All practice questions

Question 1661Question →

To qualify for the Municipal Green Architecture Grant, a building renovation project must reduce its annual energy consumption by at least 40 percent. The recent renovation of the historic Sterling Theater successfully reduced its annual energy consumption by 45 percent. Therefore, the Sterling Theater project will definitely receive the Municipal Green Architecture Grant.

Which of the following best describes the flaw in the reasoning above?

It assumes that receiving the municipal grant is what caused the Sterling Theater to achieve its energy reduction.

It bases a broad judgment about all municipal building projects on the outcome of a single theater renovation.

It treats a requirement necessary for obtaining the grant as if it were a sufficient condition to guarantee receiving the grant.

It assumes without evidence that other historic theaters in the city are unable to meet the energy reduction threshold.

It infers that achieving a 45 percent energy reduction will negatively impact the overall operating budget of the theater.

Show answer & explanation

Answer: It treats a requirement necessary for obtaining the grant as if it were a sufficient condition to guarantee receiving the grant.

Answer

The argument's flaw is that it treats a necessary prerequisite (reducing energy consumption by at least 40 percent) as though it were a sufficient condition that guarantees receiving the grant.

The passage establishes that achieving a 40 percent energy reduction is a necessary condition ('must') to qualify for the grant. The author observes that the Sterling Theater achieved a 45 percent reduction and concludes that it will definitely receive the grant. This reasoning is flawed because satisfying a necessary condition makes a project eligible, but does not guarantee that the grant will be awarded; there may be other criteria, budget limitations, or competitive evaluations involved. Thus, the argument incorrectly treats a necessary condition as a sufficient one.

Step-by-Step Solution

1

Analyze the premises and conditional statement

The text states that reducing energy consumption by at least 40 percent is a mandatory requirement ('must') to qualify for the grant. This establishes energy reduction as a necessary condition.

Identifying indicator words like 'must' helps distinguish necessary conditions from sufficient conditions.

2

Analyze the evidence and conclusion

The Sterling Theater achieved a 45 percent reduction (satisfying the necessary condition), and the author concludes that the project will 'definitely receive' the grant.

The author concludes that satisfying the entry requirement guarantees the final outcome.

3

Identify the logical vulnerability

Satisfying a necessary requirement makes an applicant eligible to be considered, but does not guarantee selection (there could be limited funds, additional criteria, or competing applicants).

Mistaking eligibility (necessary) for a guarantee of success (sufficient) is a classic formal logic flaw.

Key Concept

Confusing Necessary and Sufficient Conditions

Estimated Time:1m 30s

Question 1662Question →

The table below displays operational performance metrics for 10 regional cold-chain distribution centers operated by a pharmaceutical logistics company across two geographic zones.

Distribution Center	Zone	Cold Storage Volume ( $10^3\text{ m}^3$ )	Temperature Excursions	On-Time Delivery Rate (%)
Center H-1	Zone East	45	12	94.2
Center H-2	Zone West	80	18	91.5
Center H-3	Zone East	60	8	96.8
Center H-4	Zone East	30	22	89.0
Center H-5	Zone West	55	14	93.4
Center H-6	Zone East	75	5	98.1
Center H-7	Zone West	40	16	92.0
Center H-8	Zone East	90	11	95.5
Center H-9	Zone West	65	9	95.0
Center H-10	Zone East	50	15	92.6

By how many percentage points does the median On-Time Delivery Rate of the distribution centers in Zone East exceed the mean On-Time Delivery Rate of all 10 distribution centers?

1.04 percentage points

0.39 percentage points

1.69 percentage points

0.56 percentage points

0.26 percentage points

Show answer & explanation

Answer: 1.04 percentage points

Answer

The median On-Time Delivery Rate of Zone East distribution centers exceeds the mean On-Time Delivery Rate of all 10 centers by 1.04 percentage points.

The mean of all 10 distribution centers is calculated by summing all on-time delivery rates (

938.1\%

) and dividing by 10 to get

93.81\%

. Filtering for Zone East gives 6 centers with delivery rates

[89.0\%, 92.6\%, 94.2\%, 95.5\%, 96.8\%, 98.1\%]

. Because

N = 6

is even, the median is the average of the 3rd (

94.2\%

) and 4th (

95.5\%

) terms, yielding

94.85\%

. Subtracting

93.81\%

from

94.85\%

gives

1.04

percentage points.

Step-by-Step Solution

1

Calculate the mean On-Time Delivery Rate for all 10 distribution centers.

Sum of all delivery rates =

94.2 + 91.5 + 96.8 + 89.0 + 93.4 + 98.1 + 92.0 + 95.5 + 95.0 + 92.6 = 938.1\%

. Mean =

\frac{938.1}{10} = 93.81\%

.

To establish the overall average delivery performance benchmark across all facilities.

2

Filter the dataset to isolate the distribution centers in Zone East.

Zone East consists of 6 centers: H-1 (

94.2\%

), H-3 (

96.8\%

), H-4 (

89.0\%

), H-6 (

98.1\%

), H-8 (

95.5\%

), and H-10 (

92.6\%

).

The question specifically requires evaluating the median of the Zone East subset.

3

Sort the Zone East On-Time Delivery Rates in ascending order.

Sorted list of 6 values:

[89.0\%, 92.6\%, 94.2\%, 95.5\%, 96.8\%, 98.1\%]

.

Sorting is a mandatory prerequisite step before determining the median of any dataset.

4

Calculate the median of the even-count (N = 6) Zone East subset.

The two central values (3rd and 4th) are

94.2\%

and

95.5\%

. Median =

\frac{94.2 + 95.5}{2} = 94.85\%

.

For an even number of elements, the median is defined as the exact arithmetic mean of the two middle elements.

5

Compute the difference between the calculated median and mean.

94.85\% - 93.81\% = 1.04

percentage points.

To answer the specific target question regarding the margin by which the median exceeds the mean.

Key Concept

Descriptive Statistics Interpretation from Tabular Subsets

Question 1663Question →

Consider the following multi-source information regarding coastal ecological restoration:

Tab 1: Research Proposal (Marine Ecology Institute)
Dr. Thorne proposes planting macroalgae kelp near coral reefs in Sector B to mitigate ocean acidification. Dr. Thorne argues that kelp photosynthesis reduces dissolved carbon dioxide ( $CO_2$ ), thereby directly raising seawater pH and protecting coral calcification rates.

