=80

vs

n(P)=90, n(Q)=60

),

S_{total} = 40,000 n(P) + 50,000 n(Q) - 1,800,000

yields multiple possible total values. Statement (1) alone is INSUFFICIENT.

3

Evaluate Statement (2) alone.

Statement (2) gives

n(P \text{ only}) = 40

. Thus

n(Q) = 120 - 40 = 80

.

No revenue information or overlap count is given. Statement (2) alone is INSUFFICIENT.

4

Evaluate Statements (1) and (2) together.

From Statement (2),

n(P \text{ only}) = 40

. From Statement (1),

n(P \cap Q) = 30

. Thus

n(P) = 40 + 30 = 70

. Since

n(P) + n(Q) = 150

,

n(Q) = 80

.

We now have exact values:

n(P) = 70

,

n(Q) = 80

,

S(P \cap Q) = 1,800,000

.

S_{total} = 40,000(70) + 50,000(80) - 1,800,000 = 2,800,000 + 4,000,000 - 1,800,000 = 5,000,000

. Combined mean revenue

= \frac{5,000,000}{120} = \$41,666.67

. Both statements together are SUFFICIENT.

Anahtar Kavram

Weighted averages in overlapping sets requiring exact subgroup counts and sum reconciliations.

Soru 1515Soru →

To reduce financial losses caused by perishable produce spoilage, a regional supermarket chain plans to replace its standard delivery trucks with high-speed refrigerated vans, cutting transit time from distribution warehouses to retail stores by 40 percent. Company executives argue that because fruits and vegetables degrade continuously while in transit, this faster transport schedule will significantly decrease the proportion of produce that spoils before reaching store shelves. Which of the following, if true, most seriously weakens the executives' argument?

The vast majority of produce spoilage occurs during backroom holding periods at retail stores prior to shelf placement due to inadequate store refrigeration capacity.

High-speed refrigerated vans maintain more consistent internal storage temperatures during transit than standard delivery trucks do.

The initial capital expenditure required to purchase the new fleet of vans exceeds the expected monetary savings from reduced food waste over the first two years.

Competing grocery chains have successfully lowered their logistics expenses by outsourcing delivery routes to independent third-party carriers.

Produce shipments transported during winter months experience minimal spoilage regardless of the type of vehicle utilized.

Cevabı ve açıklamayı göster

Cevap: The vast majority of produce spoilage occurs during backroom holding periods at retail stores prior to shelf placement due to inadequate store refrigeration capacity.

Cevap

The argument is most seriously weakened by the statement that the vast majority of produce spoilage occurs during backroom holding periods at retail stores prior to shelf placement due to inadequate store refrigeration capacity.

The executives assume that transit time is a major driver of overall produce spoilage before shelf placement. The correct option demonstrates that the vast majority of spoilage happens after transit while produce waits in store backrooms with poor refrigeration. Because transit is not the primary point of failure, cutting transit time will not significantly decrease the proportion of produce that spoils.

Adım Adım Çözüm

1

Identify the premise and conclusion of the argument.

Premise: Produce degrades continuously during transit, and high-speed vans will reduce transit time by 40%. Conclusion: Faster transport will significantly decrease the proportion of produce that spoils before reaching shelves.

Understanding the precise logical link between the premise (transit time reduction) and the conclusion (spoilage reduction) is required to identify unstated assumptions.

2

Identify the central assumption.

The argument assumes that transit duration is a primary cause of total pre-shelf spoilage, and that eliminating transit time will substantially impact total spoilage rates.

A weakening statement must target this underlying assumption by showing that transit time reduction will not produce the expected outcome.

3

Evaluate the choices to find new information that undermines the central assumption.

The correct choice reveals that the primary location of spoilage is backroom store holding areas, not transit. Thus, reducing transit time leaves the main source of spoilage completely unaddressed.

Demonstrating an unaddressed major bottleneck undermines the claim that the plan will achieve its intended goal.

Anahtar Kavram

Plan-to-Goal Weakening and Bottleneck Identification

Soru 1516Soru →

### Tab 1: Corporate Remote Work Policy
Employees in the Operations division are eligible for up to two remote workdays per week, provided their quarterly performance rating is 4.0 or higher. However, any employee whose primary duties involve handling confidential financial records is strictly prohibited from working remotely, regardless of department or performance rating.

