All practice questions

Question 1681Question →

A chemist mixes $x$ liters of a $20\%$ acid solution with $y$ liters of a $50\%$ acid solution to produce $30$ liters of a $40\%$ acid solution. How many liters of the $20\%$ acid solution were used in the mixture?

Show answer & explanation

Answer: 10

Answer

10 liters of the 20% acid solution were used.

Solving the system of simultaneous linear equations

x + y = 30

and

0.20x + 0.50y = 12

yields

x = 10

liters.

Step-by-Step Solution

1

Formulate the linear system of equations representing total volume and total pure acid content.

x + y = 30

and

0.20x + 0.50y = 12

.

The sum of component volumes equals total volume, and the sum of pure acid contents equals total pure acid.

2

Substitute

y = 30 - x

into the pure acid equation.

0.20x + 0.50(30 - x) = 12

Reduces the two-variable system to a single linear equation in terms of

x

.

3

Expand and solve for

x

.

15 - 0.30x = 12 \implies -0.30x = -3 \implies x = 10

Isolates the target variable

x

representing the volume of the 20% acid solution.

Key Concept

Simultaneous Linear Equations in Mixture Problems

Estimated Time:1m 0s

Question 1682Question →

Read the argument below regarding retail pricing algorithms, then match each statement from the text to its corresponding logical role within the argument.

Argument:
Although proponents of automated dynamic pricing systems argue that such algorithms merely optimize market efficiency by responding instantly to supply fluctuations, regulators note that concurrent deployment of identical algorithms by competing retailers frequently leads to implicit price coordination. Such algorithmic tacit collusion artificially inflates consumer prices even in the absence of explicit communication among firms. Because existing antitrust laws require proof of explicit agreement to establish illegal price-fixing, current legal frameworks are fundamentally ill-equipped to curb algorithmic collusion. Regulators must therefore update antitrust standards to encompass market outcomes generated by shared pricing algorithms.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches map each excerpt to its exact structural role in the argument: the policy directive regarding updating antitrust standards is the main conclusion; the claim that current frameworks are ill-equipped is an intermediate conclusion; the observation about price coordination is a supporting premise; and the claim about optimizing market efficiency is an opposing viewpoint.

The argument builds logically toward a specific policy recommendation: updating antitrust standards. The statement regarding current frameworks being ill-equipped functions as a subsidiary conclusion supported by legal premises, which in turn justifies the main claim. The observation that identical algorithms lead to price coordination is a factual premise supporting the existence of market failure, and the assertion about optimizing market efficiency represents an opposing perspective introduced in a concessionary clause.

Step-by-Step Solution

1

Analyze the overall structure and direction of the argument.

Identify the author's primary goal: persuading the audience that antitrust standards must be updated.

The author uses 'therefore' in the final sentence to mark the overarching prescriptive recommendation.

2

Distinguish the main conclusion from supporting sub-claims.

Categorize the statement about current frameworks being ill-equipped as an intermediate conclusion.

This sub-claim is supported by the requirement of explicit agreement proof and itself explains why standards must be updated.

3

Identify evidence premises and opposing context.

Classify the statement regarding implicit price coordination as a factual premise, and the proponents' efficiency argument as an opposing viewpoint.

The efficiency claim is prefaced by 'Although proponents... argue', indicating a concession/counter-position, while the price coordination statement provides empirical evidence.

Key Concept

Identifying structural roles and distinguishing main conclusions from intermediate conclusions and premises.

Question 1683Question →

A tech company sells two types of service plans: Basic and Enterprise. Last month, what percentage of the company's total revenue from these two service plans was generated by sales of the Enterprise plan?

(1) Last month, the price of an Enterprise plan was $250\%$ of the price of a Basic plan, and the number of Basic plans sold was $60\%$ greater than the number of Enterprise plans sold.
(2) Last month, total revenue generated from sales of the Basic plan was $\$120,000$ .

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.

Show answer & explanation

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

Answer

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

Statement (1) establishes exact multiplier relationships for both price and quantity (

P_E = 2.5 P_B

and

N_B = 1.6 N_E

). When computing the proportion of revenue generated by the Enterprise plan, all unknown variables (

P_B

and

N_E

) cancel out cleanly, producing a single, deterministic percentage of

\frac{25}{41} \times 100\%

. Statement (2) only specifies the dollar revenue for the Basic plan, leaving the Enterprise plan's revenue completely unconstrained. Thus, Statement (1) alone is sufficient, while Statement (2) alone is not.

Step-by-Step Solution

1

Formulate the target ratio algebraically

Target percentage

= \frac{R_E}{R_E + R_B} \times 100\%

, where

R_E = P_E \times N_E

and

R_B = P_B \times N_B

.

Total revenue is the sum of Enterprise revenue (

R_E

) and Basic revenue (

R_B

).

2

Evaluate Statement (1)

P_E = 2.5 P_B

and

N_B = 1.6 N_E

. Therefore,

R_E = 2.5 P_B N_E

and

R_B = 1.6 P_B N_E

. The revenue ratio is

\frac{R_E}{R_B} = \frac{2.5}{1.6} = \frac{25}{16}

.

Substituting these expressions into the target formula yields

\frac{25 P_B N_E}{25 P_B N_E + 16 P_B N_E} = \frac{25}{41} \approx 60.98\%

. Because a single, unique percentage is obtained, Statement (1) alone is sufficient.

3

Evaluate Statement (2)

R_B = \$120,000

, but

R_E

remains unknown.

Knowing only the total revenue from Basic plans provides no information about the Enterprise revenue or its share of total revenue. Thus, Statement (2) alone is insufficient.

Key Concept

Data Sufficiency Evaluation of Percentages via Relative Variable Relationships

Question 1684Question →

An investment fund holds a portfolio consisting entirely of short-term bonds yielding $4\%$ annually and long-term bonds yielding $8\%$ annually. In 2025, the total dollar amount invested in short-term bonds changed by $p\%$ , and the total dollar amount invested in long-term bonds changed by $q\%$ . Was the portfolio's overall percentage yield higher in 2025 than in 2024?

(1) In 2024, the amount invested in short-term bonds was twice the amount invested in long-term bonds.
(2) In 2025, the annual interest income earned from long-term bonds was greater than the annual interest income earned from short-term bonds.