Tab 2: Environmental Monitoring Data (Sector B)
| Location | Kelp Density ( $g/m^2$ ) | Dissolved $CO_2$ ( $ppm$ ) | Seawater pH | Coral Calcification Rate ( $mg/cm^2/day$ ) |
| Sector B1 | 450 | 340 | 8.15 | 1.8 |
| Sector B2 | 120 | 410 | 7.95 | 1.1 |
| Sector B3 | 480 | 405 | 7.96 | 1.2 |

Tab 3: Oceanographic Study (Hydrodynamics Bulletin)
Sector B3 undergoes intense seasonal upwelling, drawing deep ocean water high in dissolved $CO_2$ to the surface. The high nutrient levels in upwelled water drive rapid kelp growth in B3, but the inflow of $CO_2$ far exceeds the carbon absorption capacity of the kelp population.

Statement to evaluate:
Evaluating the data from Sector B3 alongside Sector B1 weakens Dr. Thorne's argument that high kelp density is sufficient to increase local seawater pH.

True

False

Show answer & explanation

Answer: True

Answer

True. Integrating the observational data from Tab 2 with the oceanographic findings from Tab 3 reveals that Sector B3 has the highest kelp density (

480\text{ g/m}^2

) yet maintains a depressed pH level (

7.96

) because upwelled

CO_2

exceeds the absorption capacity of the kelp. This proves that kelp density is not sufficient by itself to ensure elevated seawater pH, directly weakening Dr. Thorne's argument.

The statement is true because cross-tab synthesis of Tab 2 and Tab 3 demonstrates that high kelp density in Sector B3 coincides with low seawater pH (

7.96

) due to heavy

CO_2

upwelling that exceeds biological uptake. Comparing B3 to B1 invalidates the premise that kelp planting alone is sufficient to increase localized pH.

Step-by-Step Solution

1

Identify Dr. Thorne's central argument in Tab 1.

Dr. Thorne asserts that planting kelp absorbs dissolved

CO_2

, which raises local seawater pH.

Establishing the claim is required before determining whether multi-tab evidence strengthens or weakens it.

2

Compare monitoring data across Sector B1 and Sector B3 in Tab 2.

Sector B1 has kelp density

450\text{ g/m}^2

,

CO_2

level

340\text{ ppm}

, and pH

8.15

. Sector B3 has higher kelp density (

480\text{ g/m}^2

), higher

CO_2

(

405\text{ ppm}

), and lower pH (

7.96

).

Evaluating whether higher kelp density correlates with higher pH across locations tests the sufficiency of kelp for raising pH.

3

Synthesize Tab 2 data with the contextual oceanographic mechanism in Tab 3.

Tab 3 explains that upwelling in B3 supplies nutrients for kelp growth but introduces

CO_2

in volumes exceeding kelp uptake. Thus, kelp presence cannot counteract the

CO_2

influx to raise pH in B3.

Combining cross-tab evidence reveals that high kelp density is insufficient to guarantee high pH when unmitigated carbon inputs exist, thereby weakening the proposed intervention's underlying claim.

Key Concept

Evaluating Argument Support and Weakening Across Tabs

Estimated Time:1m 30s

Question 1664Question →

If $p$ and $q$ are real numbers, what is the value of $(p + q)^2$ ?

(1) $p^2 + q^2 = 25$
(2) $pq = 12$

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.

Expanding the target expression gives

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

. Statement (1) provides

p^2 + q^2 = 25

but leaves

pq

unknown, making it insufficient alone. Statement (2) provides

pq = 12

but leaves

p^2 + q^2

unknown, making it insufficient alone. Combining both statements allows direct substitution into the identity:

(p + q)^2 = 25 + 2(12) = 49

, which yields a single unique answer.

Step-by-Step Solution

1

Rephrase the question stem algebraically.

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

Expanding the target expression shows that calculating

(p + q)^2

requires knowing the sum of squares

(p^2 + q^2)

and the product

pq

.

2

Evaluate Statement (1) independently.

Insufficient

Given

p^2 + q^2 = 25

, the term

2pq

remains unknown. For example, if

p = 5

and

q = 0

, then

(p+q)^2 = 25

; if

p = 3

and

q = 4

, then

(p+q)^2 = 49

. Since multiple outcomes exist, Statement (1) alone is insufficient.

3

Evaluate Statement (2) independently.

Insufficient

Given

pq = 12

, the term

p^2 + q^2

remains unknown. For example, if

p = 3

and

q = 4

, then

(p+q)^2 = 49

; if

p = 1

and

q = 12

, then

(p+q)^2 = 169

. Since multiple outcomes exist, Statement (2) alone is insufficient.

4

Evaluate Statements (1) and (2) together.

Sufficient

Substituting

p^2 + q^2 = 25

and

pq = 12

into

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

yields

25 + 2(12) = 49

. This determines a unique value.

Key Concept

Algebraic Identity Expansion and Substitution in Data Sufficiency

Question 1665Question →

To reduce fuel expenditure across its ocean cargo fleet, a maritime shipping company plans to apply a new hydrodynamic coating to the underwater hulls of all its vessels. In controlled tank tests, vessels treated with the coating experienced a 12 percent reduction in drag compared to untreated vessels. The company's directors conclude that applying this coating will significantly lower the fleet's total annual fuel expenditure.

Which of the following, if true, casts the most serious doubt on the directors' conclusion?

In actual ocean environments, marine organisms rapidly adhere to the specialized coating, creating surface roughness that negates the drag reduction unless the hulls undergo frequent and costly cleanings.

Computer simulations indicate that applying the same hydrodynamic coating to vessel rudders yields an additional 3 percent reduction in water resistance.

Several competing maritime shipping companies have recently placed orders for next-generation cargo vessels equipped with wind-assisted propulsion sails.

The hydrodynamic hull coating was developed by an independent naval engineering institute rather than by the shipping company's internal research team.

Fuel expenditure currently constitutes the largest single component of the shipping company's total annual operating budget.

Show answer & explanation

Answer: In actual ocean environments, marine organisms rapidly adhere to the specialized coating, creating surface roughness that negates the drag reduction unless the hulls undergo frequent and costly cleanings.

Answer

The argument is most weakened by the finding that in actual ocean environments, marine organisms rapidly adhere to the specialized coating, creating surface roughness that negates the drag reduction unless the hulls undergo frequent and costly cleanings.

The conclusion relies on the assumption that the 12 percent drag reduction measured in controlled tank tests will produce significant real-world net fuel savings. The correct option directly shatters this assumption by revealing that real ocean conditions cause biological growth on the coating that negates drag reduction and adds substantial maintenance costs, thereby preventing the expected net savings.

Step-by-Step Solution

1

Analyze the argument structure

Premise: Controlled tank tests showed a 12% reduction in drag for coated hulls. Conclusion: Applying the coating across the fleet will significantly lower total annual fuel expenditure.

