All practice questions

Question 1581Question →

To reduce severe crop damage caused by an invasive species of burrowing rodents, agricultural authorities in a rural valley plan to introduce a native raptor species known to prey heavily on small mammals. The authorities reason that establishing a population of these raptors in the valley will significantly decrease the rodent population, thereby protecting local grain harvests. Which of the following statements, if true, most seriously weakens the argument above?

The invasive rodents forage and move exclusively underground at night, whereas the raptors hunt strictly during daylight hours above open ground.

A neighboring agricultural district successfully controlled its rodent population two years ago by deploying ultrasonic deterrent devices.

The raptor species tends to reproduce more rapidly in agricultural valleys than in its natural forest habitat.

Crop losses resulting from fungal infections in the valley were higher than losses caused by rodents during the previous growing season.

Local farming associations strongly support the raptor program because it avoids the environmental hazards associated with chemical poisons.

Show answer & explanation

Answer: The invasive rodents forage and move exclusively underground at night, whereas the raptors hunt strictly during daylight hours above open ground.

Answer

The argument is most seriously weakened by the fact that the invasive rodents forage exclusively underground at night while the raptors hunt strictly during daylight hours above ground.

The conclusion relies on the assumption that introducing raptors will result in significant predation of the invasive rodents. The correct option shows a complete temporal and spatial mismatch: the rodents are active only underground at night, while the raptors hunt only above ground during the day. Because the raptors will not encounter the rodents, the plan cannot achieve its goal of reducing the rodent population.

Step-by-Step Solution

1

Identify the premise and conclusion of the argument.

Premise: Raptors prey heavily on small mammals. Conclusion: Introducing raptors will significantly decrease the population of burrowing rodents and protect grain harvests.

Understanding the logical jump from raptor predation habits to effective rodent reduction isolates the underlying assumption.

2

Identify the unstated assumption.

The argument assumes that the raptors will actually encounter and hunt these specific invasive rodents in this valley environment.

If environmental or behavioral barriers prevent raptors from preying on the rodents, the plan will fail.

3

Evaluate the answer choices for information that undermines this assumption.

The option stating that rodents are active underground at night while raptors hunt above ground during the day demonstrates that predator and prey will not interact.

A complete temporal and spatial mismatch negates the causal mechanism relied upon by the conclusion.

Key Concept

Causal Plan Weakening (Behavioral and Temporal Mismatch)

Question 1582Question →

Under the regulations of the International Civil Aviation Safety Board, any commercial airliner that completes more than 3,000 flight hours in a calendar year must undergo a comprehensive turbine ultrasound inspection unless all of its primary engine components were replaced within the preceding 12 months. Last year, Aircraft Skycraft-90 logged 3,400 flight hours, and exactly two of its four primary engine components were replaced within the preceding 12 months.

Statement: Under the board's regulations, Aircraft Skycraft-90 is required to undergo a comprehensive turbine ultrasound inspection.

True

False

Show answer & explanation

Answer: True

Answer

True. Aircraft Skycraft-90 logged 3,400 flight hours (exceeding the 3,000-hour threshold) and failed to satisfy the exemption requirement that all primary engine components be replaced within the preceding 12 months.

The rule imposes a mandatory turbine ultrasound inspection on any airliner exceeding 3,000 flight hours unless all primary engine components were replaced in the last 12 months. Skycraft-90 logged 3,400 hours (exceeding 3,000) and replaced only two of its four components. Because it fails to meet the strict requirement of replacing all components, the exemption does not apply, and the inspection is guaranteed to be required.

Step-by-Step Solution

1

Analyze the rule's logical conditions and exceptions.

An inspection is required IF annual flight hours > 3,000, UNLESS 100% of primary engine components were replaced within the past 12 months.

Formal conditional rules require identifying both the triggering condition and the exact criteria for any exemption.

2

Evaluate the trigger condition for Skycraft-90.

Skycraft-90 logged 3,400 flight hours, which exceeds 3,000 hours.

Establishes that the primary requirement for inspection has been triggered.

3

Evaluate the exemption criteria for Skycraft-90.

Only two out of four components were replaced within 12 months, which is not 'all' components.

The word 'unless' introduces a necessary condition for exemption (all components replaced). Partial replacement fails this requirement.

4

Deduce the final requirement.

Because the rule is triggered and the exemption is not met, Skycraft-90 must undergo the inspection. The statement is True.

Combining valid premise deductions leads directly to the true statement.

Key Concept

Conditional logic and valid deductions from rules containing strict exceptions ('unless all')

Question 1583Question →

The table below displays quality assurance metrics for six semiconductor lithography tools operating in a fabrication facility:

Tool ID	Process Node (nm)	Defect Density (defects/cm²)	Operational Uptime (%)	Calibration Status
TL-01	3	0.24	95.8%	Certified
TL-02	5	0.18	96.4%	Pending
TL-03	3	0.32	92.1%	Certified
TL-04	7	0.15	97.2%	Certified
TL-05	5	0.28	94.6%	Pending
TL-06	10	0.09	98.1%	Recalibrated

Based on the data provided, is the following statement True or False?

"For all lithography tools operating at a process node of $5\text{ nm}$ or smaller that also have a defect density strictly less than $0.30\text{ defects/cm}^2$ , the median operational uptime is greater than $95.0\%$ ."

True

False

Show answer & explanation

Answer: True

Answer

True. The median operational uptime for the filtered subset of tools (TL-01, TL-02, and TL-05) is 95.8%, which is greater than 95.0%.

The statement is correct (True) because applying the two compound criteria (Process Node

\le 5\text{ nm}

AND Defect Density

< 0.30\text{ defects/cm}^2

) selects tools TL-01, TL-02, and TL-05. The operational uptimes of these three tools are

95.8\%

,

96.4\%

, and

94.6\%

. Arranged in numerical order, the median value is

95.8\%

, which exceeds

95.0\%

.

Step-by-Step Solution

1

Identify the compound logical criteria specified in the statement.

Filter 1: Process Node

\le 5\text{ nm}

. Filter 2: Defect Density

< 0.30\text{ defects/cm}^2

. Target metric: Median Operational Uptime.

Both conditions must be met simultaneously (conjunction AND) before analyzing the operational uptime column.

2

Filter the rows based on the Process Node criterion.

Candidate tools meeting Process Node

\le 5\text{ nm}

: TL-01 (3 nm), TL-02 (5 nm), TL-03 (3 nm), and TL-05 (5 nm). Tools TL-04 (7 nm) and TL-06 (10 nm) are eliminated.