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.

Show answer & explanation

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

Answer

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

Rephrasing the question stem algebraically demonstrates that the overall portfolio yield increases if and only if the relative proportion of the higher-yielding asset (

8\%

) increases compared to the lower-yielding asset (

4\%

), which simplifies to the condition

q > p

. Statement (1) alone provides only the initial ratio

S = 2L

, leaving

p

and

q

unconstrained. Statement (2) alone yields

0.08L(1 + q/100) > 0.04S(1 + p/100)

, which cannot be simplified without knowing the ratio

S/L

. Combining both statements allows substituting

S = 2L

into Statement (2)'s inequality, yielding

2L(1 + q/100) > 2L(1 + p/100) \implies q > p

, which definitively answers 'Yes'. Thus, both statements together are sufficient.

Step-by-Step Solution

1

Rephrase the question target algebraically.

Overall yield in 2024 is

Y_{2024} = \frac{0.04S + 0.08L}{S + L}

. Overall yield in 2025 is

Y_{2025} = \frac{0.04S(1 + p/100) + 0.08L(1 + q/100)}{S(1 + p/100) + L(1 + q/100)}

. Since

Y

is a weighted average of two fixed values (

4\%

and

8\%

),

Y_{2025} > Y_{2024}

if and only if the weight of the higher-yielding component (

8\%

) increases relative to the lower-yielding component (

4\%

). That requires

\frac{L(1 + q/100)}{S(1 + p/100)} > \frac{L}{S}

, which simplifies to

1 + q/100 > 1 + p/100 \iff q > p

. The target question is rephrased as: 'Is

q > p

?'

Simplifying the question stem reveals that the initial investment amounts

S

and

L

drop out when asking about relative yield changes.

2

Evaluate Statement (1) independently.

Statement (1) gives

S = 2L

. This provides information about the baseline 2024 portfolio composition, but provides no information regarding

p

or

q

. Therefore, we cannot determine whether

q > p

. Statement (1) alone is NOT sufficient.

Knowing initial weights without growth rates does not allow determination of relative growth rate direction.

3

Evaluate Statement (2) independently.

Statement (2) states that interest from long-term bonds in 2025 exceeded interest from short-term bonds:

0.08L(1 + q/100) > 0.04S(1 + p/100)

, which simplifies to

2L(1 + q/100) > S(1 + p/100)

. Because the ratio

S/L

is unknown, this inequality could hold even if

q \le p

(if

S

is very small relative to

L

) or only when

q > p

(if

S

is large). Statement (2) alone is NOT sufficient.

Without knowing

S/L

, the inequality

2L(1+q/100) > S(1+p/100)

cannot be reduced to compare

q

and

p

.

4

Evaluate Statements (1) and (2) together.

From Statement (1), substitute

S = 2L

into Statement (2)'s inequality:

2L(1 + q/100) > (2L)(1 + p/100)

. Dividing both sides by

2L

(since

L > 0

) gives

1 + q/100 > 1 + p/100 \iff q > p

. This provides a definitive 'Yes' to the rephrased question target. BOTH statements together are SUFFICIENT.

Combining the baseline ratio with the interest inequality allows

S

and

L

to cancel, establishing

q > p

definitively.

Key Concept

Data Sufficiency Question Stem Rephrasing and Weighted Average Yield Ratios

Question 1685Question →

In a GMAT Data Sufficiency question asking for the specific numerical values of two variables $x$ and $y$ , if Statement (1) provides the equation $2x + 3y = 12$ and Statement (2) provides the equation $4x + 6y = 24$ , combining both statements is sufficient to determine unique values for $x$ and $y$ .

True

False

Show answer & explanation

Answer: False

Answer

The statement is False.

The correct answer is False because Statement (2) is a scalar multiple of Statement (1). Linearly dependent equations do not reduce the number of unknown variables or narrow down the solution set to a single unique pair

(x, y)

. Therefore, combining both statements does not yield sufficient information to answer the question stem.

Step-by-Step Solution

1

Analyze Statement (1) equation

Statement (1) provides

2x + 3y = 12

, which defines a line with infinitely many valid coordinate pairs

(x, y)

.

A single linear equation in two variables has infinitely many solutions.

2

Analyze Statement (2) equation and test for linear independence

Dividing Statement (2),

4x + 6y = 24

, by

2

yields

2x + 3y = 12

, which is identical to Statement (1).

Linearly dependent equations provide redundant data and do not provide a distinct second constraint.

3

Evaluate the combination of Statement (1) and Statement (2)

Combining both statements produces no new information beyond

2x + 3y = 12

, leaving infinitely many solution pairs.

Determining unique values for two variables requires two linearly independent equations. Because these statements are dependent, combining them remains insufficient.

Key Concept

Linear Independence in Statement Combination

Question 1686Question →

The table below details 2025 performance and operational metrics for seven metropolitan transit corridors:

Corridor Code	Vehicle Fleet Size (Buses)	Zero-Emission Vehicles (%)	On-Time Departure Rate (%)	Annual Passenger Trips (Millions)	Operating Cost per Passenger Trip ($)
C-North	120	45%	92%	18.0	$2.40
C-South	200	60%	85%	32.0	$1.95
C-East	80	25%	94%	10.0	$3.10
C-West	150	40%	88%	22.5	$2.20
C-Central	250	70%	81%	45.0	$1.80
C-Harbor	90	55%	90%	12.0	$2.85
C-Airport	110	30%	96%	15.0	$2.60

Match each of the three statements on the left with its correct evaluation description on the right based on the data provided.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement 1 matches the evaluation confirming it is True (

2.40 > 2.2026

); Statement 2 matches the evaluation confirming it is False because

165 > 113.33

; Statement 3 matches the evaluation confirming it is False due to C-South failing the conditional threshold.

Each statement matches its precise evaluation. Statement 1 correctly identifies that the median cost per trip (

2.40

) exceeds the weighted average system cost (

2.2026

). Statement 2 identifies that the mean fleet size for high zero-emission corridors (

165

) is higher, not lower, than for low zero-emission corridors (

113.33

). Statement 3 correctly identifies that C-South is excluded altogether because its on-time departure rate is

85\%

, below the required

88\%

threshold.