Identifying the explicit premises and conclusion reveals the underlying assumption connecting test results to real-world financial outcomes.

2

Identify the key unstated assumption

The argument assumes that performance in controlled tank tests will translate directly to real-world ocean conditions without introducing prohibitive secondary costs.

A weakening item must attack this gap between laboratory performance and net operational cost savings.

3

Evaluate the options against the key assumption

The statement regarding marine organisms accumulating on the hull demonstrates that operational ocean conditions actively destroy the drag reduction effect and introduce heavy maintenance costs.

This directly undermines the conclusion that total annual fuel expenditure will significantly decrease.

Key Concept

Weakening Arguments - Unstated Assumptions in Causal/Experimental Transitions

Estimated Time:1m 30s

Question 1666Question →

In GMAT Data Sufficiency, when evaluating whether Statement (2) alone is sufficient to answer the question stem, any algebraic conditions or variable constraints introduced exclusively within Statement (1) must be completely disregarded.

True

False

Show answer & explanation

Answer: True

Answer

True. Statement (2) must be evaluated in strict isolation from Statement (1).

Each statement in a Data Sufficiency question must be evaluated independently first. Statement (1) constraints cannot be referenced or assumed during the standalone evaluation of Statement (2).

Step-by-Step Solution

1

Recall the fundamental procedural rules of GMAT Data Sufficiency.

Statement (1) and Statement (2) must be evaluated independently before any combining step is attempted.

Independent evaluation determines whether either statement alone answers the question stem.

2

Apply the rule of independence specifically to the evaluation phase of Statement (2).

When evaluating Statement (2), Statement (1) is treated as non-existent.

Carrying over constraints from Statement (1) creates a false sense of sufficiency for Statement (2) alone.

Key Concept

Statement Independence in Data Sufficiency

Question 1667Question →

A corporate governance study monitored 60 multinational technology firms over a three-year period to evaluate the impact of introducing automated AI hiring software for mid-level managerial positions. The study observed that firms adopting the AI software experienced a 25 percent increase in annual manager turnover. Based on this observation, the lead researcher concluded that automated AI screening causes increased manager attrition because candidates selected by AI lack interpersonal compatibility with existing teams. Which of the following statements, if true, weaken the lead researcher's causal conclusion? Select all that apply.

Select all that apply

Firms experiencing elevated manager turnover prior to the study were significantly more likely to adopt the automated AI hiring software to streamline recruitment.

The increased manager attrition rates prompted affected firms to substantially expand their internal human resources departments.

Simultaneously with adopting the AI software, participating firms introduced stricter quarterly performance targets that resulted in higher rates of performance-based terminations.

Non-managerial staff turnover remained entirely stable across all 60 multinational technology firms throughout the three-year monitoring period.

The automated AI hiring software reduced the average time required to fill vacant managerial positions from 45 days to 12 days.

Show answer & explanation

Answer: Firms experiencing elevated manager turnover prior to the study were significantly more likely to adopt the automated AI hiring software to streamline recruitment.; Simultaneously with adopting the AI software, participating firms introduced stricter quarterly performance targets that resulted in higher rates of performance-based terminations.

Answer

The statements establishing selection bias in pre-existing high turnover firms and introducing an alternative explanation through stricter performance targets both weaken the causal conclusion.

The causal claim is that AI hiring software causes increased manager turnover due to team incompatibility. The option noting that high-turnover firms selectively adopted the AI software demonstrates reverse causality and selection bias, showing that turnover predated software adoption. The option noting that firms concurrently instituted stricter performance targets introduces a confounding variable that provides an alternative explanation for the increased terminations. Both statements undermine the researcher's conclusion.

Step-by-Step Solution

1

Identify the causal claim and proposed mechanism in the stem

The researcher claims that automated AI hiring software causes increased manager attrition due to poor interpersonal compatibility of AI-selected candidates.

Understanding the precise cause and effect is necessary to evaluate weakening conditions.

2

Evaluate statements for alternative causal directions or confounding variables

Showing that high turnover existed prior to adoption (reverse causality) or that stricter performance targets caused higher termination rates (confounding variable) invalidates the direct causal link.

Causal conclusions are weakened when reverse causality or confounding third variables explain the observed correlation.

Key Concept

Evaluating Causal Arguments and Weakening Causal Claims

Question 1668Question →

### Tab 1: Deep-Sea Turbidity Regulatory Standards
The International Seabed Exploration Authority (ISEA) mandates that deep-sea harvesting vessels operating in Abyssal Zone 4 must maintain daily average turbidity increases below $15.0 \text{ NTU}$ (Nephelometric Turbidity Units) above baseline levels.
- Standard Fine Penalty: Any vessel exceeding the $15.0 \text{ NTU}$ daily threshold incurs a standard fine of $\$50,000$ per day of violation.
- Eco-Tech Exemption Clause: Vessels equipped with active silt-curtain recovery systems receive a $+3.0 \text{ NTU}$ allowance (raising their daily limit to $18.0 \text{ NTU}$ before incurring penalties), provided the silt curtains are continuously deployed for at least $20 \text{ hours}$ on that operational day.
- Consecutive Violation Surcharge: If a vessel violates the applicable daily turbidity limit for $3$ or more consecutive days, a flat $50\%$ surcharge is applied to the total standard fines accrued across those consecutive violation days.

### Tab 2: Vessel Operations Log (Week 12)
The harvesting vessel *Nautilus V* operated in Abyssal Zone 4 during Week 12. Below are the recorded daily average turbidity increases and silt-curtain operation logs:
- Monday: Turbidity Increase = $16.5 \text{ NTU}$ ; Silt-Curtain Deployed = $22 \text{ hours}$
- Tuesday: Turbidity Increase = $18.5 \text{ NTU}$ ; Silt-Curtain Deployed = $21 \text{ hours}$
- Wednesday: Turbidity Increase = $17.2 \text{ NTU}$ ; Silt-Curtain Deployed = $18 \text{ hours}$
- Thursday: Turbidity Increase = $15.8 \text{ NTU}$ ; Silt-Curtain Deployed = $24 \text{ hours}$
- Friday: Turbidity Increase = $14.2 \text{ NTU}$ ; Silt-Curtain Deployed = $0 \text{ hours}$

### Tab 3: Post-Inspection Audit Findings
An independent ISEA audit revealed that on Wednesday, due to a mechanical winch failure, *Nautilus V*'s silt curtains were operational for only $18 \text{ hours}$ (failing the $20$ -hour minimum requirement for the Eco-Tech Exemption), although the crew originally logged the curtain as functional all day. No other mechanical failures or log discrepancies were identified during Week 12.