Only tools operating at 3 nm or 5 nm satisfy the condition of being 5 nm or smaller.

3

Apply the second criterion (Defect Density

< 0.30\text{ defects/cm}^2

) to the candidate tools.

Qualifying subset: TL-01 (

0.24

), TL-02 (

0.18

), and TL-05 (

0.28

). TL-03 is excluded because

0.32 \ge 0.30

.

Strict inequality requires excluding values equal to or greater than 0.30.

4

Extract operational uptime values for the qualified subset and compute the median.

Values: TL-05 (

94.6\%

), TL-01 (

95.8\%

), TL-02 (

96.4\%

). Ordered values:

94.6\%, 95.8\%, 96.4\%

. Median =

95.8\%

.

For

N = 3

, the median is the 2nd value in sorted order.

5

Compare the calculated median against the target threshold.

95.8\% > 95.0\%

, verifying that the statement is True.

The calculated median of

95.8\%

strictly exceeds the benchmark value of

95.0\%

.

Key Concept

Compound Conditional Filtering and Descriptive Statistics on Subsets

Estimated Time:2m 0s

Question 1584Question →

[Tab 1: Reimbursement Policy]
Standard business lodging allowance is capped at $200 per day. Exception Rule: If travel is booked less than 7 days prior to departure AND the destination is a designated High-Cost City, the daily allowance increases to$ 350 per day. However, if the travel itinerary includes any personal days, the allowance reverts to the standard rate of $200 per day regardless of city classification or booking notice.

[Tab 2: Travel Expense Summary]
Employee: Alex Morgan
Destination: New York City (Designated High-Cost City)
Booking Date: March 10
Departure Date: March 14
Personal Days Included: 0
Claimed Daily Lodging Expense: $310 per day

Based on the Policy Guidelines and Travel Expense Summary, what is the maximum daily lodging reimbursement allowance Alex Morgan is eligible to receive for this trip?

$200 per day

$310 per day

$350 per day

$550 per day

$0 per day

Show answer & explanation

Answer: $350 per day

Answer

The maximum daily lodging allowance Alex Morgan is eligible to receive is $350 per day.

The correct answer identifies that Alex Morgan meets all conditions for the lodging exception: the trip was booked 4 days before departure (less than the 7-day threshold), the destination is classified as a High-Cost City, and 0 personal days were included. Therefore, the daily allowance ceiling increases to $350 per day.

Step-by-Step Solution

1

Evaluate the standard rule and exception criteria from Tab 1

Standard allowance is

200/day. The exception rate of

350/day applies if: (1) booking is < 7 days before departure, (2) destination is a High-Cost City, AND (3) personal days = 0.

Establishing the precise conditional logic governing reimbursement limits.

2

Cross-reference the trip data in Tab 2 against the conditional criteria

Booking notice = 4 days (March 10 to March 14, which is less than 7 days). Destination = New York City (High-Cost City). Personal days = 0.

Verifying whether all required conditions for the policy exception are met.

3

Determine the maximum eligible daily allowance cap

Since all three exception conditions are satisfied, the maximum eligible daily lodging allowance is $350 per day.

Applying the policy rule to calculate the final allowance ceiling.

Key Concept

Multi-Source Conditional Policy Rule Application

Estimated Time:1m 0s

Question 1585Question →

The table below provides operational data for eight solar power facilities across two regions:

Facility Name	Region	Capacity (MW)	Operational Efficiency (%)
Solaria Alpha	North	120	88
Solaria Beta	South	150	91
Solaria Gamma	North	200	97
Solaria Delta	North	110	82
Solaria Epsilon	South	180	89
Solaria Zeta	North	135	92
Solaria Eta	North	160	94
Solaria Theta	North	140	85

What is the median operational efficiency, in percent, of the solar power facilities located in the North region?

Show answer & explanation

Answer: 90

Answer

The median operational efficiency of the solar power facilities in the North region is 90%.

Filtering the table for facilities in the North region yields six efficiency values: 82%, 85%, 88%, 92%, 94%, and 97%. Because the dataset contains an even count of six values, the median is the average of the two middle values (88% and 92%). Calculating

\frac{88 + 92}{2}

gives 90%.

Step-by-Step Solution

1

Filter the table to isolate facilities in the North region.

Identified 6 facilities with operational efficiency values: 88%, 97%, 82%, 92%, 94%, and 85%.

The stem specifies evaluating descriptive statistics for the North region subset only.

2

Sort the efficiency values of the filtered subset in ascending order.

Ordered set: {82, 85, 88, 92, 94, 97}.

Calculating the median requires ordering data points from lowest to highest.

3

Compute the arithmetic mean of the two central terms in the 6-element dataset.

\frac{88 + 92}{2} = 90

.

For an even-count set of

N = 6

items, the median is defined as the average of the

\frac{N}{2}

-th (3rd) and

(\frac{N}{2} + 1)

-th (4th) terms.

Key Concept

Descriptive Statistics Interpretation (Median of Even-Count Subsets)

Question 1586Question →

If $r$ and $s$ are positive integers, is $r^2 - s^2$ divisible by 8?

(1) $r$ and $s$ are both odd integers.
(2) $r + s$ is divisible by 4.

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: EACH statement ALONE is sufficient.

Answer

Each statement alone is sufficient to answer the question with a definitive 'Yes'.

The correct response identifies that each statement alone gives a definitive 'Yes' answer. Statement (1) shows that the square of any odd integer is

1 \pmod 8

, so subtracting two odd squares gives

0 \pmod 8

. Statement (2) shows

r+s

is a multiple of 4, which forces

r

and

s

to share parity, making

r-s

even and their product

(r+s)(r-s)

a multiple of

4 \times 2 = 8

.

Step-by-Step Solution

1

Rephrase the question target using algebraic factorization.

Note that

r^2 - s^2 = (r + s)(r - s)

. The question asks whether

(r + s)(r - s)

is a multiple of 8.

Factoring difference of squares isolates the sum and difference components to easily test parity and divisibility.

2

Evaluate Statement (1):

r

and

s

are both odd integers.

Any odd integer can be written as

2k + 1

. Squaring gives

(2k + 1)^2 = 4k^2 + 4k + 1 = 4k(k + 1) + 1

. Since

k(k + 1)

is the product of two consecutive integers, it is always even, making

4k(k + 1)

a multiple of 8. Thus, any odd integer squared leaves a remainder of 1 when divided by 8. Therefore,

r^2 \equiv 1 \pmod 8

and

s^2 \equiv 1 \pmod 8

, so

r^2 - s^2 \equiv 1 - 1 = 0 \pmod 8

.