Step-by-Step Solution

1

Calculate the median operating cost and system-wide weighted average operating cost for Statement 1.

Corridor operating costs in ascending order:

\$1.80, \$1.95, \$2.20, \$2.40, \$2.60, \$2.85, \$3.10

. Median =

\$2.40

. Total system operating cost =

\$340.3\text{ million}

; total trips =

154.5\text{ million}

. Weighted average =

\$340.3 / 154.5 \approx \$2.2026

. Median (

\$2.40

) > Weighted Average (

\$2.2026

). Statement 1 is True.

Evaluates median vs. weighted average accurately across unequal trip volumes.

2

Filter and calculate subset fleet means for Statement 2.

Corridors with Zero-Emission

\ge 45\%

: C-North (

120

), C-South (

200

), C-Central (

250

), C-Harbor (

90

). Mean =

660 / 4 = 165

. Corridors with Zero-Emission

< 45\%

: C-East (

80

), C-West (

150

), C-Airport (

110

). Mean =

340 / 3 \approx 113.33

.

165 > 113.33

, so the statement claiming

165 < 113.33

is False.

Compares conditional subgroup averages correctly.

3

Apply conditional filtering for Statement 3 based on On-Time Departure Rate.

Corridors with On-Time Departure Rate

\ge 88\%

include C-North, C-East, C-West, C-Harbor, and C-Airport. C-South has an On-Time Departure Rate of

85\% < 88\%

, so it is excluded from the comparison set. Statement 3 is False.

Prevents evaluating metrics on elements that do not satisfy pre-requisite conditional criteria.

Key Concept

Multi-Statement Boolean Evaluation on Tabular Data

Question 1687Question →

If $x$ and $y$ are non-zero real numbers, what is the value of the ratio $\frac{x}{y}$ ?

(1) $x + y = 10$
(2) $3x - 5y = 0$

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.

Show answer & explanation

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

Answer

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

Evaluating Statement (2) independently of Statement (1) shows that the equation

3x - 5y = 0

can be rearranged to

3x = 5y

. Dividing both sides by

3y

(since

y \neq 0

) yields

\frac{x}{y} = \frac{5}{3}

. This gives a single, unique value for the target ratio without needing any information from Statement (1). Meanwhile, Statement (1) alone (

x + y = 10

) allows infinitely many pairs of non-zero real numbers

(x, y)

, resulting in different values for the ratio

\frac{x}{y}

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

Step-by-Step Solution

1

Evaluate Statement (1) independently

Statement (1) gives

x + y = 10

. If

x = 5

and

y = 5

, then

\frac{x}{y} = 1

. If

x = 8

and

y = 2

, then

\frac{x}{y} = 4

.

Since multiple values are possible for the ratio

\frac{x}{y}

, Statement (1) alone is not sufficient.

2

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

Statement (2) gives

3x - 5y = 0 \implies 3x = 5y \implies \frac{x}{y} = \frac{5}{3}

.

Since

y \neq 0

, dividing both sides by

3y

yields a single, unique value of

\frac{5}{3}

for the ratio

\frac{x}{y}

.

3

Conclude Data Sufficiency determination

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

Statement (2) independently answers the question stem completely.

Key Concept

Evaluating Statement 2 independently of Statement 1 in Data Sufficiency

Question 1688Question →

An analysis of a technology firm's policy statement reveals a logical flaw based on equivocation:

"Our committee mandates that all software deployments must ensure user security. Comprehensive data encryption guarantees technical security against external cyberattacks. Therefore, deploying robust data encryption fully satisfies a technology firm's ethical security responsibilities toward its customer base."

Match each key term from the argument on the left to the specific shift in meaning it undergoes between the premise context and the conclusion context on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: 'Security' matches with the shift from technical protection to broad ethical safeguarding; 'Satisfies responsibilities' matches with the shift from technical compliance to fulfilling overall moral duties; and 'External cyberattacks' matches with the shift from technical network intrusions to general breaches of user trust.

The argument commits an equivocation flaw by introducing terms under narrow, technical definitions in the premises and quietly broadening their definitions in the conclusion. 'Security' shifts from technical data protection to comprehensive ethical duty; 'Satisfies responsibilities' shifts from meeting specific software parameters to fulfilling complete moral duties; and 'External cyberattacks' shifts from specific cyber intrusions to any violation of consumer trust.

Step-by-Step Solution

1

Analyze how the term 'Security' is introduced in the premise versus the conclusion.

The premise restricts 'security' to technical data encryption against cyber threats, whereas the conclusion equates it to broad corporate ethical duties.

Identifying shifts in definition is essential for exposing equivocation flaws.

2

Examine the scope shift in 'Satisfies responsibilities'.

Meeting technical encryption criteria (a narrow obligation) is conflated with fulfilling all ethical duties owed to users.

The argument uses technical compliance to improperly claim total moral compliance.

3

Evaluate the phrase 'External cyberattacks' across contexts.

Preventing unauthorized digital access is assumed to cover all dimensions of user trust and safety.

Conflating a specific threat type with overall user safety illustrates a shift in semantic scope.

Key Concept

Equivocation and Shift in Term Meaning

Question 1689Question →

If $x$ and $y$ are real numbers such that $x \neq y$ , what is the value of $\frac{x+y}{x-y}$ ?

(1) $x^2 + y^2 = 5xy$
(2) $x^2 - y^2 = 12$

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.

Show answer & explanation

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

Answer

Both statements together are sufficient, but neither statement alone is sufficient.

Evaluating statement (1) reveals that

\left(\frac{x+y}{x-y}\right)^2 = \frac{7}{3}

, leading to two possible values:

\sqrt{\frac{7}{3}}

and

-\sqrt{\frac{7}{3}}

. Thus, statement (1) alone is insufficient. Statement (2) states that

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

, which shows that

(x+y)

and

(x-y)

have the same sign, meaning their quotient must be positive. Combining both statements eliminates the negative value, yielding the unique result

\sqrt{\frac{7}{3}}

. Therefore, both statements together are sufficient.

Step-by-Step Solution

1

Analyze Statement (1) algebraically.