Evaluate the following statement as True or False based on the information provided across the three tabs:

"The total fines (including any applicable surcharges) assessed against the vessel *Nautilus V* for Week 12 equal exactly $\$150,000$ ."

True

False

Show answer & explanation

Answer: False

Answer

False. The total fines assessed against Nautilus V for Week 12 equal

100,000, not

150,000.

The statement is False because the total fines assessed equal

\$100,000

, not

\$150,000

. *Nautilus V* violated regulations on Tuesday (

18.5 \text{ NTU} > 18.0 \text{ NTU}

) and Wednesday (

17.2 \text{ NTU} > 15.0 \text{ NTU}

due to Tab 3 audit findings). Thursday was compliant (

15.8 \text{ NTU} \le 18.0 \text{ NTU}

). With only

2

consecutive violation days, no

50\%

surcharge applies.

Step-by-Step Solution

1

Evaluate Monday compliance using Tab 1 and Tab 2

Turbidity is

16.5 \text{ NTU}

with

22 \text{ hours}

of curtain deployment. Since deployment

\ge 20 \text{ hours}

, the limit is

18.0 \text{ NTU}

.

16.5 \le 18.0 \implies

No violation (

Fine = \$0

).

Exemption allowance applies when curtain deployment meets or exceeds

20 \text{ hours}

.

2

Evaluate Tuesday compliance using Tab 1 and Tab 2

Turbidity is

18.5 \text{ NTU}

with

21 \text{ hours}

of curtain deployment. The limit is

18.0 \text{ NTU}

.

18.5 > 18.0 \implies

Violation Day 1 (

Fine = \$50,000

).

Turbidity exceeds the exempted limit of

18.0 \text{ NTU}

.

3

Evaluate Wednesday compliance reconciling Tab 1, Tab 2, and Tab 3

Tab 3 confirms curtain deployment was only

18 \text{ hours} < 20 \text{ hours}

. Exemption does not apply, so the limit is

15.0 \text{ NTU}

. Turbidity is

17.2 \text{ NTU} > 15.0 \implies

Violation Day 2 (

Fine = \$50,000

).

Failing the

20

-hour operational threshold revokes the

+3.0 \text{ NTU}

allowance.

4

Evaluate Thursday and Friday compliance using Tab 1 and Tab 2

Thursday:

15.8 \text{ NTU}

with

24 \text{ hours}

deployment

\implies

limit is

18.0 \text{ NTU}

.

15.8 \le 18.0 \implies

No violation. Friday:

14.2 \text{ NTU} \le 15.0 \text{ NTU} \implies

No violation.

Neither Thursday nor Friday exceeds its respective applicable limit.

5

Calculate total fines and verify consecutive violation surcharge applicability

Total base fine =

\$50,000 \text{ (Tue)} + \$50,000 \text{ (Wed)} = \$100,000

. Consecutive violation days =

2

. Since

2 < 3

, surcharge =

0\%

. Total assessed fine =

\$100,000

.

The

50\%

surcharge triggers only upon

3

or more consecutive days of violation.

Key Concept

Multi-Source Reasoning Dichotomous Choice Evaluation

Question 1669Question →

The table below provides operational metrics for 10 international clinical trial sites participating in a multi-center biopharmaceutical study:

Site ID	Therapeutic Area	Patients Enrolled	Drop-out Rate (%)	Average Treatment Duration (Days)
Site A	Oncology	42	12.5	180
Site B	Immunology	56	8.0	120
Site C	Oncology	30	15.0	225
Site D	Neurology	64	6.25	90
Site E	Oncology	78	10.0	150
Site F	Immunology	48	12.5	135
Site G	Oncology	50	14.0	165
Site H	Neurology	32	9.375	105
Site I	Oncology	60	5.0	195
Site J	Immunology	40	10.0	150

Statement: For the subset of clinical trial sites with a drop-out rate of at least 10.0%, the median Average Treatment Duration exceeds the median Patients Enrolled by more than 110 days.

True

False

Show answer & explanation

Answer: True

Answer

True. The median Average Treatment Duration for the filtered subset of 6 sites is 157.5 days, and the median Patients Enrolled is 45 patients. The difference of 112.5 days exceeds 110 days.

The statement is correct (True) because filtering for sites with a drop-out rate of at least

10.0\%

yields exactly 6 sites. The median of Patients Enrolled across these 6 sites is

\frac{42+48}{2} = 45

, and the median of Average Treatment Duration is

\frac{150+165}{2} = 157.5

. The difference

157.5 - 45 = 112.5

is strictly greater than 110.

Step-by-Step Solution

1

Filter the dataset by the given condition

Subset consists of 6 sites with Drop-out Rate

\ge 10.0\%

: Site A, Site C, Site E, Site F, Site G, and Site J.

Only sites meeting the threshold of

\ge 10.0\%

drop-out rate must be analyzed.

2

Determine the median of Patients Enrolled for the filtered subset

Ordered values:

30, 40, 42, 48, 50, 78

. Median =

\frac{42 + 48}{2} = 45

.

Because the subset size

N = 6

is even, the median is the arithmetic mean of the two middle elements (3rd and 4th).

3

Determine the median of Average Treatment Duration for the filtered subset

Ordered values:

135, 150, 150, 165, 180, 225

. Median =

\frac{150 + 165}{2} = 157.5

.

Because

N = 6

is even, the median is the arithmetic mean of the 3rd and 4th ordered values.

4

Calculate the difference between the two medians and evaluate the statement

Difference =

157.5 - 45 = 112.5

days, which is greater than 110 days.

Since

112.5 > 110

, the statement is True.

Key Concept

Descriptive Statistics Interpretation on Filtered Even-Count Subsets

Question 1670Question →

If $x$ and $y$ are positive real numbers, is the product $xy$ an odd integer?

(1) $x^2y$ is an odd integer.
(2) $xy^2$ is an odd integer.

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

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

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

EACH statement ALONE is sufficient.

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

Show answer & explanation

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

Answer

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

The correct option is the choice stating that Statements (1) and (2) together are NOT sufficient. Since

x

and

y

are positive real numbers, setting

x = y = \sqrt[3]{3}

satisfies both

x^2y = 3

and

xy^2 = 3

(both odd integers), but gives

xy = \sqrt[3]{9}

, which is not an integer. Conversely, setting

x = 1/\sqrt[3]{3}

and

y = \sqrt[3]{9}

yields

x^2y = 3

and

xy^2 = 9

(both odd integers), giving

xy = 3

, which is an odd integer. Because both a 'No' and a 'Yes' answer are possible, the information remains insufficient even when both statements are combined.