Statement (1) alone yields a definitive 'Yes', so Statement (1) is sufficient.

3

Evaluate Statement (2):

r + s

is divisible by 4.

If

r + s

is divisible by 4, then

r + s = 4m

for some integer

m

. Since

r + s

is even,

r

and

s

must have the same parity (either both even or both odd). Consequently, their difference

r - s = (r + s) - 2s = 4m - 2s = 2(2m - s)

is an even integer (a multiple of 2). Multiplying

(r + s)

by

(r - s)

yields

(\text{multiple of } 4) \times (\text{multiple of } 2) = \text{multiple of } 8

.

Statement (2) alone yields a definitive 'Yes', so Statement (2) is sufficient.

Key Concept

Divisibility Rules of Difference of Squares and Parity of Integers

Estimated Time:2m 0s

Question 1587Question →

A bio-refinery processes two grades of raw biomass, Grade Alpha and Grade Beta, to produce liquid biofuel. Grade Alpha yields $15\%$ biofuel per ton, while Grade Beta yields $35\%$ biofuel per ton. If a single production batch used a combined total of $1,200$ tons of Grade Alpha and Grade Beta biomass, resulting in $V$ total tons of biofuel, is $V > 300$ ?

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.

The correct answer is the option stating that Statement (1) ALONE is sufficient, but Statement (2) alone is not. Rephrasing the target condition

V > 300

yields

A < 600

. Statement (1) provides

A < 533.33

, which definitively proves

A < 600

(a conclusive YES). Statement (2) provides

A < 700

, which permits values of

A

both above and below

600

, rendering it insufficient.

Step-by-Step Solution

1

Set up algebraic equations for total biomass and total biofuel yield.

Let

A

be the tons of Grade Alpha biomass and

B

be the tons of Grade Beta biomass. Given

A + B = 1,200

, we have

B = 1,200 - A

. Total biofuel yield is

V = 0.15A + 0.35B

.

Expressing

V

in terms of a single variable

A

simplifies the target question.

2

Rephrase the target question 'Is

V > 300

?' in terms of variable

A

.

Substitute

B = 1,200 - A

into the yield equation:

V = 0.15A + 0.35(1,200 - A) = 420 - 0.20A

. The condition

V > 300

becomes

420 - 0.20A > 300 \implies 120 > 0.20A \implies A < 600

. Thus, the question asks: 'Is

A < 600

?'

Rephrasing reduces the complex weighted average inequality to a straightforward threshold check on

A

.

3

Evaluate Statement (1): The ratio of Grade Alpha to Grade Beta tonnage was less than

4:5

.

\frac{A}{B} < \frac{4}{5} \implies 5A < 4B

. Substituting

B = 1,200 - A

gives

5A < 4(1,200 - A) \implies 9A < 4,800 \implies A < 533.33

. Since

A < 533.33

guarantees that

A < 600

, the answer to 'Is

A < 600

?' is a definitive YES. Statement (1) is SUFFICIENT.

Determining if Statement (1) alone guarantees

A < 600

.

4

Evaluate Statement (2): More than

500

tons of Grade Beta biomass was used in the batch.

B > 500 \implies 1,200 - A > 500 \implies A < 700

. If

A = 500

, then

A < 600

is TRUE (YES). If

A = 650

, then

A < 600

is FALSE (NO). Because both YES and NO outcomes are possible, Statement (2) is NOT SUFFICIENT.

Checking whether Statement (2) produces a single definitive YES/NO answer.

Key Concept

Data Sufficiency Question Stem Rephrased for Weighted Averages and Mixture Ratios

Question 1588Question →

Consider the following passage:

In an industrial audit of 40 manufacturing plants that adopted Calcined Clay Technology (CCT) to reduce industrial emissions, every audited plant achieved at least a 25 percent reduction in per-ton carbon output compared to traditional production methods. However, operating costs per ton rose by an average of 12 percent across all 40 facilities, primarily due to the energy consumed during clay calcination. Furthermore, plants that sourced raw clay locally recorded 15 percent lower transportation expenses than plants that imported raw clay.

Based on the passage, match each statement on the left to its proper logical classification on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement 1 matches Valid Inference; Statement 2 matches Unstated Assumption; Statement 3 matches Unwarranted Speculation.

The correct pairings accurately categorize each statement based on formal logical standards: Statement 1 strictly follows from the passage facts (Valid Inference); Statement 2 supplies a required unstated condition for net savings (Unstated Assumption); Statement 3 predicts an unsupported long-term industry shift (Unwarranted Speculation).

Step-by-Step Solution

1

Analyze the passage premises for explicit facts

Identified three facts: all 40 plants reduced carbon output by

\ge 25\%

, operating costs increased by an average of

12\%

across all 40 plants due to calcination energy, and local clay users saved

15\%

on transport.

Establishing factual boundaries is essential to separate strict deductions from unstated assumptions and speculative leaps.

2

Evaluate Statement 1 against factual premises

Statement 1 states that at least one plant experienced higher per-ton operating costs. Since all 40 audited plants had an average increase of

12\%

, this statement must be true strictly from the text.

A valid inference requires no outside information or unstated premises.

3

Evaluate Statement 2 and Statement 3 for unstated dependencies and scope leaps

Statement 2 fills a logical gap required to prove net raw-material savings (making it an unstated assumption), while Statement 3 makes an unproven projection about future industry-wide market trends (making it unwarranted speculation).

Assumptions bridge logical gaps within an argument, whereas speculations extrapolate beyond given data.

Key Concept

Distinguishing Inferences from Assumptions and Speculations

Question 1589Question →

If $x$ and $y$ are real numbers, is $x^2 + y^2 < 25$ ?

(1) $x + y = 7$
(2) $(x - 3)^2 + (y - 4)^2 = 0$

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.

Statement (1) allows multiple outcomes for

x^2 + y^2

(both values less than 25 and values greater than or equal to 25), so it is not sufficient. Statement (2) forces

x=3

and

y=4

because the sum of non-negative real squares can only be zero when each square term is zero. Substituting

x=3

and

y=4

yields

x^2 + y^2 = 25

, which conclusively answers 'No' to the question stem (

25 < 25

is false). Hence, Statement (2) alone is sufficient.

Step-by-Step Solution

1

Evaluate Statement (1) independently

Statement (1) gives

x + y = 7

. If

x = 3.5

and

y = 3.5

, then

x^2 + y^2 = 12.25 + 12.25 = 24.5 < 25

(Yes). If

x = 7

and

y = 0

, then

x^2 + y^2 = 49 + 0 = 49 \not< 25

(No).