From

x^2 + y^2 = 5xy

, add

2xy

to both sides to obtain

(x+y)^2 = 7xy

, and subtract

2xy

from both sides to obtain

(x-y)^2 = 3xy

. Taking the ratio gives

\left(\frac{x+y}{x-y}\right)^2 = \frac{7xy}{3xy} = \frac{7}{3}

. Taking the square root yields

\frac{x+y}{x-y} = \pm \sqrt{\frac{7}{3}}

.

Since two distinct numerical values are possible, Statement (1) alone is NOT sufficient.

2

Analyze Statement (2) algebraically.

Statement (2) gives

x^2 - y^2 = 12

, which factors as

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

.

Knowing only the product of

(x+y)

and

(x-y)

does not provide enough information to determine the value of their quotient

\frac{x+y}{x-y}

. Statement (2) alone is NOT sufficient.

3

Combine Statement (1) and Statement (2).

Rewrite the target ratio using Statement (2):

\frac{x+y}{x-y} = \frac{(x+y)(x-y)}{(x-y)^2} = \frac{12}{(x-y)^2}

. Because

(x-y)^2 > 0

for

x \neq y

, the ratio must be strictly positive. Combining this with Statement (1), which requires

\frac{x+y}{x-y} = \pm \sqrt{\frac{7}{3}}

, uniquely isolates the positive solution

\frac{x+y}{x-y} = \sqrt{\frac{7}{3}}

.

Together, the statements determine a single, unique value for the target expression.

Key Concept

Algebraic Rephrasing and Sign Constraints in Data Sufficiency

Estimated Time:2m 0s

Question 1690Question →

A manufacturing plant produces two types of solar panels: Model X and Model Y. Each Model X panel requires $2$ hours of assembly and $1$ hour of quality testing. Each Model Y panel requires $3$ hours of assembly and $2$ hours of quality testing. During a single week, the assembly line logged a total of $140$ hours and the quality testing line logged $80$ hours, with both departments operating at full capacity. How many Model X solar panels were produced during the week?

20

30

40

50

60

Show answer & explanation

Answer: $40$

Answer

40

Model X solar panels were produced during the week.

Setting up the simultaneous linear equations for assembly time (

2x + 3y = 140

) and testing time (

x + 2y = 80

) and solving for

x

gives

x = 40

, which accurately satisfies both constraints.

Step-by-Step Solution

1

Define variables and set up the system of linear equations based on resource constraints.

Let

x

be the number of Model X panels and

y

be the number of Model Y panels.
Assembly constraint:

2x + 3y = 140

Quality testing constraint:

x + 2y = 80

Each department's total logged hours must equal the sum of hours required by both panel types.

2

Express

x

in terms of

y

using the testing constraint equation.

x = 80 - 2y

Isolating

x

allows substitution into the assembly equation.

3

Substitute

x = 80 - 2y

into the assembly equation and solve for

y

.

2(80 - 2y) + 3y = 140 160 - 4y + 3y = 140 160 - y = 140 y = 20

Solving a single-variable equation determines the quantity of Model Y panels.

4

Substitute

y = 20

back to find

x

.

x = 80 - 2(20) = 40

Evaluating

x

determines the quantity of Model X panels requested in the question stem.

Key Concept

Solving simultaneous linear equations by substitution or elimination

Question 1691Question →

The table below details semiconductor fabrication performance metrics across eight production lines during Q2 2026:

Fab Line	Process Node (nm)	Monthly Wafers (thousands)	Defect Density (defects/cm²)	Yield Rate (%)	R&D Intensity ($/wafer)
Line A	3	45	0.28	78.5%	420
Line B	5	80	0.22	84.0%	310
Line C	7	120	0.15	91.2%	180
Line D	14	150	0.08	95.6%	95
Line E	3	35	0.34	72.0%	460
Line F	5	90	0.18	86.5%	290
Line G	7	110	0.12	93.0%	210
Line H	28	200	0.04	98.2%	50

Evaluate the truth value of the following claim regarding three boolean statements about the dataset:

Statement I: Among the Fab Lines with a Process Node of 7 nm or smaller, the median Defect Density is greater than the mean Defect Density of lines producing more than 100 thousand Monthly Wafers.
Statement II: The weighted average Yield Rate across all 3 nm and 5 nm Fab Lines combined (weighted by Monthly Wafers) is less than 82.0%.
Statement III: When the table is sorted in descending order of R&D Intensity ($/wafer), the Fab Line in the third row has a higher Yield Rate than the Fab Line with the lowest overall Defect Density.

Claim: Evaluating statements I, II, and III yields True, False, and False, respectively.

True

False

Show answer & explanation

Answer: True

Answer

True

The claim stating that evaluating statements I, II, and III yields True, False, and False, respectively, is correct because mathematical evaluation confirms Statement I is True (

0.20 > 0.0975

), Statement II is False (

82.23\% > 82.0\%

), and Statement III is False (

84.0\% < 98.2\%

).

Step-by-Step Solution

1

Filter table for Process Node ≤ 7 nm and calculate median Defect Density, then compare with mean Defect Density of lines with Monthly Wafers > 100k.

Process Node ≤ 7 nm values: {0.12, 0.15, 0.18, 0.22, 0.28, 0.34} → Median = 0.20 defects/cm². Monthly Wafers > 100k values: {0.15, 0.08, 0.12, 0.04} → Mean = 0.0975 defects/cm². 0.20 > 0.0975 → Statement I is True.

Evaluates conditional filtering and statistical medians versus means across filtered subsets.

2

Compute the weighted average Yield Rate for 3 nm and 5 nm lines combined.

Total Wafers = 250k; Total Conforming Wafers = 205.575k → Weighted Yield = 82.23%. Since 82.23% ≥ 82.0%, Statement II is False.

Evaluates multi-row weighted average calculation versus simple unweighted averaging.

3

Sort table by R&D Intensity descending, identify 3rd row line, and compare its Yield Rate with the line having lowest overall Defect Density.

3rd row line by R&D Intensity is Line B (Yield Rate = 84.0%). Lowest Defect Density line is Line H (Yield Rate = 98.2%). 84.0% < 98.2% → Statement III is False.

Tests column sorting, positional indexing, and cross-column correlation comparison.

4

Combine the evaluations of Statements I, II, and III.