Step-by-Step Solution

1

Analyze the stem constraints and target question.

The target asks whether

xy

is an odd integer, given that

x

and

y

are positive real numbers (not necessarily integers).

Recognizing that

x

and

y

are not restricted to integers is essential to avoid invalid integer assumption traps.

2

Evaluate Statement (1) independently.

Statement (1) gives

x^2y = k

for some odd integer

k

. If

x = \sqrt{3}

and

y = 1

, then

x^2y = 3

(an odd integer), but

xy = \sqrt{3}

(not an integer). If

x = 3

and

y = 1

, then

x^2y = 9

(an odd integer) and

xy = 3

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

Testing non-integer values demonstrates that

xy

may or may not be an integer.

3

Evaluate Statement (2) independently.

Statement (2) gives

xy^2 = m

for some odd integer

m

. If

x = 1

and

y = \sqrt{3}

, then

xy^2 = 3

(an odd integer), but

xy = \sqrt{3}

(not an integer). If

x = 1

and

y = 3

, then

xy^2 = 9

(an odd integer) and

xy = 3

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

Symmetry with Statement (1) confirms that Statement (2) alone produces variable outcomes.

4

Evaluate Statements (1) and (2) combined.

Multiplying the two expressions gives

(x^2y)(xy^2) = x^3y^3 = (xy)^3 = km

. Since

k

and

m

are odd integers, their product

km

is also an odd integer, say

P

. Thus,

(xy)^3 = P \implies xy = \sqrt[3]{P}

. If

k = 3

and

m = 3

, then

P = 9

, so

xy = \sqrt[3]{9}

(not an integer). If

k = 3

and

m = 9

, then

P = 27

, so

xy = \sqrt[3]{27} = 3

(an odd integer). Because

xy

can be either an odd integer or a non-integer, the combined statements are NOT sufficient.

Combining the statements yields

(xy)^3

equal to an odd integer, which does not guarantee that

xy

itself is an integer.

Key Concept

Implicit Real vs. Integer Constraints in Data Sufficiency

Estimated Time:2m 0s

Question 1671Question →

A theater sold a total of $100$ tickets for a performance, consisting of standard tickets ( $s$ ) at $\$25$ each and VIP tickets ( $v$ ) at $\$50$ each. The total revenue from ticket sales was $\$3,500$ . Match each ticket category to the correct number of tickets sold.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Standard Tickets matches to 60; VIP Tickets matches to 40.

The correct matches are Standard Tickets to 60 and VIP Tickets to 40 because solving the system

s + v = 100

and

25s + 50v = 3500

gives

s = 60

and

v = 40

.

Step-by-Step Solution

1

Set up the simultaneous linear equations from the text.

s + v = 100

and

25s + 50v = 3500

The total count equation represents total tickets, and the price equation represents total revenue.

2

Divide the revenue equation by 25 to simplify terms.

s + 2v = 140

Simplifying the coefficients reduces calculation complexity.

3

Subtract the first equation (

s + v = 100

) from the simplified second equation (

s + 2v = 140

).

v = 40

Subtracting eliminates the variable

s

directly.

4

Substitute

v = 40

back into

s + v = 100

.

s = 60

Yields the value for the remaining variable

s

.

Key Concept

Solving simultaneous linear equations in two variables.

Question 1672Question →

A municipal water treatment plant fills a main reservoir by pumping water from Inlet Pipe $A$ and Inlet Pipe $B$ simultaneously for 6 hours. The water entering through Pipe $A$ has a mineral concentration of $a$ milligrams per liter ( $\text{mg/L}$ ), and the water entering through Pipe $B$ has a mineral concentration of $b\text{ mg/L}$ , where $a < b$ . Is the final mineral concentration of the water in the reservoir less than $\frac{a + b}{2}\text{ mg/L}$ ?

(1) The rate at which Pipe $A$ pumps water is 20 percent greater than the rate at which Pipe $B$ pumps water.
(2) The total volume of water pumped by Pipe $B$ during the 6 hours is 4,500 liters.

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 stem shows that the overall mineral concentration is less than the midpoint

\frac{a+b}{2}

if and only if a larger volume of water is drawn from the pipe with lower concentration (Pipe A), i.e.,

V_A > V_B

. Statement (1) establishes that Pipe A's pumping rate is

1.2

times Pipe B's rate, so over any identical time frame,

V_A > V_B

. This yields a definitive 'Yes' answer, making Statement (1) alone sufficient. Statement (2) provides only the total volume from Pipe B without any information about Pipe A, which is insufficient.

Step-by-Step Solution

1

Simplify and rephrase the question target mathematically.

The final concentration is

C = \frac{V_A a + V_B b}{V_A + V_B}

. The question asks if

C < \frac{a + b}{2}

, which expands to

2(V_A a + V_B b) < (V_A + V_B)(a + b) \iff 2V_A a + 2V_B b < V_A a + V_A b + V_B a + V_B b \iff V_A(a - b) < V_B(a - b)

. Since

a < b

, we know that

(a - b) < 0

. Dividing both sides of the inequality by

(a - b)

reverses the inequality sign, yielding

V_A > V_B

. Thus, the question asks: 'Is the volume of water supplied by Pipe A greater than the volume supplied by Pipe B?'

Rephrasing the question stem reveals the underlying relationship required to determine sufficiency.

2

Evaluate Statement (1) independently.

Statement (1) states that Pipe A's pumping rate

R_A

is 20 percent greater than Pipe B's rate

R_B

, so

R_A = 1.2 R_B

. Since both pipes operate for the exact same duration of 6 hours,

V_A = 6 R_A = 7.2 R_B

and

V_B = 6 R_B

. Since

R_B > 0

,

V_A = 1.2 V_B > V_B

is guaranteed to be true. Statement (1) gives a definitive 'Yes' to the rephrased question.

A statement that yields a definitive 'Yes' answer to a Yes/No question is sufficient.

3

Evaluate Statement (2) independently.

Statement (2) gives

V_B = 4,500

liters, but provides no information regarding Pipe A's pumping rate or total volume

V_A

. If

V_A = 5,000

liters, then

V_A > V_B

(Yes); if

V_A = 3,000

liters, then

V_A < V_B

(No). Because multiple outcomes are possible, Statement (2) is not sufficient.

An inability to determine a unique 'Yes' or 'No' answer makes a statement insufficient.

Key Concept

Question Stem Simplification and Weighted Average Inequalities in Data Sufficiency

Estimated Time:2m 0s

Question 1673Question →

If $m$ and $n$ are real numbers, what is the value of $m^2 - n^2$ ?