Since both 'Yes' and 'No' are possible, Statement (1) alone is insufficient.

2

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

Statement (2) states

(x - 3)^2 + (y - 4)^2 = 0

. Since the square of a real number is non-negative, the sum of two squared terms can equal zero if and only if each term is zero:

x - 3 = 0 \implies x = 3

and

y - 4 = 0 \implies y = 4

.

This uniquely fixes the values of

x

and

y

.

3

Calculate the target expression using values from Statement (2)

Substitute

x = 3

and

y = 4

into

x^2 + y^2

:

3^2 + 4^2 = 9 + 16 = 25

. The question asks if

x^2 + y^2 < 25

. Since

25 < 25

is false, the answer is a definitive 'No'.

A definitive 'No' answer means the statement provides enough information to answer the question, so Statement (2) alone is sufficient.

Key Concept

Statement Independence in Data Sufficiency and Definitive Yes/No Decision Rules

Estimated Time:2m 0s

Question 1590Question →

Passage: An educational study evaluated high schools across several districts and observed that schools offering a mandatory financial literacy course had significantly higher average student savings account balances at graduation than schools without such a course. Based on this observation, the researchers concluded that mandatory financial literacy courses directly cause students to accumulate greater savings.

Statement: The researchers' conclusion is vulnerable to a confounding variable flaw if the schools offering the financial literacy course were located primarily in high-income communities where students received larger personal allowances.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True. High-income community status and higher personal allowances represent a confounding variable that provides an alternative causal explanation for the higher savings balances.

The statement is correct because introducing a systematic background difference—such as student allowance size driven by community wealth—creates an alternative explanation for why savings balances were higher. In GMAT Critical Reasoning, a causal argument is flawed if it assumes an observed correlation must mean one factor caused the other while ignoring plausible third-variable confounders.

Step-by-Step Solution

1

Identify the author's causal conclusion and evidence

Evidence: Schools with mandatory financial literacy courses have students with higher average savings. Conclusion: Financial literacy courses directly cause students to accumulate greater savings.

Understanding the premise-to-conclusion structure isolates the specific causal mechanism being claimed.

2

Evaluate the impact of the condition described in the statement

If course-offering schools are predominantly in affluent areas where students get larger allowances, those larger allowances could cause the higher savings regardless of the course.

A confounding variable is an external factor correlated with both the presumed cause and the effect that provides an alternative explanation for the observed outcome.

3

Assess whether the statement correctly characterizes this flaw

The statement correctly asserts that the argument is vulnerable to a confounding variable flaw under these conditions.

Failing to account for socioeconomic background invalidates the claim of direct causality from the course alone.

Key Concept

Causal Flaws and Confounding Variables

Question 1591Question →

An agronomist conducted a study of wheat farms across an agricultural county and observed that farms using a specialized microbial soil supplement achieved significantly higher crop yields per acre than farms that did not use the supplement. Based on this observation, the agronomist concluded that applying the microbial supplement directly causes an increase in wheat yields.

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

The farms that chose to adopt the microbial supplement were also those that utilized advanced drip-irrigation and targeted nutrient management systems.

Soil samples from fields treated with the microbial supplement showed a rapid increase in beneficial bacterial populations within two weeks of application.

Wheat produced on farms using sustainable agricultural practices commands a higher market price per bushel than conventionally grown wheat.

Synthetic chemical fertilizers have been shown to increase crop yields in corn and soybean cultivation in neighboring counties.

The retail purchase price of the microbial soil supplement increased significantly during the final year of the agronomist's study.

Show answer & explanation

Answer: The farms that chose to adopt the microbial supplement were also those that utilized advanced drip-irrigation and targeted nutrient management systems.

Answer

The argument is most seriously weakened by the choice stating that farms adopting the microbial supplement also utilized advanced drip-irrigation and targeted nutrient management systems.

The conclusion asserts a direct causal link between the microbial supplement and increased wheat yield. The correct choice reveals that the farms using the supplement were self-selected operations that simultaneously employed advanced irrigation and nutrient systems. These additional practices represent confounding variables that could fully account for the higher crop yields, severely undercutting the agronomist's conclusion.

Step-by-Step Solution

1

Identify the premise and conclusion of the causal argument

Premise: Farms using a microbial supplement had higher wheat yields per acre than farms not using it. Conclusion: The microbial supplement directly causes higher wheat yields.

Understanding the precise gap between observed correlation and claimed causation is essential for evaluating critical reasoning items.

2

Evaluate the logical vulnerability

The argument assumes that no third factor (confounding variable) accounts for the difference in crop yields between the two groups of farms.

Causal conclusions drawn from observational studies are vulnerable to selection bias and confounding variables.

3

Identify the option that introduces a confounding factor

The option pointing out that supplement-using farms also implemented advanced drip-irrigation and targeted nutrient systems establishes an alternative explanation for the increased yield.

If another major yield-enhancing factor was systematically present on the same farms, the observed increase in yield cannot be reliably attributed to the microbial supplement.

Key Concept

Causal Flaws and Confounding Variables

Estimated Time:1m 30s

Question 1592Question →

A logistics center uses two sorting systems, Line 1 and Line 2, to process package inventory. Line 1 operates at a constant rate of $r_1$ packages per minute, and Line 2 operates at a constant rate of $r_2$ packages per minute. During a testing run, Line 1 operated for $t_1$ minutes and Line 2 operated for $t_2$ minutes, sorting a total of $P$ packages. Was the combined average sorting rate during the test run—defined as the total packages sorted divided by total machine-minutes worked, $\frac{P}{t_1 + t_2}$ —greater than $40$ packages per minute?

(1) Line 1's sorting rate $r_1$ was $50\%$ greater than Line 2's sorting rate $r_2$ , and Line 1 operated for a duration $t_1$ that was $50\%$ longer than Line 2's operating duration $t_2$ .
(2) If Line 1 and Line 2 were to operate simultaneously for $1$ hour, they would sort a combined total of $3{}000$ packages.

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 that the combined average rate is 26 packages per minute, which definitively answers the question with a 'No'. Neither statement alone is sufficient.

The correct option is the one stating that both statements together are sufficient, but neither alone is sufficient. Statement (1) simplifies the weighted average rate to

1.3 r_2

, which is insufficient by itself because

r_2

is unknown. Statement (2) provides

r_1 + r_2 = 50

, which is insufficient alone because individual rates and time proportions are unknown. Combining both statements allows us to solve for

r_2 = 20

and compute the exact weighted average rate of

26

packages per minute. Since

26

is not greater than

40

, we obtain a definitive 'No' answer, establishing sufficiency.