Evaluation sequence is (True, False, False), matching the claim exactly.

Confirms the ultimate boolean evaluation of the composite claim.

Key Concept

Multi-Statement Boolean Evaluation using tabular data filtering, weighted averages, and multi-column sorting.

Estimated Time:3m 0s

Question 1692Question →

A bakery sells two types of artisanal bread: Sourdough and Brioche. Last week, the bakery sold a total of $1,200$ loaves of bread. Did Sourdough account for more than $60\%$ of the total revenue generated from sales of these two types of bread?

(1) The selling price of a loaf of Brioche was $25\%$ greater than the selling price of a loaf of Sourdough.
(2) The number of Sourdough loaves sold was $70\%$ of the total number of loaves sold.

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.

Show answer & explanation

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

Answer

Both statements together are sufficient, but neither statement alone is sufficient.

The correct answer identifies that neither statement alone gives both the price ratio and quantity ratio, but taking both statements together provides

\frac{P_S}{P_B} = \frac{4}{5}

and

\frac{N_S}{N_B} = \frac{7}{3}

. Multiplying these yields

\frac{N_S P_S}{N_B P_B} = \frac{28}{15} \approx 1.867

, which is greater than

1.5

(the threshold required for a

60\%

revenue share). Thus, both statements together provide a definitive 'Yes' answer.

Step-by-Step Solution

1

Rephrase the question stem target into an algebraic condition.

Let

N_S

and

N_B

be the quantities of Sourdough and Brioche sold, and

P_S

and

P_B

be their respective unit prices. Sourdough revenue is

R_S = N_S P_S

and total revenue is

R_{total} = N_S P_S + N_B P_B

. We need to test if

\frac{N_S P_S}{N_S P_S + N_B P_B} > 0.60

, which simplifies to

\frac{N_S P_S}{N_B P_B} > 1.5

.

Simplifying the target inequality shows that knowing the combined ratio

\frac{N_S P_S}{N_B P_B} = \left(\frac{N_S}{N_B}\right) \times \left(\frac{P_S}{P_B}\right)

is necessary and sufficient.

2

Evaluate Statement (1) independently.

Statement (1) states

P_B = 1.25 P_S = \frac{5}{4} P_S

, so

\frac{P_S}{P_B} = \frac{4}{5}

.

Since no information is given about the ratio of quantities

\frac{N_S}{N_B}

, the overall revenue ratio cannot be determined. Statement (1) alone is insufficient.

3

Evaluate Statement (2) independently.

Statement (2) states

N_S = 0.70 \times 1,200 = 840

, which means

N_B = 360

. Thus

\frac{N_S}{N_B} = \frac{840}{360} = \frac{7}{3}

.

Since no information is given about the relative unit prices

\frac{P_S}{P_B}

, the overall revenue ratio cannot be determined. Statement (2) alone is insufficient.

4

Evaluate Statements (1) and (2) together.

Combine the price ratio

\frac{P_S}{P_B} = \frac{4}{5}

and quantity ratio

\frac{N_S}{N_B} = \frac{7}{3}

. The revenue ratio is

\frac{N_S P_S}{N_B P_B} = \left(\frac{7}{3}\right) \times \left(\frac{4}{5}\right) = \frac{28}{15} \approx 1.867

.

Since

1.867 > 1.5

, Sourdough's revenue share is strictly greater than

60\%

. This yields a definitive 'Yes', so both statements together are sufficient.

Key Concept

Data Sufficiency evaluation of revenue proportions using combined quantity and price ratios.

Estimated Time:1m 30s

Question 1693Question →

A regional freight company operates two transport fleets: Fleet X and Fleet Y. Last quarter, what was the ratio of the total operating expense of Fleet X to the total operating expense of Fleet Y?

(1) Fleet X's fuel expense was $40\%$ of its total operating expense, and Fleet Y's fuel expense was $25\%$ of its total operating expense.
(2) The combined fuel expense of both fleets was $30\%$ of their combined total operating expenses.

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.

Show answer & explanation

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

Answer

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

The statement expressing that both statements together are sufficient while neither alone is sufficient is correct because Statement (1) gives the component percentages (

40\%

and

25\%

) and Statement (2) gives the overall weighted percentage (

30\%

). Equating the component sum

0.40E_X + 0.25E_Y

to the weighted total

0.30(E_X + E_Y)

yields a single linear equation that solves directly for the ratio

E_X / E_Y = 1/2

.

Step-by-Step Solution

1

Define variables and target ratio

Let

E_X

be the total operating expense of Fleet X and

E_Y

be the total operating expense of Fleet Y. The target is to determine the ratio

\frac{E_X}{E_Y}

.

Rephrasing the question stem into a formal mathematical expression highlights what relationship needs to be determined.

2

Evaluate Statement (1) alone

Fuel expense of Fleet X

= 0.40 E_X

and Fuel expense of Fleet Y

= 0.25 E_Y

.

Statement (1) provides individual percentages, but contains no information relating

E_X

to

E_Y

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

3

Evaluate Statement (2) alone

Total combined fuel expense

= 0.30 (E_X + E_Y)

.

Without knowing the individual fuel percentages for Fleet X and Fleet Y, we cannot express the total combined fuel expense in terms of

E_X

and

E_Y

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

4

Evaluate Statements (1) and (2) together

Equate the sum of individual fuel expenses to the total combined fuel expense:

0.40 E_X + 0.25 E_Y = 0.30 (E_X + E_Y)

0.40 E_X + 0.25 E_Y = 0.30 E_X + 0.30 E_Y

0.10 E_X = 0.05 E_Y

\frac{E_X}{E_Y} = \frac{0.05}{0.10} = \frac{1}{2}

Setting the two expressions for total fuel expense equal creates a linear homogeneous equation that uniquely determines the exact ratio of

E_X

to

E_Y

.

Key Concept

Weighted Average Ratios in Data Sufficiency

Practice More

Practice Data Sufficiency questions involving weighted average mixtures where component percentages lie on opposite sides of the combined percentage.

Alternative Method

Alligation / Weighted Average Formula: The distance between Fleet X's percentage (

40\%

) and the combined percentage (

30\%

) is

10\%

. The distance between Fleet Y's percentage (

25\%

) and the combined percentage (

30\%

) is

5\%

. The ratio of Fleet X to Fleet Y is inversely proportional to these distances:

E_X / E_Y = 5 / 10 = 1 / 2

.