(1) $(m + n)^2 = 36$
(2) $m^2 + n^2 = 20$

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

Answer

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

The correct response identifies that statements (1) and (2) together leave sign ambiguity in the difference of squares because

m

and

n

can swap values while maintaining the same sum and sum of squares.

Step-by-Step Solution

1

Rephrase the target question

The target expression is

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

. To find a unique value, we need a unique numerical value for

(m + n)(m - n)

.

Factoring the difference of squares clarifies what information is necessary.

2

Evaluate Statement (1) alone

(m + n)^2 = 36 \implies m + n = 6

or

m + n = -6

. We have no information about

m - n

.

Since

m - n

can take infinitely many values,

m^2 - n^2

is not uniquely determined. Statement (1) is insufficient.

3

Evaluate Statement (2) alone

m^2 + n^2 = 20

.

Different pairs of numbers like

(m, n) = (\sqrt{20}, 0)

give

m^2 - n^2 = 20

, while

(m, n) = (0, \sqrt{20})

give

m^2 - n^2 = -20

. Statement (2) is insufficient.

4

Evaluate Statements (1) and (2) combined

Expand Statement (1):

m^2 + 2mn + n^2 = 36

. Substitute Statement (2):

20 + 2mn = 36 \implies 2mn = 16 \implies mn = 8

.
Now test values satisfying

m + n = 6

and

mn = 8

:
Case 1:

m = 4, n = 2 \implies m^2 - n^2 = 4^2 - 2^2 = 16 - 4 = 12

.
Case 2:

m = 2, n = 4 \implies m^2 - n^2 = 2^2 - 4^2 = 4 - 16 = -12

.
Since

m^2 - n^2

yields two distinct values (

12

and

-12

), the statements together are insufficient.

Symmetry between variables in a non-linear system creates multiple possible values for non-symmetric target expressions.

Key Concept

Symmetry and Degree Ambiguity in Algebraic Data Sufficiency

Question 1674Question →

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

(1) $x^2 - y^2 = 15$
(2) $x^2 y - x y^2 = 12$

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 each statement individually reveals that neither provides enough constraints on its own to solve for the sum of the variables. When both statements are combined, substituting the expression for the sum into the product equation yields a quartic polynomial in terms of the difference of the variables. Because the function is strictly increasing for positive values, it possesses exactly one positive real root. This single valid root uniquely determines the sum of the variables, making both statements together sufficient.

Step-by-Step Solution

1

Evaluate Statement (1) independently.

Statement (1) gives

x^2 - y^2 = (x-y)(x+y) = 15

. Multiple pairs of positive real numbers satisfy this (e.g.,

x=4, y=1

gives

x+y=5

;

x=8, y=7

gives

x+y=15

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

A single non-linear equation in two variables does not restrict

x+y

to a unique value.

2

Evaluate Statement (2) independently.

Statement (2) gives

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

. Infinitely many positive real pairs satisfy this condition (e.g.,

x=4, y=1

gives

x+y=5

;

x=3, y=1

does not yield 12, but continuous choices of

x, y > 0

allow multiple sums). Thus, Statement (2) alone is NOT sufficient.

Knowing the product

xy(x-y) = 12

leaves the value of

x+y

undetermined.

3

Combine Statement (1) and Statement (2).

Let

u = x-y

and

v = x+y

. Note that

u > 0

because

x^2 - y^2 = 15 > 0

and

x, y > 0

.
From (1),

v = \frac{15}{u}

.
Also,

xy = \frac{(x+y)^2 - (x-y)^2}{4} = \frac{v^2 - u^2}{4}

.
Substituting into (2):

\left(\frac{v^2 - u^2}{4}\right) u = 12 \implies u(v^2 - u^2) = 48

.
Substitute

v = \frac{15}{u}

into the equation:

u\left(\frac{225}{u^2} - u^2\right) = 48 \implies \frac{225}{u} - u^3 = 48 \implies u^4 + 48u - 225 = 0

.

Express the system in terms of the difference

u = x-y

and sum

v = x+y

to analyze uniqueness.

4

Determine the number of positive real roots for

u^4 + 48u - 225 = 0

.

Let

f(u) = u^4 + 48u - 225

. For

u > 0

, the derivative

f'(u) = 4u^3 + 48 > 0

, meaning

f(u)

is strictly increasing for all positive

u

. Since

f(0) = -225 < 0

and

\lim_{u \to \infty} f(u) = +\infty

, there is exactly ONE positive real root for

u

. Testing integer values shows

f(3) = 3^4 + 48(3) - 225 = 81 + 144 - 225 = 0

, so

u = 3

uniquely. Substituting

u = 3

into

v = \frac{15}{u}

yields

v = x+y = 5

uniquely (with positive numbers

x = 4, y = 1

).

A strictly increasing continuous function transitioning from negative to positive values has exactly one root.

Key Concept

Non-Linear Algebraic Systems and Root Uniqueness in Data Sufficiency

Question 1675Question →

A manufacturing facility produced two types of products, Type X and Type Y. In July, the total cost to produce $N$ units of Type X and $M$ units of Type Y was $4,200. What was the unit manufacturing cost of a Type X product?

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 provides sufficient data because the total cost for Type X products is given as

2,800 for

N = 70

units. Dividing

2,800 by 70 gives a unique unit manufacturing cost of $40 for Type X products, completely independent of Statement (1) and without needing information regarding Type Y.

Step-by-Step Solution

1

Rephrase the target question

Let

C_x

be the unit cost of Type X and

C_y

be the unit cost of Type Y. Total cost is

N \cdot C_x + M \cdot C_y = 4200

. The target question asks for the unique value of

C_x

.

Clarify what specific variable needs to be solved for.

2

Evaluate Statement (1) independently

Statement (1) tells us

C_y = 30

and

N = 2M

. Substituting into the total cost equation gives

N \cdot C_x + (N/2) \cdot 30 = 4200

, which simplifies to

N(C_x + 15) = 4200

. Since

N

is unknown,

C_x

cannot be uniquely determined. Statement (1) alone is NOT sufficient.

Determine if Statement (1) yields a single unique numerical value for

C_x

.

3

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

Statement (2) states that the total cost for Type X products is

N \cdot C_x = 2800

, and

N = 70

. Solving for

C_x

gives

C_x = 2800 / 70 = 40

. This uniquely answers the question stem directly. Statement (2) alone IS sufficient.

Test Statement (2) strictly in isolation.