### Tab 2: IT Security Memorandum
Employees assigned to the Operations Billing unit routinely process wire transfers and customer payment details, classifying their duties as handling confidential financial records. Employees assigned to the Operations Logistics unit focus solely on inventory dispatch and do not handle confidential financial records.

Based on the Corporate Remote Work Policy and the IT Security Memorandum, which of the following statements are supported? Select all that apply.

Geçerli olan tümünü seçin

An employee in the Operations Logistics unit with a performance rating of 4.5 is eligible for up to two remote workdays per week.

An employee in the Operations Billing unit with a performance rating of 5.0 is prohibited from working remotely.

All employees in the Operations division with a performance rating of 4.0 or higher are eligible for remote work.

Employees in the Operations Logistics unit are eligible for remote work regardless of their quarterly performance rating.

Operations Billing employees may work remotely if their quarterly performance rating exceeds 4.5.

Cevabı ve açıklamayı göster

Cevap: An employee in the Operations Logistics unit with a performance rating of 4.5 is eligible for up to two remote workdays per week.; An employee in the Operations Billing unit with a performance rating of 5.0 is prohibited from working remotely.

Cevap

The supported statements are: 1) An employee in the Operations Logistics unit with a performance rating of 4.5 is eligible for up to two remote workdays per week; and 2) An employee in the Operations Billing unit with a performance rating of 5.0 is prohibited from working remotely.

Synthesizing Tab 1 and Tab 2 shows that remote work eligibility requires being in Operations, having a performance rating of 4.0 or higher, and NOT handling confidential financial records. For an Operations Logistics employee with a 4.5 rating, all conditions are satisfied because Tab 2 states Logistics does not handle financial records. For an Operations Billing employee, Tab 2 classifies their duties as handling confidential financial records, triggering the strict prohibition in Tab 1 regardless of their 5.0 rating.

Adım Adım Çözüm

1

Analyze general eligibility and exception criteria from Tab 1.

General rule: Operations division + rating

\geq 4.0 \rightarrow

up to 2 remote days/week. Absolute exception: Handling confidential financial records

\rightarrow

remote work prohibited.

Establishing the policy baseline and override rules.

2

Cross-reference unit roles from Tab 2 with Tab 1 rules.

Operations Billing handles confidential financial records (prohibited from remote work). Operations Logistics does NOT handle confidential financial records (eligible if rating

\geq 4.0

).

Synthesizing text across documents to evaluate specific employee profiles.

3

Evaluate each option against the synthesized rules.

Logistics employee with 4.5 rating meets both conditions. Billing employee with 5.0 rating is blocked by the confidentiality exception.

Determining which statements are fully supported by combining both sources.

Anahtar Kavram

Cross-tab conditional rule evaluation and policy exception synthesis.

Soru 1517Soru →

To receive authorization for deployment across state government networks, a software vendor is required to undergo a comprehensive third-party cybersecurity audit and remediate all critical vulnerabilities identified. Apex Systems recently completed a third-party cybersecurity audit and successfully resolved every critical vulnerability highlighted in the auditor's report. Therefore, Apex Systems will certainly receive authorization to deploy its software across state government networks next month.

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

It assumes that completing a cybersecurity audit causes an increase in software performance rather than merely coinciding with it.

It presumes that state government networks have stricter security standards than private commercial networks.

It treats a condition that is essential for obtaining deployment authorization as though it were sufficient to guarantee that authorization.

It fails to consider that resolving critical vulnerabilities might inadvertently introduce new, minor software glitches.

It relies on a shift in the meaning of the term 'critical vulnerabilities' between the premises and the conclusion.

Cevabı ve açıklamayı göster

Cevap: It treats a condition that is essential for obtaining deployment authorization as though it were sufficient to guarantee that authorization.

Cevap

The argument incorrectly treats a mandatory requirement (a necessary condition) for deployment authorization as a guarantee (a sufficient condition) that authorization will be granted.

The correct answer accurately highlights the core logical error in the passage. The author establishes that completing an audit and fixing critical vulnerabilities is a mandatory prerequisite (necessary condition) for deployment authorization. However, the author incorrectly concludes that fulfilling this prerequisite is enough to guarantee authorization (treating it as a sufficient condition), ignoring the possibility that additional requirements must be met.

Adım Adım Çözüm

1

Identify the premises and main conclusion of the argument.