Estimated Time:1m 30s

Question 1694Question →

If $a$ and $b$ are non-zero real numbers, what is the value of $\frac{a^2 + b^2}{ab}$ ?

(1) $a + b = 3ab$
(2) $a - b = ab$

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.

Show answer & explanation

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

Answer

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

Evaluating each statement independently shows that Statement (1) reduces the expression to

9ab - 2

and Statement (2) reduces it to

ab + 2

, both of which depend on the value of

ab

. Combining both statements yields a system of linear equations in

a

and

b

, giving

a = 1

and

b = 1/2

. This uniquely determines the value of the target expression as

5/2

. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

Step-by-Step Solution

1

Rephrase the target expression.

\frac{a^2 + b^2}{ab} = \frac{a}{b} + \frac{b}{a}

. Alternatively, squaring identities give

\frac{a^2+b^2}{ab} = \frac{(a+b)^2 - 2ab}{ab} = \frac{(a+b)^2}{ab} - 2

.

Simplifying the target expression shows what combination of variables is required.

2

Evaluate Statement (1) alone:

a + b = 3ab

.

Substituting

a+b = 3ab

into the target expression yields

\frac{(3ab)^2 - 2ab}{ab} = 9ab - 2

.

Since the value depends on

ab

, and

ab

can take multiple non-zero values (e.g., if

a=1, b=1/2

,

ab=1/2

and the expression is

2.5

; if

a=2, b=2/5

,

ab=4/5

and the expression is

5.2

), Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) alone:

a - b = ab

.

Expressing

a^2+b^2 = (a-b)^2 + 2ab = (ab)^2 + 2ab

, the target expression becomes

\frac{(ab)^2 + 2ab}{ab} = ab + 2

.

Since the value depends on

ab

, which is not fixed by Statement (2) alone, Statement (2) alone is NOT sufficient.

4

Evaluate Statements (1) and (2) together.

Adding the two equations

(a + b) + (a - b) = 3ab + ab

gives

2a = 4ab

. Since

a \neq 0

, dividing by

2a

yields

b = \frac{1}{2}

.

Substituting

b = \frac{1}{2}

into

a - b = ab

gives

a - \frac{1}{2} = \frac{1}{2}a \implies a = 1

. With

a=1

and

b=\frac{1}{2}

,

ab = \frac{1}{2}

, and

\frac{a^2+b^2}{ab} = \frac{1 + 1/4}{1/2} = \frac{5}{2}

, giving a single unique value.

Key Concept

Algebraic System Reduction and Target Rephrasing in Data Sufficiency

Estimated Time:2m 0s

Question 1695Question →

The table below presents quarterly operational metrics for 10 semiconductor fabrication plants:

Plant ID	Region	Wafer Size	Defect Density (defects/cm²)	Operational Yield (%)
Fab 101	Asia-Pacific	300 mm	1.8	94.2
Fab 102	Asia-Pacific	300 mm	2.4	92.6
Fab 103	Asia-Pacific	300 mm	3.1	89.5
Fab 104	Asia-Pacific	300 mm	3.7	88.0
Fab 105	Asia-Pacific	300 mm	4.3	86.4
Fab 106	Asia-Pacific	300 mm	5.1	83.1
Fab 107	North America	300 mm	2.2	93.0
Fab 108	North America	200 mm	4.8	85.0
Fab 109	Europe	300 mm	3.5	87.5
Fab 110	Europe	200 mm	5.5	81.0

Statement: For semiconductor fabrication plants with a $300\text{ mm}$ wafer size located in the Asia-Pacific region, the median defect density is greater than $3.3\text{ defects/cm}^2$ .

True

False

Show answer & explanation

Answer: True

Answer

True

The correct response is True because the filtered subset of 6 plants in the Asia-Pacific region with 300 mm wafer sizes has defect densities of 1.8, 2.4, 3.1, 3.7, 4.3, and 5.1 defects/cm². Averaging the two middle values (3.1 and 3.7) yields a median of 3.4 defects/cm², which exceeds 3.3 defects/cm².

Step-by-Step Solution

1

Filter the dataset according to specified criteria

Identified 6 relevant plants: Fab 101, Fab 102, Fab 103, Fab 104, Fab 105, and Fab 106 (Region = Asia-Pacific AND Wafer Size = 300 mm).

The question requires analyzing descriptive statistics specifically for 300 mm wafer plants in the Asia-Pacific region.

2

Extract and sort the defect density data for the filtered subset

Sorted list of defect densities (

N = 6

):

1.8, 2.4, 3.1, 3.7, 4.3, 5.1

.

Calculating a median requires arranging the data points in ascending order.

3

Calculate the median of the even-count dataset

The 3rd element is

3.1

and the 4th element is

3.7

. The median is

\frac{3.1 + 3.7}{2} = 3.4\text{ defects/cm}^2

.

When

N

is even, the median is defined as the mean of the two middle numbers at positions

\frac{N}{2}

and

\frac{N}{2} + 1

.

4

Evaluate the statement

The calculated median of

3.4\text{ defects/cm}^2

is strictly greater than

3.3\text{ defects/cm}^2

. Therefore, the statement is True.

Comparing the calculated value (

3.4

) directly against the threshold in the stem (

3.3

) confirms the statement.

Key Concept

Descriptive Statistics Interpretation (Median of Even-Count Subsets)

Question 1696Question →

A municipal public transit authority plans to address its operational deficit by installing automated turnstile gates at all underground metro stations and laying off all human ticket inspectors. The authority's financial analysts claim that because the annual maintenance cost of the automated gates will be significantly less than the total annual salaries of the inspectors, implementing this plan is guaranteed to decrease the authority's net operating deficit in its first year. Which of the following would it be most useful to determine in order to evaluate the validity of the financial analysts' conclusion?