Step-by-Step Solution

1

Rephrase the target question algebraically.

The combined average sorting rate is

\text{Average Rate} = \frac{P}{t_1 + t_2} = \frac{r_1 t_1 + r_2 t_2}{t_1 + t_2}

. The target question asks: Is

\frac{r_1 t_1 + r_2 t_2}{t_1 + t_2} > 40

?

Establishing the target formula in terms of

r_1, r_2, t_1,

and

t_2

allows direct evaluation of each statement.

2

Evaluate Statement (1) independently.

Statement (1) gives

r_1 = 1.5 r_2

and

t_1 = 1.5 t_2

. Substituting these into the average rate formula gives

\frac{(1.5 r_2)(1.5 t_2) + r_2 t_2}{1.5 t_2 + t_2} = \frac{2.25 r_2 t_2 + r_2 t_2}{2.5 t_2} = \frac{3.25 r_2 t_2}{2.5 t_2} = 1.3 r_2

.

Since the value of

r_2

is unknown, we cannot determine whether

1.3 r_2 > 40

. Statement (1) alone is INSUFFICIENT.

3

Evaluate Statement (2) independently.

Operating simultaneously for

1

hour (

60

minutes) produces

3{}000

packages:

60(r_1 + r_2) = 3000 \implies r_1 + r_2 = 50

packages per minute.

Knowing

r_1 + r_2 = 50

does not fix the ratio of durations

t_1 / t_2

or individual rates

r_1, r_2

. The weighted average could be anywhere between

r_1

and

r_2

. Statement (2) alone is INSUFFICIENT.

4

Evaluate Statements (1) and (2) together.

From Statement (1),

r_1 = 1.5 r_2

. Substituting into Statement (2)'s equation

r_1 + r_2 = 50

yields

1.5 r_2 + r_2 = 50 \implies 2.5 r_2 = 50 \implies r_2 = 20

. Consequently,

r_1 = 30

. Substituting

r_2 = 20

into the expression from Statement (1) gives an average rate of

1.3 \times 20 = 26

packages per minute.

Since

26

is not greater than

40

, we can answer the question with a definitive 'No'. A definitive 'No' means the combined statements are SUFFICIENT.

Key Concept

Weighted average rate simplification and Yes/No sufficiency determination in Data Sufficiency.

Estimated Time:2m 30s

Question 1593Question →

### Tab 1: Strategic Bio-Licensing Protocol (Policy 808)
Under BioPharma Corp's Policy 808, cross-border commercialization sub-licenses for Class III biologic therapies require prior written approval from the Global Licensing Board (GLB) unless the sub-licensor operates in a Tier 1 jurisdiction AND has maintained full compliance with ISO-13485 standards for at least 3 consecutive fiscal years.

Exception Clause 4B: If a sub-license or underlying therapy involves co-development with a state-backed entity, GLB prior written approval is mandatory regardless of jurisdiction tier or ISO certification status.

### Tab 2: Regulatory Audit Memorandum (Project Orion)
Entity Evaluated: Apex Biotherapeutics Ltd. (operating in Region Alpha, a designated Tier 1 jurisdiction).

Background: Apex entered a Class III biologic co-development partnership in Q1 2025 with the National Health Research Institute (NHRI), a state-backed public research institute.

Compliance Record: Apex achieved ISO-13485 certification in January 2023 and has maintained clean annual audit ratings through Q2 2026 (completing 3 consecutive fiscal years of full compliance: 2023, 2024, and 2025).

Action Taken: In March 2026, Apex issued a commercial sub-license for the co-developed biologic therapy to a regional distributor without submitting a prior written approval request to the GLB.

Based on the information provided in the documents, determine whether the following statement is True or False:

Apex Biotherapeutics Ltd.'s issuance of the sub-license in March 2026 without prior written approval from the Global Licensing Board constituted a violation of Policy 808.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True.

The statement is True because Exception Clause 4B in Policy 808 explicitly mandates prior written approval from the Global Licensing Board whenever co-development involves a state-backed entity, regardless of the sub-licensor's jurisdiction tier or ISO compliance history. Since Apex co-developed the therapy with NHRI (a state-backed entity) and issued the sub-license without GLB approval, it violated Policy 808.

Step-by-Step Solution

1

Analyze the baseline policy rule and standard exemption requirements in Tab 1.

General Rule: Sub-licensing Class III biologics requires GLB approval unless (1) sub-licensor is in a Tier 1 jurisdiction AND (2) has maintained ISO-13485 compliance for at least 3 consecutive fiscal years.

Establishing the default compliance threshold.

2

Analyze the entity's profile in Tab 2 against the baseline requirements.

Apex operates in Region Alpha (Tier 1) and achieved ISO compliance for 2023, 2024, and 2025 (3 consecutive fiscal years). Under general rules alone, Apex would appear exempt.

Checking if standard exemption criteria are met.

3

Check for overarching policy exceptions across both documents.

Tab 1 contains Exception Clause 4B: GLB approval is mandatory if the therapy involves co-development with a state-backed entity. Tab 2 reveals the therapy was co-developed with NHRI, a state-backed public research institute.

Identifying overriding clauses that supersede standard exemptions.

4

Synthesize the findings to evaluate the statement.

Because Clause 4B applies, GLB approval was mandatory. Omitting GLB approval constituted a violation of Policy 808.

Determining final truth value.

Key Concept

Synthesizing text documents to evaluate conditional rules and overriding policy exceptions across tabs.

Question 1594Question →

The table below details the quarterly electricity consumption (in kWh) for six regional branches of a commercial enterprise:

Branch	Region	Q1 (kWh)	Q2 (kWh)	Q3 (kWh)	Q4 (kWh)
Alpha	North	12,000	14,000	15,000	11,000
Beta	South	18,000	16,000	17,000	19,000
Gamma	North	9,000	10,000	11,000	10,000
Delta	East	22,000	25,000	24,000	21,000
Epsilon	West	15,000	15,000	16,000	14,000
Zeta	South	11,000	13,000	12,000	12,000

Based on the table, evaluate the following statement:
"The median Q1 electricity consumption of branches in the North region is greater than the median Q1 electricity consumption of branches in the South region."

Is this statement True or False?

True

False

Show answer & explanation

Answer: False

Answer

The statement is False. The median Q1 electricity consumption for branches in the North region (

10,500\text{ kWh}

) is less than the median Q1 electricity consumption for branches in the South region (

14,500\text{ kWh}

).