Premise: Undergoing an audit and remediating critical vulnerabilities is required ('is required to') for authorization. Premise: Apex Systems completed the audit and remediated all critical vulnerabilities. Conclusion: Apex Systems will certainly receive deployment authorization.

Deconstructing the argument isolates the conditional relationship established by the author.

2

Analyze the formal logic of the conditional requirement.

The phrase 'is required to' indicates a necessary condition: Authorization → Audit & Remediation. Fulfilling the requirement means the necessary condition is satisfied, but it does not mean no other requirements exist.

Distinguishing necessary conditions from sufficient conditions is essential to evaluating argument validity.

3

Evaluate the logical gap in the conclusion.

The author concludes that satisfying the requirement guarantees authorization (Audit & Remediation → Authorization). This is a classic formal fallacy of confusing a necessary condition with a sufficient condition.

Matching the structural breakdown to the correct flaw description reveals the correct answer choice.

Anahtar Kavram

Confusing Necessary and Sufficient Conditions

Soru 1518Soru →

The table below details the quarterly revenues for four operating divisions of a logistics firm in 2025:

Division	Q1 Revenue ($)	Q2 Revenue ($)
North	$80,000$	$100,000$
South	$150,000$	$180,000$
East	$120,000$	$144,000$
West	$200,000$	$230,000$

What is the percentage increase in revenue from Q1 to Q2 for the North division?

20\%

25\%

80\%

125\%

12.5\%

Cevabı ve açıklamayı göster

Cevap: $25\%$

Cevap

The percentage increase in revenue for the North division from Q1 to Q2 is

25\%

.

The percentage increase is calculated as

\frac{\text{Q2 Revenue} - \text{Q1 Revenue}}{\text{Q1 Revenue}} \times 100\%

. For the North division,

\frac{100,000 - 80,000}{80,000} = \frac{20,000}{80,000} = 0.25 = 25\%

.

Adım Adım Çözüm

1

Find the absolute change in revenue for the North division from Q1 to Q2.

Change =

\$100,000 - \$80,000 = \$20,000

.

Percentage increase requires comparing the change relative to the initial starting value.

2

Identify the base (initial) value for the percentage calculation.

Base value = Q1 revenue =

\$80,000

.

The base for percentage change calculation is always the initial period value (Q1).

3

Calculate the percentage increase by dividing the change by the base value and multiplying by

100\%

.

Percentage Increase =

\frac{20,000}{80,000} \times 100\% = 0.25 \times 100\% = 25\%

.

To convert a ratio to a percentage, multiply the fractional increase by

100

.

Anahtar Kavram

Percentage Change from Table Data

Tahmini Süre:45s

Soru 1519Soru →

To reduce urban air pollution and traffic congestion, the municipality of Ardenville plans to construct a light-rail line connecting its dense outer suburbs to the commercial downtown core. City planners argue that because traveling by light rail generates significantly fewer carbon emissions per passenger-mile than driving a private automobile, building the light-rail system will lead to a net decrease in Ardenville's total commuter-related carbon emissions over the next decade.

Which of the following would it be most useful to determine in evaluating the validity of the city planners' argument?

Whether a substantial proportion of the projected light-rail passengers will consist of individuals who currently commute by walking or cycling rather than by driving private automobiles.

Whether neighboring municipalities are considering similar light-rail expansion projects within their own suburban corridors during the next decade.

Whether the municipal government will need to raise local property taxes to cover potential construction budget overruns for the light-rail project.

Whether driving a private automobile produces higher carbon emissions per passenger-mile than riding a conventional heavy-rail locomotive.

Whether commuters who switch from private automobiles to light rail will also report lower overall daily stress levels during peak hours.

Cevabı ve açıklamayı göster

Cevap: Whether a substantial proportion of the projected light-rail passengers will consist of individuals who currently commute by walking or cycling rather than by driving private automobiles.

Cevap

Determining whether a substantial proportion of projected light-rail passengers previously walked or cycled rather than drove private automobiles is most useful for evaluating the argument.

The correct answer directly tests the core assumption of the argument using the Test of Variance. The planners claim that total carbon emissions will fall because light rail emits less per passenger-mile than private cars. However, if the new ridership is drawn primarily from people who currently produce zero emissions by walking or biking, adding a light-rail system will add new emissions to the environment, causing total emissions to increase. Conversely, if riders are drawn almost entirely from car commuters, total emissions will fall. Because extreme answers to this question yield opposite outcomes for the argument's validity, it is the crucial information to determine.

Adım Adım Çözüm

1

Deconstruct the argument structure

Premise: Light rail produces fewer emissions per passenger-mile than private automobiles. Conclusion: Constructing a light-rail system will decrease Ardenville's total commuter-related emissions.

Identifying the logic leap between relative emissions per passenger-mile and total net emissions.

2

Identify the unstated assumption

The argument assumes that light-rail riders will primarily be drawn from high-emission private automobile drivers, not zero-emission pedestrians or cyclists.

If riders shift from zero-emission modes to light rail, overall emissions will rise despite the light rail being cleaner than automobiles.

3

Apply the Test of Variance to the correct option

Answering 'Yes' to whether riders come from walking/cycling undermines the conclusion (emissions increase). Answering 'No' supports the conclusion (emissions decrease).

Opposite extreme answers produce opposite impacts on the validity of the conclusion.

Anahtar Kavram

Evaluating Argument Validity and Test of Variance

Soru 1520Soru →

In a laboratory, $80$ experimental trials were conducted. Each trial was monitored by Sensor P, Sensor Q, or both. The average (arithmetic mean) duration of the trials monitored by Sensor P only was $45$ minutes, and the average duration of the trials monitored by Sensor Q only was $60$ minutes. What was the average duration of all $80$ trials?

(1) Exactly $20$ trials were monitored by Sensor P only, and $30$ trials were monitored by Sensor Q only.
(2) The average duration of all trials monitored by Sensor Q was $55$ minutes, and the average duration of the trials monitored by both sensors was $50$ minutes.

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 to answer the question, but neither statement alone is sufficient.

Evaluating Statement (1) gives the counts for all three disjoint regions (

20

P-only,

30

Q-only, and

30

Both), but does not provide the mean duration of the

30

trials in the 'Both' category. Evaluating Statement (2) gives the mean duration of the 'Both' category (

50

minutes) and establishes that

n_{B} = n_{Q}

, but does not give absolute counts. Combining both statements provides all subgroup sizes and their respective means, allowing us to calculate the exact weighted average of

52.5

minutes.

Adım Adım Çözüm

1

Formulate the algebraic expressions for total trials and total duration.

Let

n_{P}

,

n_{Q}

, and

n_{B}

be the counts for Sensor P only, Sensor Q only, and Both sensors respectively.

n_{P} + n_{Q} + n_{B} = 80

. The total duration is

45 n_{P} + 60 n_{Q} + M_{B} n_{B}

, where

M_{B}

is the mean duration of the trials monitored by both sensors.

Deconstruct the overlapping sets into three mutually exclusive subgroups: P only, Q only, and Both.

2

Evaluate Statement (1) alone.

n_{P} = 20

and

n_{Q} = 30 \implies n_{B} = 80 - 20 - 30 = 30

. Total duration

= 45(20) + 60(30) + M_{B}(30) = 2700 + 30 M_{B}

.

Since the mean duration

M_{B}

for trials monitored by both sensors is unknown, Statement (1) is insufficient.

3

Evaluate Statement (2) alone.

The total group Q consists of Q only (

n_{Q}

, mean

60

) and Both (

n_{B}

, mean

50

). Average for Q is

55 \implies \frac{60 n_{Q} + 50 n_{B}}{n_{Q} + n_{B}} = 55 \implies 5 n_{B} = 5 n_{Q} \implies n_{B} = n_{Q}

.

Statement (2) proves

n_{B} = n_{Q}

, which gives

n_{P} + 2 n_{Q} = 80

, but without specific numbers for

n_{Q}

or

n_{P}

, the overall average cannot be uniquely determined. Thus Statement (2) is insufficient.

4

Evaluate Statements (1) and (2) together.

From (1),

n_{P} = 20

and

n_{Q} = 30

, so

n_{B} = 30

. From (2),

M_{B} = 50

. Total duration

= 45(20) + 60(30) + 50(30) = 900 + 1800 + 1500 = 4200

. Overall average

= \frac{4200}{80} = 52.5

minutes.

Combining both statements yields a unique numeric value for the overall average duration.

Anahtar Kavram

Weighted Averages and Overlapping Sets Partitioning

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