Whether passenger fare evasion is likely to increase significantly following the removal of human ticket inspectors

Whether neighboring municipalities with similar transit networks have successfully implemented automated gate systems to reduce overall municipal debt

Whether human ticket inspectors currently receive performance-based monetary bonuses in addition to their base annual salaries

Whether the automated turnstile gates will require an initial software calibration period prior to being fully deployed to the public

Whether decreasing the net operating deficit of the transit authority guarantees that total municipal government debt will also decline

Show answer & explanation

Answer: Whether passenger fare evasion is likely to increase significantly following the removal of human ticket inspectors

Answer

Determining whether passenger fare evasion is likely to increase significantly following the removal of human ticket inspectors is most useful for evaluating the argument.

The correct option addresses an unstated financial variable: revenue from ticket sales. Operating deficit equals operating expenses minus revenue. The premises establish that one category of expenses (maintenance) is lower than another (salaries). However, if replacing human inspectors with automated gates leads to higher fare evasion, the resulting loss in ticket revenue could outweigh the net expense savings. Applying the Test of Variance: if fare evasion increases significantly, the plan will fail to decrease the deficit; if fare evasion does not increase, the plan will succeed. Because extreme answers produce opposite impacts on the conclusion's validity, this information is critical.

Step-by-Step Solution

1

Deconstruct the argument structure

Premise: Automated gate annual maintenance costs are significantly lower than total annual inspector salaries. Conclusion: Installing gates and laying off inspectors is guaranteed to decrease the net operating deficit in the first year.

The conclusion relies on the assumption that salary savings minus maintenance costs represents the total net financial impact of the policy change.

2

Identify the unstated logical gap

The argument considers expenses (salaries vs. maintenance) but completely ignores revenue impacts (ticket sales and fare enforcement).

Net operating deficit is calculated as Total Operating Expenses minus Total Revenue. Any change affecting revenue directly impacts the deficit.

3

Apply the Test of Variance to the evaluating question

If fare evasion increases significantly without human inspectors, the revenue lost from unpaid fares could easily exceed the net salary savings, causing the net operating deficit to increase (weakening the conclusion). Conversely, if fare evasion does not increase, the net cost savings will reduce the deficit as claimed (strengthening the conclusion).

The opposite extreme answers to this question yield opposite effects on the validity of the analysts' conclusion, confirming it as the correct evaluation criteria.

Key Concept

Evaluating Argument Validity and Test of Variance

Question 1697Question →

The table below presents operational patient data across five regional health centers for fiscal year 2025.

Regional Health Center	Total Inpatient Admissions	Emergency Department Visits	Outpatient Telehealth Consultations	30-Day Inpatient Readmissions
Central Metro	12,000	45,000	18,000	1,440
North Ridge	8,000	25,000	15,000	880
Eastside	15,000	60,000	20,000	1,500
Valley Pines	6,000	18,000	12,000	540
West Coast	10,000	32,000	14,000	1,100

Across all five regional health centers combined, what percentage of total inpatient admissions resulted in a 30-day inpatient readmission?

2.4%

3.0%

10.6%

10.7%

12.0%

Show answer & explanation

Answer: 10.7%

Answer

10.7%

To calculate the aggregate percentage across all five regional health centers, sum the total number of readmissions (

1,440 + 880 + 1,500 + 540 + 1,100 = 5,460

) and divide by the sum of total inpatient admissions (

12,000 + 8,000 + 15,000 + 6,000 + 10,000 = 51,000

). Dividing

5,460

by

51,000

yields approximately

0.10706

, or

10.7\%

.

Step-by-Step Solution

1

Calculate the total number of 30-day inpatient readmissions across all five regional health centers.

1,440 + 880 + 1,500 + 540 + 1,100 = 5,460

To find aggregate percentage, the combined numerator must be determined.

2

Calculate the total number of inpatient admissions across all five regional health centers.

12,000 + 8,000 + 15,000 + 6,000 + 10,000 = 51,000

The question specifically asks for readmissions as a percentage of total inpatient admissions, establishing the base denominator.

3

Divide total readmissions by total inpatient admissions and convert to a percentage.

\frac{5,460}{51,000} \times 100\% \approx 10.70588\% \approx 10.7\%

Determines the combined weighted percentage of readmissions.

Key Concept

Weighted aggregate percentage calculation from tabular data

Estimated Time:1m 30s

Question 1698Question →

An agricultural supplier sells two grades of organic fertilizer: Premium grade and Standard grade. Last month, all inventory of both grades was sold. What percentage of the supplier's total revenue last month came from sales of Premium grade fertilizer?

(1) The price per bag of Premium grade fertilizer was $50\%$ higher than the price per bag of Standard grade fertilizer.
(2) The number of bags of Standard grade fertilizer sold last month was $20\%$ less than the number of bags of Premium grade fertilizer sold.

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.

Show answer & explanation

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

Answer

Both statements together are sufficient to determine the exact percentage of total revenue coming from Premium grade fertilizer, but neither statement alone is sufficient.

The correct choice identifies that neither statement alone gives both the price ratio and the quantity ratio required to calculate the percentage contribution to total revenue. Statement (1) provides only the relative prices (

\frac{p_P}{p_S} = 1.5

), while Statement (2) provides only the relative quantities sold (

S = 0.8P

). Combining both gives the combined revenue ratio

\frac{S \cdot p_S}{P \cdot p_P} = \frac{4}{5} \times \frac{2}{3} = \frac{8}{15}

, which allows calculating the exact percentage

\frac{15}{23}

. Thus, both statements together are sufficient.

Step-by-Step Solution

1

Rephrase the question target algebraically.

Let

P

and

S

be the quantities of Premium and Standard bags sold, and let

p_P

and

p_S

be their respective unit prices. Total revenue is

R_{total} = P \cdot p_P + S \cdot p_S

. The target percentage is

\frac{P \cdot p_P}{P \cdot p_P + S \cdot p_S} = \frac{1}{1 + \frac{S \cdot p_S}{P \cdot p_P}}

. Finding this percentage requires knowing the ratio of total revenues

\frac{S \cdot p_S}{P \cdot p_P}

, which simplifies to

\left(\frac{S}{P}\right) \times \left(\frac{p_S}{p_P}\right)

.

Simplifying the target expression reduces the problem from requiring four individual variable values to requiring only one combined ratio.

2

Evaluate Statement (1) independently.

Statement (1) states

p_P = 1.5 \cdot p_S

, which gives

\frac{p_S}{p_P} = \frac{1}{1.5} = \frac{2}{3}

. However, no information is given regarding the ratio of quantities sold

\frac{S}{P}

. Statement (1) alone is NOT sufficient.

Knowing only the price ratio leaves the quantity ratio unknown.

3

Evaluate Statement (2) independently.

Statement (2) states

S = 0.8 \cdot P

, which gives

\frac{S}{P} = 0.8 = \frac{4}{5}

. However, no information is given regarding the price ratio

\frac{p_S}{p_P}

. Statement (2) alone is NOT sufficient.

Knowing only the quantity ratio leaves the price ratio unknown.

4

Evaluate Statements (1) and (2) together.

Combining both statements yields

\frac{S \cdot p_S}{P \cdot p_P} = \left(\frac{4}{5}\right) \times \left(\frac{2}{3}\right) = \frac{8}{15}

. Substituting this into the target expression gives

\frac{1}{1 + \frac{8}{15}} = \frac{15}{23} \approx 65.2\%

. Therefore, both statements together are sufficient.

Combining the relative prices and relative quantities provides the exact ratio of revenues.

Key Concept

Data Sufficiency Target Rephrasing for Percentage of Total Revenue

Estimated Time:2m 0s

Question 1699Question →

The table lists performance and cost metrics for 10 municipal water treatment facilities during the 2025 fiscal year:

Facility ID	Region	Daily Capacity (MGD)	Average Turbidity (NTU)	Operating Cost ($/thousand gallons)
W-01	North	24.0	0.12	1.42
W-02	South	18.0	0.25	1.85
W-03	North	32.0	0.08	1.28
W-04	Central	12.0	0.19	1.65
W-05	South	28.0	0.15	1.56
W-06	Central	40.0	0.10	1.18
W-07	North	15.0	0.22	1.70
W-08	South	22.0	0.14	1.50
W-09	Central	35.0	0.11	1.34
W-10	North	10.0	0.28	1.92

Based on the data provided, what is the median operating cost, in dollars per thousand gallons, for the facilities that have a daily capacity greater than 20.0 MGD?

Show answer & explanation

Answer: 1.38

Answer

The median operating cost for facilities with a daily capacity greater than 20.0 MGD is $1.38 per thousand gallons.

Filtering the table for facilities with Daily Capacity > 20.0 MGD yields 6 facilities (W-01, W-03, W-05, W-06, W-08, W-09). Sorting their operating costs in ascending order produces:

1.18,

1.28,

1.34,

1.42,

1.50,

1.56. Because the count of elements is even (6), the median is the average of the 3rd element (

1.34) and the 4th element (

1.42), which equals $1.38.

Step-by-Step Solution

1

Filter the dataset by the given capacity constraint.

Identified 6 facilities with Daily Capacity > 20.0 MGD: W-01 (24.0 MGD), W-03 (32.0 MGD), W-05 (28.0 MGD), W-06 (40.0 MGD), W-08 (22.0 MGD), and W-09 (35.0 MGD).

Only facilities meeting the criterion 'Daily Capacity > 20.0 MGD' must be evaluated.

2

Extract and order the operating costs for the filtered subset.

Operating costs in ascending order:

1.18,

1.28,

1.34,

1.42,

1.50,

1.56.

Determining the median of a dataset requires arranging values sequentially.

3

Calculate the median for an even-numbered dataset.

Average of the 3rd and 4th values: $\frac{1.34 + 1.42}{2} = 1.38$.

When a dataset contains an even number of elements $N = 6$, the median is the arithmetic mean of the two central numbers at positions $N/2 = 3$ and $N/2 + 1 = 4$.

Key Concept

Calculating the median of a filtered even-count subset from tabular data.

Alternative Method

As a verification step, sum all operating costs in the filtered set:

1.18 + 1.28 + 1.34 + 1.42 + 1.50 + 1.56 = 8.28

. The mean is

8.28 / 6 = 1.38

. In this symmetric subset, the mean and median coincide at

1.38

.

Estimated Time:2m 0s

Question 1700Question →

Consider the following argument: An agricultural biotechnology firm plans to market a automated seed-analysis device to commercial grain farmers. The firm predicts that launching this device will significantly increase its annual operating profits because the device reduces sample processing time by 50 percent, allowing farmers to test twice as many seeds in a single day without incurring additional labor costs.

Evaluating the following statement: Determining whether commercial grain farmers currently experience a bottleneck in seed testing that restricts their total volume of seed purchases is a relevant test of variance for evaluating the validity of the firm's profit prediction.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. Evaluating whether farmers currently face a testing bottleneck passes the Test of Variance because opposite answers directly strengthen or weaken the conclusion that the device will increase operating profits.

The statement is correct because the proposed criterion directly satisfies the Test of Variance. If farmers are currently bottlenecked by testing speed, doubling speed creates real economic value and drives sales, strengthening the conclusion. If farmers have no unfulfilled testing demand, extra speed provides no incentive to purchase, weakening the conclusion.

Step-by-Step Solution

1

Deconstruct the argument structure

Premise: The new device reduces processing time by 50%, enabling farmers to test twice as many seeds at no extra labor cost. Conclusion: Marketing this device will significantly increase the firm's annual operating profits.

Identifying the link between the mechanism (higher processing capacity) and the outcome (increased profit) exposes the underlying assumption of market demand.

2

Apply the Test of Variance to the proposed evaluation criterion

Evaluate extreme outcome 1 (Yes, a bottleneck exists): Farmers need more capacity, so faster testing leads to increased device adoption and sales, supporting higher profits. Evaluate extreme outcome 2 (No, no bottleneck exists): Farmers already test all necessary seeds, so faster testing yields no added commercial value or extra sales, defeating the profit expectation.

The Test of Variance assesses whether opposite extreme answers to a question produce opposing impacts on the conclusion's logical strength.

3

Determine statement truth value

Since the proposed question produces opposite evaluative outcomes, it is a valid and crucial factor in assessing argument validity.

A factor that differentiates between a viable financial plan and an ineffective one is inherently relevant to evaluating argument validity.

Key Concept

Test of Variance in Evaluating Argument Validity

Estimated Time:1m 30s

Answer

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Practice More

Alternative Method

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Alternative Method