The evaluation shows that the median Q1 value for the North region (

10,500\text{ kWh}

) is strictly less than the median Q1 value for the South region (

14,500\text{ kWh}

). Therefore, the assertion that North is greater than South evaluates to False.

Step-by-Step Solution

1

Identify Q1 consumption figures for branches in the North region and calculate their median.

Branches in the North region are Alpha (

12,000\text{ kWh}

) and Gamma (

9,000\text{ kWh}

). The median is

\frac{12,000 + 9,000}{2} = 10,500\text{ kWh}

.

Filtering rows by the condition 'Region = North' isolates the correct values for statistical evaluation.

2

Identify Q1 consumption figures for branches in the South region and calculate their median.

Branches in the South region are Beta (

18,000\text{ kWh}

) and Zeta (

11,000\text{ kWh}

). The median is

\frac{18,000 + 11,000}{2} = 14,500\text{ kWh}

.

Filtering rows by the condition 'Region = South' isolates the comparison dataset.

3

Compare the two median values to evaluate the boolean statement.

Comparing

10,500\text{ kWh}

to

14,500\text{ kWh}

shows that

10,500 < 14,500

, making the statement false.

The statement claims North is greater than South, which contradicts the calculated result.

Key Concept

Filtered subset descriptive statistics comparison

Estimated Time:1m 0s

Question 1595Question →

A renewable energy research laboratory tested four experimental photovoltaic panel coatings (Coating Alpha, Coating Beta, Coating Gamma, and Coating Delta) across three sunlight intensity levels (Low, Medium, and High). The table below displays the measured power output, in watts per square meter ( $\text{W/m}^2$ ), for each coating under each sunlight intensity level:

Coating	Low Intensity	Medium Intensity	High Intensity
Coating Alpha	80	180	280
Coating Beta	90	195	310
Coating Gamma	75	170	$x$
Coating Delta	$y$	200	320

What is the average (arithmetic mean) power output of Coating Gamma across all three sunlight intensity levels?

(1) Under High Intensity, the power output of Coating Gamma is 10% greater than the power output of Coating Alpha under High Intensity.

(2) The average (arithmetic mean) power output of Coating Delta across the three intensity levels is equal to the average (arithmetic mean) power output of Coating Beta across the three intensity levels.

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.

Rephrasing the question target shows that finding the average power output of Coating Gamma requires finding the unknown value

x

. Statement (1) directly gives a percentage relationship between

x

and Coating Alpha's high-intensity output (

280 \text{ W/m}^2

), allowing us to calculate

x = 308

and thus the exact mean. Statement (2) allows us to solve for

y

(Coating Delta's low-intensity output), but provides no information about

x

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

Step-by-Step Solution

1

Rephrase the question stem target

The average power output of Coating Gamma is

\frac{75 + 170 + x}{3} = \frac{245 + x}{3}

. To find this average, we only need to determine the value of

x

.

Simplifying the question target clarifies that finding

x

is both necessary and sufficient.

2

Evaluate Statement (1)

Statement (1) states that under High Intensity, Coating Gamma (

x

) is 10% greater than Coating Alpha (280). Thus,

x = 280 \times 1.10 = 308 \text{ W/m}^2

. We can compute the average as

\frac{245 + 308}{3} = 184.33 \text{ W/m}^2

.

Since a single unique numerical value for

x

is found, Statement (1) ALONE is sufficient.

3

Evaluate Statement (2)

Statement (2) gives the mean of Coating Delta as equal to the mean of Coating Beta. Mean of Coating Beta =

\frac{90 + 195 + 310}{3} = \frac{595}{3}

. Setting

\frac{y + 200 + 320}{3} = \frac{595}{3}

yields

y = 75 \text{ W/m}^2

.

Finding

y

gives information about Coating Delta, but provides no information regarding

x

for Coating Gamma. Thus, Statement (2) ALONE is not sufficient.

Key Concept

Target Rephrasing and Independent Statement Evaluation in Tabular Data Sufficiency

Estimated Time:2m 0s

Question 1596Question →

A pharmaceutical laboratory manufactures a specialized compound by blending two liquid preparations, Solution $X$ and Solution $Y$ . Solution $X$ contains Active Ingredient $P$ and water in the ratio $3:2$ by weight. Solution $Y$ contains Active Ingredient $P$ and water in the ratio $1:4$ by weight. A master batch is created by mixing $x$ grams of Solution $X$ with $y$ grams of Solution $Y$ , where $x > 0$ and $y > 0$ . Is the percentage of Active Ingredient $P$ in the master batch greater than $40\%$ by weight?

(1) $3x - 4y > 0$
(2) After adding $50$ grams of pure water to the master batch, Active Ingredient $P$ accounts for less than $\frac{1}{3}$ of the total weight of the resulting mixture.

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.

The correct response identifies that Statement (1) alone is sufficient while Statement (2) alone is not. By rephrasing the question stem, the target condition 'Is the active ingredient concentration greater than 40%?' simplifies directly to the inequality condition

x > y

. Statement (1) guarantees that

x > \frac{4}{3}y

, which directly implies

x > y

since

y > 0

, providing a definitive 'Yes'. Statement (2) simplifies to

2x - y < 125

, which is satisfied by parameter pairs where

x > y

as well as pairs where

x < y

, making it insufficient.

Step-by-Step Solution

1

Rephrase the question stem target algebraically.

Solution X is

\frac{3}{3+2} = \frac{3}{5} = 0.60

(or

60\%

) Ingredient P by weight. Solution Y is

\frac{1}{1+4} = \frac{1}{5} = 0.20

(or

20\%

) Ingredient P by weight. The total weight of Ingredient P in the master batch is

0.6x + 0.2y

, and the total weight of the batch is

x + y

. The question asks whether

\frac{0.6x + 0.2y}{x + y} > 0.40

. Since

x > 0

and

y > 0

, multiplying across by

(x + y)

gives

0.6x + 0.2y > 0.4x + 0.4y \implies 0.2x > 0.2y \implies x > y

. Thus, the rephrased question is: 'Is

x > y

?'

Simplifying the question stem before evaluating statements prevents unnecessary system solving and clarifies the exact threshold needed for sufficiency.

2

Evaluate Statement (1):

3x - 4y > 0

.

Rearranging

3x - 4y > 0

gives

3x > 4y \implies x > \frac{4}{3}y

. Because

y > 0

,

\frac{4}{3}y > y

. Therefore, if

x > \frac{4}{3}y

, it must strictly be true that

x > y

. This yields a definitive 'Yes' to the rephrased question. Hence, Statement (1) ALONE is sufficient.

Since statement 1 establishes a lower bound for x relative to y that is strictly greater than 1y, it answers the question 'Is x > y?' definitively.

3

Evaluate Statement (2): Adding 50 grams of water results in P accounting for less than

\frac{1}{3}

of total weight.

Total weight of P remains

0.6x + 0.2y

. The new total weight is

x + y + 50

. The statement gives

\frac{0.6x + 0.2y}{x + y + 50} < \frac{1}{3}

. Multiplying by

3(x + y + 50)

yields

1.8x + 0.6y < x + y + 50 \implies 0.8x - 0.4y < 50 \implies 2x - y < 125

. Testing values:
- Case A: Let

x = 10, y = 50

. Then

2(10) - 50 = -30 < 125

holds. Here

x < y

, so the answer is 'No'.
- Case B: Let

x = 100, y = 90

. Then

2(100) - 90 = 110 < 125

holds. Here

x > y

, so the answer is 'Yes'.
Since Statement (2) permits both 'Yes' and 'No' outcomes, Statement (2) ALONE is not sufficient.

An inequality involving absolute scale (50 grams) fails to determine a purely proportional relationship between x and y without additional constraints on total batch size.

Key Concept

Question Stem Simplification and Mixture Ratio Inequalities

Question 1597Question →

[Tab 1: Global Data Infrastructure Directive on Workload Offloading]

Global Data Center Policy Rules (2026 Revision):
- Standard Carbon Credit: Facilities in Region A that offload at least $30\%$ of their monthly compute workloads to certified renewable cloud providers earn a carbon offset credit of $\$50$ per Megawatt-hour (MWh) of offloaded energy.
- Peak Summer PUE Condition: During peak summer months (June, July, and August), if a facility's average Power Usage Effectiveness (PUE) exceeds $1.50$ , the carbon offset credit rate is reduced to $\$25$ per MWh for that month.
- Liquid Cooling Exemption: The peak summer PUE rate reduction does not apply—and the full $\$50$ per MWh rate is retained—if a facility utilizes direct liquid cooling on more than $40\%$ of its server racks during that month.

[Tab 2: Data Center Alpha-9 Operational Metrics]

Month	Total Energy (MWh)	Workload Offloaded (%)	Average PUE	Liquid Cooling Racks (%)
May	1,000	35%	1.42	35%
June	1,200	40%	1.55	35%
July	1,500	30%	1.60	35%
August	1,400	25%	1.52	35%
September	1,100	35%	1.45	35%

Based on the information provided across both tabs, evaluate the following statement:

Data Center Alpha-9 earned a total carbon offset credit of exactly $\$23,250$ for energy offloaded during the peak summer months of June, July, and August combined.

True

False

Show answer & explanation

Answer: True

Answer

True. Data Center Alpha-9 earned a total carbon offset credit of $23,250 across June, July, and August by correctly applying the 30% offload threshold and the peak summer PUE rate reduction.

The statement is correct because synthesizing Tab 1 policy rules with Tab 2 operational data shows that June earns

12,000 (480 MWh at

25/MWh due to PUE > 1.50), July earns

11,250 (450 MWh at

25/MWh due to PUE > 1.50), and August earns

0 (offload percentage of 25% fails the 30% minimum threshold). The total across June, July, and August equals exactly

23,250.

Step-by-Step Solution

1

Identify peak summer months and basic eligibility criteria

Peak summer months are June, July, and August. Tab 1 specifies a mandatory minimum offload threshold of 30% to qualify for any carbon credit.

Establishes time parameters and primary threshold eligibility.

2

Evaluate June credit eligibility and rate

June offloaded 40% of 1,200 MWh = 480 MWh. Since PUE = 1.55 (> 1.50) and liquid cooling is 35% (≤ 40%), the reduced rate of

25/MWh applies. June credit = 480 ×

25 = $12,000.

Applies conditional PUE rate reduction logic to qualifying June data.

3

Evaluate July credit eligibility and rate

July offloaded 30% of 1,500 MWh = 450 MWh. Since PUE = 1.60 (> 1.50) and liquid cooling is 35% (≤ 40%), the reduced rate of

25/MWh applies. July credit = 450 ×

25 = $11,250.

Applies conditional PUE rate reduction logic to qualifying July data.

4

Evaluate August credit eligibility

August offloaded 25% of compute workload, failing the 30% minimum threshold. August credit = $0.

Excludes non-qualifying months based on policy threshold bounds.

5

Sum total credit for June, July, and August

Total summer credit =

12,000 +

11,250 +

0 =

23,250.

Reconciles multi-month data to evaluate the statement.

Key Concept

Multi-Source Policy Enforcement and Threshold Reconciliation

Estimated Time:2m 30s

Question 1598Question →

A coffee roaster creates a signature blend using only two types of beans: Arabica and Robusta. In a specific batch of this signature blend, what percentage of the total weight of the batch consists of Arabica beans?

(1) If 10 kilograms of Arabica beans were added to the batch, the ratio of the weight of Arabica beans to the weight of Robusta beans in the batch would be $3:2$ .
(2) The total cost of the Arabica beans in the batch is $50\%$ greater than the total cost of the Robusta beans in the batch, and Arabica beans cost $25\%$ more per kilogram than Robusta beans.

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.

Statement (2) alone allows us to express the price per kilogram of Arabica beans in terms of Robusta beans (

p_A = 1.25 p_R

) and set up an equation equating total costs (

A \cdot p_A = 1.50 R \cdot p_R

). Dividing out the unit price

p_R

gives a direct constant value for the weight ratio

\frac{A}{R} = \frac{6}{5}

, which uniquely determines the percentage of Arabica beans in the batch.

Step-by-Step Solution

1

Define target variables and simplify the question stem.

Let

A

be the weight of Arabica beans (in kg) and

R

be the weight of Robusta beans (in kg). The target percentage is

\frac{A}{A + R} \times 100\%

, which requires finding the ratio

\frac{A}{R}

.

Rephrasing the stem to finding the ratio

\frac{A}{R}

isolates the exact relation needed to answer the question.

2

Evaluate Statement (1) independently.

Statement (1) gives

\frac{A + 10}{R} = \frac{3}{2} \Rightarrow 2A + 20 = 3R \Rightarrow 3R - 2A = 20

. This is one linear equation with two unknowns (

A

and

R

).

Since the ratio

\frac{A}{R}

varies depending on the specific values of

A

and

R

(e.g., if

A=2, R=8

,

\frac{A}{R}=\frac{1}{4}

; if

A=14, R=16

,

\frac{A}{R}=\frac{7}{8}

), Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) independently.

Let

p_A

and

p_R

be the price per kg of Arabica and Robusta beans, respectively. We are given

p_A = 1.25 p_R = \frac{5}{4} p_R

. Total cost of Arabica =

A \cdot p_A

and total cost of Robusta =

R \cdot p_R

. Statement (2) states

A \cdot p_A = 1.50 (R \cdot p_R) = \frac{3}{2} R \cdot p_R

. Substituting

p_A = \frac{5}{4} p_R

gives

A \left(\frac{5}{4} p_R\right) = \frac{3}{2} R \cdot p_R

. Dividing both sides by

p_R

yields

\frac{5}{4} A = \frac{3}{2} R \Rightarrow \frac{A}{R} = \frac{3/2}{5/4} = \frac{6}{5}

.

Knowing

\frac{A}{R} = \frac{6}{5}

allows us to calculate

\frac{A}{A + R} = \frac{6}{6 + 5} = \frac{6}{11}

, giving a unique percentage of

\frac{600}{11}\% \approx 54.55\%

. Thus, Statement (2) alone IS sufficient.

Key Concept

Data Sufficiency Evaluation of Weighted Ratios and Multiplicative Pricing Relationships

Estimated Time:2m 0s

Question 1599Question →

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

(1) $a^2 + b^2 = 4ab$
(2) $a > b > 0$

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

Answer

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

Statement (1) allows us to determine that the square of the target expression

(a+b)/(a-b)

equals 3, which gives two possible values:

\sqrt{3}

and

-\sqrt{3}

. Statement (2) provides the condition

a > b > 0

, ensuring that both

a+b

and

a-b

are positive, so their quotient must be positive. Combining both statements eliminates

-\sqrt{3}

, uniquely determining that the expression equals

\sqrt{3}

. Thus, both statements together are sufficient.

Step-by-Step Solution

1

Express the square of the target expression in terms of basic algebraic components.

Let

E = \frac{a + b}{a - b}

. Squaring both sides yields

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

.

Rewriting the ratio in squared form allows substitution of expressions involving

a^2 + b^2

and

ab

.

2

Evaluate Statement (1) independently.

Substitute

a^2 + b^2 = 4ab

into the squared ratio:

E^2 = \frac{4ab + 2ab}{4ab - 2ab} = \frac{6ab}{2ab} = 3

. Taking the square root gives

E = \sqrt{3}

or

E = -\sqrt{3}

.

Because Statement (1) allows two distinct possible values for

E

, Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) independently.

Statement (2) states

a > b > 0

. This implies

a + b > 0

and

a - b > 0

, so

E > 0

, but no numerical value is specified.

Without quantitative equations, Statement (2) alone is NOT sufficient.

4

Evaluate Statements (1) and (2) combined.

From Statement (1),

E = \pm\sqrt{3}

. From Statement (2),

E > 0

. Combining both rules out

-\sqrt{3}

, leaving uniquely

E = \sqrt{3}

.

The two statements together establish a single, unique value for the target expression.

Key Concept

Evaluating algebraic ratios via squared identities and applying inequality sign constraints to eliminate redundant roots in Data Sufficiency.

Estimated Time:1m 30s

Question 1600Question →

The table below presents technical specifications and operational parameters for seven Earth-observation satellites in a commercial constellation:

Satellite ID	Operational Status	Orbital Altitude (km)	Sensor Resolution (m)	Downlink Speed (Gbps)
Sat-01	Active	420	0.4	10
Sat-02	Active	580	1.1	20
Sat-03	Active	640	0.5	16
Sat-04	Active	490	0.9	12
Sat-05	Standby	510	0.6	18
Sat-06	Active	550	0.5	14
Sat-07	Active	450	1.5	8

What is the average (arithmetic mean) Downlink Speed, in Gbps, of all satellites that are currently Active, have an Orbital Altitude of at most 600 km, and satisfy AT LEAST ONE of the following criteria: a Sensor Resolution of less than 0.8 m OR a Downlink Speed of at least 15 Gbps?

12.00

12.80

14.67

15.00

15.50

Show answer & explanation

Answer: 14.67

Answer

14.67 Gbps

The correct response identifies the three satellites (Sat-01, Sat-02, and Sat-06) that satisfy all mandatory criteria (Active status and altitude

\leq 600

km) as well as at least one of the secondary criteria (resolution

< 0.8

m or downlink

\geq 15

Gbps). Their downlink speeds are 10, 20, and 14 Gbps respectively, yielding an arithmetic mean of

\frac{10 + 20 + 14}{3} = 14.67

Gbps.

Step-by-Step Solution

1

Evaluate mandatory conditions (Operational Status = Active AND Orbital Altitude

\leq 600

km).

Satellites meeting these two conditions are Sat-01 (420 km), Sat-02 (580 km), Sat-04 (490 km), Sat-06 (550 km), and Sat-07 (450 km). Sat-03 is excluded due to altitude (640 km

> 600

km), and Sat-05 is excluded due to status (Standby).

Conjunctive criteria require all mandatory parameters to be met simultaneously.

2

Evaluate the disjunctive condition (Sensor Resolution

< 0.8

m OR Downlink Speed

\geq 15

Gbps) among the candidate satellites.

- Sat-01: Resolution

= 0.4

m (

< 0.8

)

\rightarrow

QUALIFIES
- Sat-02: Downlink

= 20

Gbps (

\geq 15

)

\rightarrow

QUALIFIES
- Sat-04: Resolution

= 0.9

m and Downlink

= 12

Gbps

\rightarrow

FAILS
- Sat-06: Resolution

= 0.5

m (

< 0.8

)

\rightarrow

QUALIFIES
- Sat-07: Resolution

= 1.5

m and Downlink

= 8

Gbps

\rightarrow

FAILS

An OR condition requires a candidate to satisfy at least one of the sub-criteria.

3

Calculate the arithmetic mean Downlink Speed for the qualifying satellites (Sat-01, Sat-02, Sat-06).

Sum of downlink speeds =

10 + 20 + 14 = 44

Gbps.
Mean =

\frac{44}{3} \approx 14.67

Gbps.

The mean is the total sum of downlink speeds divided by the count of filtered rows.

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Multi-column compound filtering combining conjunctive AND and disjunctive OR conditions prior to aggregation.

Estimated Time:2m 30s

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