Key Concept

Evaluating Statement Independence in Data Sufficiency

Question 1676Question →

Although proponents of government price caps on essential prescription drugs argue that such measures are vital to protect low-income patients from exorbitant healthcare costs, economic analysts point out that artificial price ceilings drastically reduce the projected revenue from newly developed therapies. Consequently, pharmaceutical companies will inevitably divert their funding away from high-risk, groundbreaking drug discovery toward safer, incremental modifications of existing medications. Because long-term therapeutic progress relies fundamentally on pioneering research rather than minor product iterations, implementing strict price caps on prescription drugs will ultimately undermine public health outcomes.

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

Government price caps on essential prescription drugs are effective mechanisms for ensuring low-income patients can access necessary medical treatment.

Artificial price ceilings significantly lower the financial returns that drug companies expect to earn from developing new medical therapies.

Pharmaceutical firms will respond to drug price controls by shifting research investments away from breakthrough discovery toward minor medicine modifications.

Enacting strict government regulation on prescription drug prices will in the long run prove detrimental to overall public health.

Abolishing price controls on prescription drugs would guarantee a rapid increase in the development of pioneering healthcare therapies.

Show answer & explanation

Answer: Enacting strict government regulation on prescription drug prices will in the long run prove detrimental to overall public health.

Answer

Enacting strict government regulation on prescription drug prices will in the long run prove detrimental to overall public health.

The correct answer accurately states the author's final claim: that implementing strict price caps on prescription drugs will ultimately undermine public health outcomes. The preceding sentences detail how price caps reduce revenue, leading pharmaceutical companies to shift R&D to safer modifications, which in turn leads to the overall negative impact on public health.

Step-by-Step Solution

1

Identify structural indicators and separate premises from conclusions.

The word 'Although' introduces a counter-perspective ('protect low-income patients'), followed by supporting evidence regarding reduced revenues and R&D shift.

Understanding the structural flow reveals which claims serve as support and which serves as the destination of the argument.

2

Distinguish between intermediate conclusions and the ultimate final claim.

The claim that firms will shift funding away from discovery is supported by revenue evidence, but itself supports the final sentence introduced by 'will ultimately undermine...'.

The main conclusion is the claim for which all other statements in the passage provide support, directly or indirectly.

3

Select the option that accurately paraphrases the ultimate final claim.

The final claim asserts that implementing strict price caps on prescription drugs will ultimately undermine public health outcomes.

The correct paraphrase directly captures this final judgment without overstating its scope.

Key Concept

Identifying the Main Conclusion by distinguishing it from premises, concessions, and intermediate conclusions.

Question 1677Question →

The table below details performance and financial metrics for 10 municipal express bus routes operated by a regional transit authority:

Route ID	Zone Type	Daily Ridership (Thousands)	On-Time Performance (%)	Operating Cost per Passenger ($)
Route U1	Urban Core	$14.2$	$82.5\%$	$3.40$
Route U2	Urban Core	$18.5$	$76.0\%$	$2.90$
Route U3	Urban Core	$22.0$	$88.0\%$	$4.10$
Route U4	Urban Core	$11.0$	$91.5\%$	$3.70$
Route U5	Urban Core	$16.4$	$79.0\%$	$2.50$
Route U6	Urban Core	$25.1$	$84.0\%$	$4.80$
Route S1	Suburban	$8.2$	$94.0\%$	$5.20$
Route S2	Suburban	$6.5$	$92.5\%$	$5.80$
Route S3	Suburban	$9.0$	$89.0\%$	$4.90$
Route S4	Suburban	$5.4$	$95.5\%$	$6.10$

Based on the table, what is the median Operating Cost per Passenger ($) for the express bus routes operating in the Urban Core zone?

3.40

3.55

3.57

3.70

3.90

Show answer & explanation

Answer: $3.55$

Answer

The median Operating Cost per Passenger for the Urban Core routes is $3.55.

Filtering the table for 'Urban Core' yields 6 routes. Sorting their Operating Cost per Passenger in ascending order gives:

2.50,

2.90,

3.40,

3.70,

4.10, and

4.80. Because there is an even number of items (6), the median is the arithmetic average of the middle two values (

3.40 and

3.70), which equals $3.55.

Step-by-Step Solution

1

Filter the table data for routes located in the 'Urban Core' Zone Type.

Identified 6 Urban Core routes: Route U1 (

3.40), Route U2 (

2.90), Route U3 (

4.10), Route U4 (

3.70), Route U5 (

2.50), and Route U6 (

4.80).

The question specifies finding descriptive statistics exclusively for the Urban Core zone routes.

2

Order the Operating Cost per Passenger values of the filtered Urban Core routes from least to greatest.

Sorted list of costs:

2.50,

2.90,

3.40,

3.70,

4.10,

4.80.

Finding a median requires ascending or descending order of values.

3

Calculate the median for the even dataset size (

N = 6

).

The two central values are the 3rd (

3.40) and 4th (

3.70) elements. Median =

\frac{\$3.40 + \$3.70}{2} = \$3.55

.

When a dataset contains an even number of elements, the median is the arithmetic mean of the two middle elements.

Key Concept

Descriptive Statistics Interpretation (Median of Filtered Even-Count Datasets)

Question 1678Question →

Tab 1: Cloud Provider Tiered Pricing Policy

CloudOps Enterprise Tier charges a flat base rate of $\$10,000$ per month, which includes up to $50,000$ Compute Hours (CH). Additional compute hours beyond $50,000$ CH up to $100,000$ CH are billed at a discounted overage rate of $\$0.15$ per CH. Compute hours exceeding $100,000$ CH in a given month are billed at the standard overage rate of $\$0.25$ per CH. Furthermore, a data egress surcharge of $\$0.02$ per Gigabyte (GB) is applied to all egress data exceeding $10$ Terabytes (TB) in a month (where $1\text{ TB} = 1,000\text{ GB}$ ).

Tab 2: Q3 Server Log Summary (Region Alpha)

- August 2026: Region Alpha logged a total of $85,000$ Compute Hours and transferred $15\text{ TB}$ of egress data.
- September 2026: Region Alpha logged a total of $110,000$ Compute Hours and transferred $8\text{ TB}$ of egress data.

Based on the pricing policy in Tab 1 and the usage logs in Tab 2, evaluate whether the following statement is True or False:

"The total combined cloud infrastructure invoice for Region Alpha for August 2026 and September 2026 combined exceeds $\$33,000$ ."

True

False

Show answer & explanation

Answer: True

Answer

True. Reconciling the tiered pricing policy with the usage logs yields an August invoice of

15,350 and a September invoice of

20,000, giving a combined total of

35,350, which exceeds

33,000.

The correct answer is True because calculated billing for August 2026 is

15,350 (

10,000 base +

5,250 Tier 1 overage +

100 egress surcharge) and for September 2026 is

20,000 (

10,000 base +

7,500 Tier 1 overage +

2,500 Tier 2 overage +

0 egress surcharge). The combined total of

35,350 exceeds the target threshold of $33,000.

Step-by-Step Solution

1

Calculate August 2026 compute cost and data egress surcharge.

August compute cost =

10,000 + (35,000 *

0.15) =

15,250. Egress excess = 15,000 GB - 10,000 GB = 5,000 GB, so surcharge = 5,000 *

0.02 =

100. Total August invoice =

15,350.

Compute usage of 85,000 CH fills the base 50,000 CH plus 35,000 CH in Tier 1 overage ($0.15/CH). Egress of 15 TB exceeds the 10 TB allowance by 5 TB (5,000 GB).

2

Calculate September 2026 compute cost and data egress surcharge.

September compute cost =

10,000 + (50,000 *

0.15) + (10,000 *

0.25) =

20,000. Egress surcharge =

0. Total September invoice =

20,000.

Compute usage of 110,000 CH fills the base 50,000 CH, the maximum 50,000 CH in Tier 1 overage (

7,500), and 10,000 CH in Tier 2 overage (

0.25/CH = $2,500). Egress of 8 TB does not exceed the 10 TB threshold.

3

Reconcile combined invoice total and compare against the $33,000 threshold.

Combined total =

15,350 +

20,000 =

35,350. Since

35,350 > $33,000, the statement is True.

Summing both monthly totals reconciles data across both tabs to evaluate the benchmark condition.

Key Concept

Quantitative Data Reconciliation Across Multi-Tier Pricing Policies and Usage Logs

Question 1679Question →

The table below presents energy and cost metrics for six commercial data center facilities operated by a cloud computing provider in fiscal year 2025.

Facility	IT Load Capacity (MW)	Renewable Energy Used (GWh)	Total Energy Consumption (GWh)	Operational Cost ($M)
Alpha	40	180	240	36.0
Beta	65	312	390	54.6
Gamma	25	100	160	22.4
Delta	80	360	480	72.0
Epsilon	50	225	300	42.0
Zeta	90	486	540	75.6

Statement: If the operational cost of facility Beta increases by 15% in 2026 while its IT load capacity remains unchanged, its 2026 operational cost per megawatt (MW) of IT load capacity will exceed the 2025 operational cost per megawatt of facility Alpha by more than 8%.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False because facility Beta's 2026 operational cost per MW (

0.966M/MW) exceeds facility Alpha's 2025 operational cost per MW (

0.900M/MW) by approximately 7.33%, which is less than 8%.

The correct evaluation is False. Facility Alpha's unit operational cost is

0.900M per MW (

36.0M / 40 MW). Facility Beta's unit cost in 2025 is

0.840M per MW (

54.6M / 65 MW). A 15% increase brings Beta's 2026 unit cost to

0.966M per MW. Comparing Beta's 2026 rate (

0.966M) to Alpha's 2025 rate (

0.900M) gives a relative increase of (

0.966 -

0.900) /

0.900 = 7.33%, which does not exceed 8%.

Step-by-Step Solution

1

Calculate facility Alpha's 2025 operational cost per MW of IT load capacity.

Facility Alpha cost per MW =

36.0M / 40 MW =

0.900M per MW.

Establishes the base value against which the 2026 rate will be compared.

2

Calculate facility Beta's 2025 operational cost per MW and its updated 2026 rate after a 15% increase.

Facility Beta 2025 rate =

54.6M / 65 MW =

0.840M per MW. Facility Beta 2026 rate =

0.840M × 1.15 =

0.966M per MW.

Applies the 15% growth rate to Beta's cost per unit capacity.

3

Compute the percentage change (excess) of facility Beta's 2026 rate relative to facility Alpha's 2025 rate.

Percentage excess = (

0.966M -

0.900M) / $0.900M = 0.066 / 0.900 = 7.33%.

Evaluates whether the percentage difference exceeds the 8% threshold requested in the statement.

Key Concept

Unit Rate Calculations and Percentage Change Base Selection

Question 1680Question →

To receive Series A funding from Vantage Ventures, a biotech startup must demonstrate successful Phase I safety trials for its lead drug candidate. BioSphere Therapeutics recently completed its Phase I trials with zero reported adverse events among all trial participants. The company's founders concluded that because they satisfied the firm's mandate by completing Phase I safety trials, Vantage Ventures will definitely approve their application for Series A funding. Which of the following best describes the vulnerability in the founders' reasoning?

It treats a condition that is necessary for securing funding as though it were sufficient to guarantee that funding.

It presumes without justification that completing Phase I safety trials causes a drug candidate to perform effectively in Phase II efficacy trials.

It relies on a sample of trial participants that is too small to draw statistically sound conclusions regarding long-term drug safety.

It overlooks the possibility that satisfying Phase I safety requirements actually decreases a startup's likelihood of attracting institutional investors.

It fails to consider whether competing venture capital firms offer more favorable investment terms than Vantage Ventures.

Show answer & explanation

Answer: It treats a condition that is necessary for securing funding as though it were sufficient to guarantee that funding.

Answer

The argument incorrectly treats a necessary prerequisite (completing Phase I safety trials) as a sufficient condition that guarantees funding approval.

The passage establishes that completing Phase I safety trials is a requirement (a necessary condition) for receiving Series A funding from Vantage Ventures. However, the founders conclude that meeting this single requirement guarantees funding approval (treating it as a sufficient condition). The argument fails to consider that other necessary conditions, such as commercial viability or valuation agreements, might also need to be satisfied.

Step-by-Step Solution

1

Identify the premises and modal qualifiers in the argument.

Premise: Securing funding requires Phase I safety trials ('must demonstrate'). Fact: BioSphere completed Phase I safety trials.

This establishes that Phase I safety trials are a necessary condition for obtaining funding.

2

Analyze the conclusion reached by the founders.

Conclusion: Vantage Ventures will definitely approve the funding application because Phase I safety trials were completed.

The founders treat fulfilling the prerequisite as a guarantee of the outcome ('definitely approve').

3

Evaluate the logical gap between the premises and conclusion.

Confusing a necessary condition with a sufficient condition.

Meeting a requirement is necessary to be considered, but other factors (financials, market size, team) may also be required before funding is granted.

Key Concept

Confusing Necessary and Sufficient Conditions

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

Answer

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Common Mistakes

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Common Mistakes

Answer

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Common Mistakes

Answer

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Common Mistakes

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Common Mistakes

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Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept