Multi-Statement Boolean Evaluation Practice Questions — GMAT

Question 1Question →

The table below details operational telemetry for eight municipal battery energy storage system (BESS) microgrid zones during 2025:

Zone Code	Battery Capacity (MWh)	Annual Energy Discharged (GWh)	Peak Efficiency (%)	Unplanned Maintenance (Hours)
Zone Alpha	120	43.2	92.5	48
Zone Beta	200	84.0	95.0	12
Zone Gamma	150	51.0	89.0	72
Zone Delta	300	117.0	94.2	24
Zone Epsilon	80	26.4	91.0	96
Zone Zeta	250	105.0	96.5	18
Zone Eta	180	59.4	88.5	60
Zone Theta	220	85.8	93.0	36

Consider the following three independent statements:

I. If the zones are sorted in ascending order by Battery Capacity (MWh), the median Peak Efficiency (%) of the lower half of the sorted zones is greater than $90.5\%$ .
II. The average annual energy discharged per MWh of battery capacity across the three zones with the fewest unplanned maintenance hours is strictly greater than $0.40\text{ GWh per MWh}$ .
III. Among the zones with a Peak Efficiency of at least $92.0\%$ , exactly four zones recorded fewer than $40$ unplanned maintenance hours.

Based on the table provided, is the evaluation that Statement I is False, Statement II is True, and Statement III is True correct?

True

False

Show answer & explanation

Answer: True

Answer

The overall evaluation is True because Statement I is False, Statement II is True, and Statement III is True.

Evaluating all three statements shows that Statement I is False (

90.0\% \ngtr 90.5\%

), Statement II is True (

0.408 > 0.40

), and Statement III is True (

4

zones meet both criteria). Thus, the proposed outcome (False, True, True) accurately describes the dataset.

Step-by-Step Solution

1

Evaluate Statement I by sorting zones by Battery Capacity and finding the median Peak Efficiency of the lower half.

Sorted capacity order: Epsilon (

80

), Alpha (

120

), Gamma (

150

), Eta (

180

), Beta (

200

), Theta (

220

), Zeta (

250

), Delta (

300

). Lower half: Epsilon (

91.0\%

), Alpha (

92.5\%

), Gamma (

89.0\%

), Eta (

88.5\%

). Efficiencies sorted:

88.5\%

,

89.0\%

,

91.0\%

,

92.5\%

. Median =

\frac{89.0\% + 91.0\%}{2} = 90.0\%

. Since

90.0\% \le 90.5\%

, Statement I is False.

Determines whether Statement I is correctly classified as False.

2

Evaluate Statement II by identifying the three zones with the minimum unplanned maintenance hours and computing their aggregate discharge per MWh of capacity.

Fewest maintenance hours: Zone Beta (

12\text{ hrs}

), Zone Zeta (

18\text{ hrs}

), Zone Delta (

24\text{ hrs}

). Sum of energy discharged =

84.0 + 105.0 + 117.0 = 306.0\text{ GWh}

. Sum of capacity =

200 + 250 + 300 = 750\text{ MWh}

. Rate =

\frac{306.0}{750} = 0.408\text{ GWh/MWh}

. Since

0.408 > 0.40

, Statement II is True.

Determines whether Statement II is correctly classified as True.

3

Evaluate Statement III by filtering zones with Peak Efficiency

\ge 92.0\%

and counting how many have unplanned maintenance hours under

40

.

Zones with Peak Efficiency

\ge 92.0\%

: Alpha (

92.5\%

,

48\text{ hrs}

), Beta (

95.0\%

,

12\text{ hrs}

), Delta (

94.2\%

,

24\text{ hrs}

), Zeta (

96.5\%

,

18\text{ hrs}

), Theta (

93.0\%

,

36\text{ hrs}

). Those with maintenance hours

< 40

: Beta, Delta, Zeta, Theta (

4

zones). Statement III is True.

Determines whether Statement III is correctly classified as True.

Key Concept

Multi-Statement Boolean Evaluation in Tabular Data

Question 2Question →

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 3Question →

The table below shows logistics performance data for six regional warehouses during the third quarter:

Warehouse	Region	Total Shipments	On-Time Delivery Rate	Avg. Processing Time (Hours)
Alpha	East	12,000	94%	14.5
Beta	West	8,500	96%	12.0
Gamma	East	15,200	91%	16.0
Delta	South	9,100	98%	10.5
Epsilon	West	11,400	95%	13.0
Zeta	South	14,000	93%	15.0

Match each statement on the left with its correct evaluation outcome on the right based on the table.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement I matches with True (West region average is 12.5 hours); Statement II matches with True (Gamma has highest shipments and lowest delivery rate); Statement III matches with False (3 out of 6 is exactly half, not more than half).

Each statement is evaluated against the data in the table: Statement I evaluates to True because the average for West warehouses (12.0 and 13.0) is 12.5 hours. Statement II evaluates to True because Gamma holds both the maximum shipment volume (15,200) and minimum delivery rate (91%). Statement III evaluates to False because exactly 3 out of 6 warehouses (50%) have delivery rates above 94%, which does not exceed half.

Step-by-Step Solution

1

Evaluate Statement I by filtering by Region = West.

Beta (12.0 hrs) and Epsilon (13.0 hrs) are in the West. Average = (12.0 + 13.0) / 2 = 12.5 hours. 12.5 < 13.0 is True.

Calculate the mean value of processing time for the specified subset.

2

Evaluate Statement II by identifying the maximum shipment count and minimum delivery rate.

Maximum shipments = 15,200 (Gamma). Minimum delivery rate = 91% (Gamma). The condition holds True.

Determine if both extreme statistical properties apply to the same entity.

3

Evaluate Statement III by filtering for delivery rates > 94%.

Beta (96%), Delta (98%), and Epsilon (95%) qualify (3 warehouses). 3 out of 6 equals 50%, which is not > 50%. The statement is False.

Compare the count of matching rows against the threshold 'more than half' (strictly greater than 50%).

Key Concept

Multi-Statement Boolean Evaluation on Tabular Data

Question 4Question →

The table below provides financial performance metrics for five corporate divisions of Vertex Global:

Division	Revenue ($M)	Operating Cost ($M)	Profit Margin (%)	Employees
Alpha	120	90	25.0%	450
Beta	200	170	15.0%	800
Gamma	80	50	37.5%	250
Delta	150	105	30.0%	500
Epsilon	300	270	10.0%	1,200

Evaluate the following statement as True or False based on the provided table:

Statement: For more than half of the divisions listed, the Revenue per employee strictly exceeds $250,000.

True

False

Show answer & explanation

Answer: True

Answer

True. Exactly 3 out of the 5 divisions (Alpha, Gamma, and Delta) have a Revenue per employee greater than $250,000, which satisfies the condition of being more than half.

The correct evaluation is True because calculating the ratio of Revenue to Employees for each of the five divisions shows that Alpha (

266,667), Gamma (

320,000), and Delta (

300,000) all have a Revenue per employee above

250,000. Three out of five divisions represents 60% of the divisions, which is more than half.

Step-by-Step Solution

1

Understand the condition and metric required

Need to calculate Revenue per employee (Revenue in dollars divided by number of employees) for each division and check if it is strictly greater than $250,000.

The statement specifies 'strictly exceeds $250,000' and applies to 'more than half' (at least 3 out of 5) of the divisions.

2

Compute Revenue per employee for each division

Alpha:

120M / 450 =

266,667; Beta:

200M / 800 =

250,000; Gamma:

80M / 250 =

320,000; Delta:

150M / 500 =

300,000; Epsilon:

300M / 1,200 =

250,000.

Performing explicit division allows precise comparison against the threshold value of $250,000.

3

Evaluate the threshold condition across all divisions

Divisions exceeding

250,000: Alpha, Gamma, Delta (Total = 3 divisions). Divisions equal to

250,000: Beta, Epsilon (Total = 2 divisions).

Values exactly equal to $250,000 do not satisfy 'strictly exceeds'.

4

Determine overall Boolean truth value

3 out of 5 divisions is 60%, which is more than half (50%). Thus, the statement evaluates to True.

Comparing the count of meeting divisions (3) against half of the dataset size (2.5).

Key Concept

Table Analysis & Boolean Statement Evaluation

Question 5Question →

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

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

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

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement 1 matches the evaluation confirming it is True (

2.40 > 2.2026

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

165 > 113.33

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

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

2.40

) exceeds the weighted average system cost (

2.2026

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

165

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

113.33

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

85\%

, below the required

88\%

threshold.

Step-by-Step Solution

1

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

Corridor operating costs in ascending order:

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

. Median =

\$2.40

. Total system operating cost =

\$340.3\text{ million}

; total trips =

154.5\text{ million}

. Weighted average =

\$340.3 / 154.5 \approx \$2.2026

. Median (

\$2.40

) > Weighted Average (

\$2.2026

). Statement 1 is True.

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

2

Filter and calculate subset fleet means for Statement 2.

Corridors with Zero-Emission

\ge 45\%

: C-North (

120

), C-South (

200

), C-Central (

250

), C-Harbor (

90

). Mean =

660 / 4 = 165

. Corridors with Zero-Emission

< 45\%

: C-East (

80

), C-West (

150

), C-Airport (

110

). Mean =

340 / 3 \approx 113.33

.

165 > 113.33

, so the statement claiming

165 < 113.33

is False.

Compares conditional subgroup averages correctly.

3

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

Corridors with On-Time Departure Rate

\ge 88\%

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

85\% < 88\%

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

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

Key Concept

Multi-Statement Boolean Evaluation on Tabular Data

Question 6Question →

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

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

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

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

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

True

False

Show answer & explanation

Answer: True

Answer

True

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

0.20 > 0.0975

), Statement II is False (

82.23\% > 82.0\%

), and Statement III is False (

84.0\% < 98.2\%

).

Step-by-Step Solution

1

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

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

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

2

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

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

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

3

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

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

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

4

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

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

Confirms the ultimate boolean evaluation of the composite claim.

Key Concept

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

Estimated Time:3m 0s

Question 7Question →

The table below presents operational and usage metrics for eight branch locations within a regional public library network during 2025:

Branch Code	Total Volumes (thousands)	Active Cardholders (thousands)	Annual Circulations (thousands)	Operating Expenses ($ thousands)	Digital Resource Accesses (thousands)
CEN	450	60	900	3,600	300
NOR	120	25	300	1,000	150
EAS	80	16	160	640	80
WES	150	20	240	960	120
SOU	200	40	500	1,500	250
RIV	90	18	225	720	90
HAR	110	22	220	880	110
UPL	160	32	480	1,440	160

Consider the following three statements regarding the data:

I. The median number of Annual Circulations among the branches with more than 20,000 Active Cardholders is greater than 350,000.
II. For Eastgate (EAS), the ratio of Annual Circulations per Total Volume is higher than that for West End (WES).
III. Exactly three branches satisfy both of the following conditions: Operating Expenses per Circulation are strictly less than $4.00, AND Digital Resource Accesses exceed 140,000.

Which of the following correctly identifies the truth values (True or False) of Statements I, II, and III, respectively?

Statement I: True; Statement II: True; Statement III: True

Statement I: False; Statement II: True; Statement III: True

Statement I: True; Statement II: False; Statement III: True

Statement I: True; Statement II: True; Statement III: False

Statement I: False; Statement II: False; Statement III: True

Show answer & explanation

Answer: Statement I: True; Statement II: True; Statement III: True

Answer

Statement I: True; Statement II: True; Statement III: True

The correct option is the one identifying all three statements as True. Statement I is True because the median circulation of the 5 filtered branches is 480,000, which exceeds 350,000. Statement II is True because EAS has a circulation-to-volume ratio of 2.0 compared to 1.6 for WES. Statement III is True because NOR, SOU, and UPL are the exactly three branches that satisfy both expenses per circulation < $4.00 and digital accesses > 140,000.

Step-by-Step Solution

1

Evaluate Statement I by filtering and sorting.

Branches with Active Cardholders > 20 (in thousands) are CEN (60), NOR (25), SOU (40), HAR (22), and UPL (32), total 5 branches. Their Annual Circulations (in thousands) are 900, 300, 500, 220, and 480. Sorting these values yields 220, 300, 480, 500, 900. The median (3rd value) is 480 thousand (480,000). Since 480,000 > 350,000, Statement I is True.

Filtering required strict application of the cardholder threshold before ordering the circulation data.

2

Evaluate Statement II by calculating row ratios.

For EAS, Circulations / Volumes = 160 / 80 = 2.0. For WES, Circulations / Volumes = 240 / 150 = 1.6. Since 2.0 > 1.6, Statement II is True.

Ratio comparison requires placing Circulations in the numerator and Volumes in the denominator.

3

Evaluate Statement III using dual-condition logical filtering.

Calculate Operating Expenses (

thousands) / Annual Circulations (thousands) to get

per circulation: CEN (3,600 / 900 =

4.00), NOR (1,000 / 300 =

3.33), EAS (640 / 160 =

4.00), WES (960 / 240 =

4.00), SOU (1,500 / 500 =

3.00), RIV (720 / 225 =

3.20), HAR (880 / 220 =

4.00), UPL (1,440 / 480 =

3.00). Branches with expense per circulation strictly less than $4.00 are NOR, SOU, RIV, and UPL. Among these, Digital Resource Accesses (> 140 thousand) are NOR (150), SOU (250), and UPL (160). RIV has only 90. Exactly 3 branches meet both conditions. Statement III is True.

Strict inequality rules out branches with expenses per circulation equal to $4.00.

Key Concept

Multi-Statement Boolean Evaluation on Tabular Data

Question 8Question →

The table below details 2025 annual operational metrics for eight commercial container terminals at a regional maritime port hub:

Terminal	Annual Cargo Volume (Thousand TEUs)	Automated Crane Ratio (%)	Average Berth Dwell Time (Hours)	On-Time Vessel Clearance Rate (%)
Terminal A	1,250	80%	18.5	92%
Terminal B	840	65%	24.0	85%
Terminal C	2,100	90%	14.2	96%
Terminal D	620	40%	31.0	74%
Terminal E	1,600	75%	21.5	88%
Terminal F	950	50%	26.8	81%
Terminal G	1,850	85%	16.0	94%
Terminal H	1,100	60%	22.4	86%

Based on the table, evaluate the following claim: Exactly two of the three statements below are True.

Statement I: When the terminals are sorted in descending order by Annual Cargo Volume, the median Average Berth Dwell Time for the top 4 terminals is less than $17.0$ hours.
Statement II: For every terminal where the Automated Crane Ratio is at least $75\%$ , the On-Time Vessel Clearance Rate is greater than $87\%$ .
Statement III: The mean Annual Cargo Volume across all 8 terminals is greater than $1,350$ thousand TEUs.

True

False

Show answer & explanation

Answer: False

Answer

False. Only Statement II is True (Statement I and Statement III are both False). Therefore, exactly one statement is True, making the overall claim False.

Evaluating each component statement reveals that Statement I is False (median is

17.25

hours, which is not less than

17.0

), Statement II is True (all four terminals with

\ge 75\%

crane automation exceed

87\%

clearance rate), and Statement III is False (mean cargo volume is

1,288.75

, not greater than

1,350

). Because only one statement is True, the claim stating that exactly two statements are True is False.

Step-by-Step Solution

1

Evaluate Statement I by sorting terminals descending by Annual Cargo Volume and finding the median dwell time of the top 4.

Top 4 terminals by volume: Terminal C (

2,100

), Terminal G (

1,850

), Terminal E (

1,600

), and Terminal A (

1,250

). Their Average Berth Dwell Times are

14.2

,

16.0

,

21.5

, and

18.5

hours, respectively. Ordered ascending, these values are

14.2, 16.0, 18.5, 21.5

. The median is the average of the two middle values:

\frac{16.0 + 18.5}{2} = 17.25

hours. Since

17.25 > 17.0

, Statement I is False.

Correctly identifying the median of an even set requires ordering the values and taking the midpoint of the two central numbers.

2

Evaluate Statement II by checking the On-Time Vessel Clearance Rate for terminals with an Automated Crane Ratio

\ge 75\%

.

Terminals with Automated Crane Ratio

\ge 75\%

are Terminal A (

80\%

, Clearance

92\%

), Terminal C (

90\%

, Clearance

96\%

), Terminal E (

75\%

, Clearance

88\%

), and Terminal G (

85\%

, Clearance

94\%

). All four have Clearance Rates strictly greater than

87\%

. Statement II is True.

Conditional filtering requires verifying every single row that satisfies the specified antecedent condition.

3

Evaluate Statement III by calculating the aggregate arithmetic mean of Annual Cargo Volume across all 8 terminals.

Sum of volume

= 1250 + 840 + 2100 + 620 + 1600 + 950 + 1850 + 1100 = 10,310

thousand TEUs. Mean

= \frac{10,310}{8} = 1,288.75

thousand TEUs. Since

1,288.75 < 1,350

, Statement III is False.

Computing aggregate mean requires dividing total cargo sum by total terminal count.

4

Synthesize the boolean values of the three statements to evaluate the claim.

Statement I = False, Statement II = True, Statement III = False. Exactly 1 statement is True. The claim asserts that exactly 2 statements are True, which is False.

Comparing the count of True statements to the claim's requirement determines the overall boolean result.

Key Concept

Multi-Statement Boolean Evaluation using tabular data sorting, conditional filtering, and descriptive statistics.

Question 9Question →

The table below details Q1 2026 operational and financial performance metrics for seven urban vertical farming facilities operated by GreenGrid AgriTech:

Facility Code	Crop Yield (metric tons)	Energy Consumption (MWh)	Water Recycled (%)	Operating Cost ($/kg)	Revenue ($ thousands)
VF-101	120	480	92%	4.50	720
VF-102	85	315	88%	5.20	460
VF-103	150	600	95%	3.80	975
VF-104	95	418	84%	4.80	513
VF-105	110	462	90%	4.10	682
VF-106	70	294	86%	5.60	364
VF-107	130	546	94%	3.90	858

Evaluate the truth value of the following overarching claim:

Statement: Exactly two of the three statements below evaluate to True based on the table data.

I. For all facilities where Water Recycled is at least 90%, the median Revenue per metric ton of Crop Yield is greater than $6,000.
II. The facility with the highest Energy Consumption per metric ton of Crop Yield also has the highest Operating Cost per kg.
III. The mean Energy Consumption across all seven facilities is less than 450 MWh.

True

False

Show answer & explanation

Answer: True

Answer

The statement is True because Statements I and III evaluate to True, while Statement II evaluates to False, making exactly two statements True.

The overarching statement is correct because evaluating each of the three sub-statements shows that Statement I is True (median is \$6,350/ton), Statement II is False (VF-104 has the highest energy per ton but not the highest operating cost), and Statement III is True (mean energy is 445 MWh). Therefore, exactly two statements are True.

Step-by-Step Solution

1

Filter facilities with Water Recycled

\ge 90\%

and calculate their Revenue per metric ton of Crop Yield.

Matching facilities: VF-101 (

92\%

), VF-103 (

95\%

), VF-105 (

90\%

), VF-107 (

94\%

).
Revenue per metric ton calculations:
- VF-101:

\frac{\$720,000}{120} = \$6,000/\text{ton}

- VF-103:

\frac{\$975,000}{150} = \$6,500/\text{ton}

- VF-105:

\frac{\$682,000}{110} = \$6,200/\text{ton}

- VF-107:

\frac{\$858,000}{130} = \$6,600/\text{ton}

Statement I requires computing revenue yield efficiency for a subset of rows filtered by water recycling rate.

2

Find the median of the filtered revenue per metric ton values to test Statement I.

Ordered set:

\{\$6,000, \$6,200, \$6,500, \$6,600\}

. Median =

\frac{\$6,200 + \$6,500}{2} = \$6,350

. Since

\$6,350 > \$6,000

, Statement I is TRUE.

The median of an even-numbered dataset is the arithmetic mean of the two middle values.

3

Calculate Energy Consumption per metric ton of Crop Yield for all facilities to identify the maximum, then compare with Operating Cost per kg to test Statement II.

Energy per metric ton rates:
- VF-101:

\frac{480}{120} = 4.0\text{ MWh/ton}

- VF-102:

\frac{315}{85} \approx 3.71\text{ MWh/ton}

- VF-103:

\frac{600}{150} = 4.0\text{ MWh/ton}

- VF-104:

\frac{418}{95} = 4.4\text{ MWh/ton}

(Highest)
- VF-105:

\frac{462}{110} = 4.2\text{ MWh/ton}

- VF-106:

\frac{294}{70} = 4.2\text{ MWh/ton}

- VF-107:

\frac{546}{130} = 4.2\text{ MWh/ton}

VF-104 has the highest Energy per metric ton (

4.4

). Its Operating Cost is \$4.80/kg. However, VF-106 has the highest Operating Cost at \$5.60/kg. Thus, Statement II is FALSE.

Testing Statement II requires identifying the maximum value of a calculated row-level ratio and checking if it coincides with the column maximum of another metric.

4

Calculate the mean Energy Consumption across all seven facilities to test Statement III.

Sum of Energy Consumption =

480 + 315 + 600 + 418 + 462 + 294 + 546 = 3,115\text{ MWh}

. Mean =

\frac{3,115}{7} = 445\text{ MWh}

. Since

445 < 450

, Statement III is TRUE.

Determining the truth value of Statement III requires computing an aggregate mean across the entire dataset.

5

Synthesize the boolean evaluations of the three statements to determine the final truth value.

Statement I: True, Statement II: False, Statement III: True. Exactly two of the three statements are True, which confirms that the overarching statement is True.

The main question stem asserts that exactly two statements are True.

Key Concept

Multi-Statement Boolean Evaluation using tabular filtering, ratio calculation, descriptive statistics (median and mean), and multi-column comparison.

Question 10Question →

The table below presents operational data for seven regional flight routes operated by an airline during Q1 2026:

Route Code	Distance (miles)	Flights Scheduled	On-Time Arrival Rate	Average Passenger Load Factor	Fuel Consumption (gallons/flight)
R-101	450	120	88%	82%	1,400
R-102	820	90	75%	86%	2,300
R-103	1,250	60	92%	78%	3,600
R-104	310	150	84%	74%	1,100
R-105	960	80	80%	90%	2,850
R-106	1,500	45	94%	85%	4,200
R-107	680	110	85%	88%	1,950

Match each of the following statements to its corresponding truth value and evaluation justification based on the table.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement I matches with the evaluation of True (median rate is 86%). Statement II matches with the evaluation of False (R-105 has 80 flights while minimum is 45). Statement III matches with the evaluation of False (the ratio increases from R-102 to R-105).

Each statement is evaluated against the quantitative data provided in the table. Statement I correctly identifies the four routes exceeding 800 miles and calculates their median as 86%. Statement II correctly identifies that R-105 has the highest load factor (90%) but 80 flights, whereas R-106 has the minimum flights (45). Statement III correctly identifies a counterexample where the fuel-to-distance ratio increases from R-102 to R-105.

Step-by-Step Solution

1

Filter and compute the median for Statement I.

Qualifying routes (>800 miles): R-102 (75%), R-105 (80%), R-103 (92%), R-106 (94%). Sorted rates: [75%, 80%, 92%, 94%]. Median = $\frac{80\% + 92\%}{2} = 86\%$ > 85%.

Identify sub-population based on distance criterion and determine the median of an even-sized dataset.

2

Locate maximum load factor and compare scheduled flights for Statement II.

Max load factor = 90% (R-105, 80 flights). Fewest flights overall = 45 flights (R-106). Since 80 != 45, statement is False.

Identify row-level extrema across two independent columns (Load Factor and Flights Scheduled).

3

Calculate rates/ratios for Statement III across increasing distances.

R-102 (820 miles): $\frac{2300}{820} \approx 2.805$ gal/mi. R-105 (960 miles): $\frac{2850}{960} = 2.96875$ gal/mi. Ratio increases, so trend is not strictly decreasing.

Test monotonic trend hypothesis by evaluating specific calculated ratios across sorted distances.

Key Concept

Multi-statement boolean verification requiring subset filtering, descriptive statistics (median of even-sized set), cross-column extrema matching, and rate trend testing.

Question 11Question →

The table below presents monthly operational and climate metrics for seven commercial cold-storage logistics facilities operated by a regional food distributor during 2025:

Facility Code	Storage Volume ( $1000\text{ m}^3$ )	Energy Consumed ( $\text{MWh/month}$ )	Avg Storage Temp ( $^\circ\text{C}$ )	Capacity Utilization	Operating Cost ( $\$1000/\text{month}$ )
F-1	120	480	-22	85%	144
F-2	200	700	-18	92%	210
F-3	150	525	-25	78%	175
F-4	90	390	-20	95%	120
F-5	250	875	-22	80%	260
F-6	180	630	-24	88%	198
F-7	300	1050	-19	75%	315

True or False: Among the facilities maintaining an average storage temperature colder than $-20^\circ\text{C}$ , the median monthly operating cost is greater than $\$180,000$ .

True

False

Show answer & explanation

Answer: True

Answer

True

The statement is True because the four facilities with average storage temperatures strictly below

-20^\circ\text{C}

(F-1, F-3, F-5, and F-6) have monthly operating costs of

\$144,000

,

\$175,000

,

\$198,000

, and

\$260,000

. The median of these four values is

\frac{175 + 198}{2} \times 1000 = \$186,500

, which is strictly greater than

\$180,000

.

Step-by-Step Solution

1

Filter the facilities based on the specified temperature condition.

Identified facilities F-1 (

-22^\circ\text{C}

), F-3 (

-25^\circ\text{C}

), F-5 (

-22^\circ\text{C}

), and F-6 (

-24^\circ\text{C}

). Facility F-4 (

-20^\circ\text{C}

) is excluded because

-20^\circ\text{C}

is not strictly colder than

-20^\circ\text{C}

.

The criterion requires temperatures strictly below

-20^\circ\text{C}

.

2

Extract and order the monthly operating costs (in thousands of dollars) for the filtered subset.

Ordered values:

144, 175, 198, 260

.

Sorting values in ascending order is necessary to calculate the median.

3

Calculate the median of the four operating cost values.

\text{Median} = \frac{175 + 198}{2} = 186.5

thousand dollars, which equals

\$186,500

.

For an even number of observations (

n = 4

), the median is the mean of the 2nd and 3rd ordered values.

4

Compare the calculated median to the threshold value in the statement.

\$186,500 > \$180,000

, confirming the statement is True.

The median operating cost exceeds the threshold of

\$180,000

.

Key Concept

Conditional Table Filtering and Median Calculation

Question 12Question →

The table below presents 2025 operational performance and cost metrics for eight regional commercial biofuel production facilities:

Facility Name	Feedstock Type	Annual Output (Million L)	Operating Cost ($/L)	Carbon Intensity Reduction (%)	Capacity Utilization Rate (%)
BioAlpha	Cellulosic	85	0.72	68%	88%
EcoEthanol	Corn Stover	120	0.55	45%	92%
GreenFuel X	Algae	40	1.10	82%	75%
PureBio	Used Cooking Oil	95	0.64	74%	95%
TerraFuel	Cellulosic	110	0.68	65%	82%
Vanguard Bio	Algae	60	0.98	85%	80%
SunFuel North	Corn Stover	150	0.50	42%	90%
NextGen Fuel	Used Cooking Oil	75	0.76	70%	85%

Based on the data provided, evaluate whether the following overall assertion is True or False:

"Exactly two of the three statements below are True:
- Statement 1: The median Annual Output among facilities with a Carbon Intensity Reduction of at least 70% is 67.5 Million Liters.
- Statement 2: For all facilities utilizing Cellulosic or Algae feedstock, the Operating Cost per Liter is strictly greater than $0.65.
- Statement 3: The facility with the highest Capacity Utilization Rate incurred a lower total annual operating cost (calculated as Annual Output × Operating Cost) than the facility with the lowest Capacity Utilization Rate."

True

False

Show answer & explanation

Answer: True

Answer

True. Statements 1 and 2 are True, while Statement 3 is False, meaning exactly two of the three statements are True.

Evaluating the individual statements reveals that Statement 1 is True (the median of {40, 60, 75, 95} is 67.5), Statement 2 is True (operating costs for Cellulosic and Algae facilities are

0.72,

1.10,

0.68, and

0.98, all greater than

0.65), and Statement 3 is False (PureBio's total cost of

60.8 Million exceeds GreenFuel X's total cost of $44.0 Million). Since exactly two statements are True, the overall compound assertion is True.

Step-by-Step Solution

1

Evaluate Statement 1: Identify facilities with Carbon Intensity Reduction ≥ 70% and calculate their median Annual Output.

Facilities satisfying the condition are GreenFuel X (82%), PureBio (74%), Vanguard Bio (85%), and NextGen Fuel (70%). Their outputs are 40, 95, 60, and 75 Million Liters, respectively. Ordering these values: 40, 60, 75, 95. The median of an even set of four numbers is

(60 + 75) / 2 = 67.5

Million Liters. Thus, Statement 1 is True.

Correctly filtering by the conditional threshold (70%) and sorting the output values is required to calculate the median of an even dataset.

2

Evaluate Statement 2: Filter for facilities using Cellulosic or Algae feedstock and compare their Operating Costs to $0.65.

Facilities matching Cellulosic or Algae feedstock are BioAlpha (

0.72), GreenFuel X (

1.10), TerraFuel (

0.68), and Vanguard Bio (

0.98). Every single one of these operating costs is strictly greater than $0.65. Thus, Statement 2 is True.

A universal condition ('for all') requires checking every matching row to ensure no counterexample exists.

3

Evaluate Statement 3: Identify facilities with the highest and lowest Capacity Utilization Rates, compute their total annual operating costs, and compare.

Highest Capacity Utilization Rate: PureBio (95%). Total annual operating cost =

95 \text{ Million L} \times \$0.64/\text{L} = \$60.8 \text{ Million}

. Lowest Capacity Utilization Rate: GreenFuel X (75%). Total annual operating cost =

40 \text{ Million L} \times \$1.10/\text{L} = \$44.0 \text{ Million}

. Since

\$60.8 \text{ Million} > \$44.0 \text{ Million}

, the highest utilization facility did NOT incur a lower cost. Thus, Statement 3 is False.

Row-level product calculations must be performed accurately for both extreme values before evaluating the inequality.

4

Synthesize the truth values of the three statements to evaluate the overall assertion.

Statement 1 = True, Statement 2 = True, Statement 3 = False. Total number of True statements = 2. Therefore, the assertion 'Exactly two of the three statements below are True' is True.

The top-level boolean logic requires assessing whether the count of True individual statements equals 2.

Key Concept

Multi-Statement Boolean Evaluation

Question 13Question →

The table below presents operating and compliance metrics for seven municipal water treatment plants during 2025:

Plant Name	Daily Capacity (MGD)	Operating Cost ($/MG)	Compliance Rate (%)	Energy Consumption (kWh/MG)	Staff Count
Clearwater Station	45	320	98.4%	1,450	28
Blue River Plant	80	280	99.1%	1,200	42
Oak Valley Works	30	410	97.8%	1,680	22
Pine Creek Facility	110	250	99.5%	1,150	50
Cedar Ridge Station	60	340	98.9%	1,380	35
Ironwood Treatment	25	450	96.5%	1,750	18
Laurel Heights	70	310	98.7%	1,300	31

Match each statement on the left with its correct boolean evaluation outcome and quantitative justification on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Statement I matches with the outcome stating it evaluates to FALSE (

310 <

337.14); Statement II matches with the outcome stating it evaluates to TRUE (2.03 > 2.0); Statement III matches with the outcome stating it evaluates to FALSE (70 MGD < 110 MGD).

Each statement matches its exact evaluation outcome based on standard tabular data calculations: Statement I evaluates to False because

310 per MG is below the

337.14 per MG mean; Statement II evaluates to True because 320 divided by 158 equals approximately 2.03, which is greater than 2.0; Statement III evaluates to False because a capacity of 70 MGD is less than 110 MGD.

Step-by-Step Solution

1

Evaluate Statement I by determining the median staff count and mean operating cost.

Sorted staff counts: 18, 22, 28, 31 (Laurel Heights), 35, 42, 50. Median plant is Laurel Heights with an operating cost of

310. Mean operating cost = (320 + 280 + 410 + 250 + 340 + 450 + 310) / 7 = 2360 / 7 ≈

337.14. Since

310 is less than

337.14, Statement I is False.

Identify the median position (4th out of 7) and compare its specific column value to the unweighted mean across all rows.

2

Evaluate Statement II by filtering plants with compliance > 98.5% and calculating aggregate capacity to staff ratio.

Qualifying plants are Blue River, Pine Creek, Cedar Ridge, and Laurel Heights. Total capacity = 80 + 110 + 60 + 70 = 320 MGD. Total staff = 42 + 50 + 35 + 31 = 158. Ratio = 320 / 158 ≈ 2.025 MGD/staff. Since 2.025 > 2.0, Statement II is True.

Filter rows according to a conditional threshold, aggregate columns across the selected subset, and perform ratio division.

3

Evaluate Statement III by sorting by Energy Consumption and comparing capacities of the 3rd-lowest energy plant and 1st-lowest cost plant.

Energy ordered plants: Pine Creek (1,150), Blue River (1,200), Laurel Heights (1,300). 3rd-lowest is Laurel Heights (Capacity = 70 MGD). Lowest operating cost plant is Pine Creek ($250, Capacity = 110 MGD). Comparing capacities: 70 MGD < 110 MGD. Statement III is False.

Sort table columns independently to locate specified ordinal positions (3rd-lowest energy, 1st-lowest cost) and compare their respective cross-column properties.

Key Concept

Multi-Statement Boolean Evaluation using tabular sorting, descriptive statistics, conditional filtering, and cross-column ratios.

Estimated Time:2m 0s

Question 14Question →

The table below presents 2025 operational and patient triage metrics for seven regional emergency departments:

Hospital Name	Annual Patient Volume (thousands)	Median Wait Time (min)	Mean Treatment Duration (hrs)	Left Without Being Seen (LWBS) Rate	30-Day Readmission Rate
St. Jude Regional	48	24	3.5	1.8%	4.2%
Metro Central	85	42	4.8	3.5%	5.8%
Valley General	62	30	4.0	2.4%	4.5%
Highland Medical	35	18	3.2	1.2%	3.8%
Pinecrest Community	28	15	2.8	0.9%	3.5%
University Health	92	48	5.2	4.1%	6.2%
Riverside Care	54	28	3.8	2.1%	4.9%

Evaluate whether the following statement is True or False:
"For every hospital with an annual patient volume exceeding 50,000, the ratio of Median Wait Time (in minutes) to Mean Treatment Duration (in hours) is strictly greater than 7.0."

True

False

Show answer & explanation

Answer: True

Answer

True. All four hospitals with annual patient volume exceeding 50,000 have a wait-to-treatment duration ratio greater than 7.0.

Filtering the table for hospitals with annual patient volume exceeding 50 thousand isolates Metro Central, Valley General, University Health, and Riverside Care. Calculating the ratio of median wait time (minutes) to mean treatment duration (hours) yields 8.75, 7.50, 9.23, and 7.37 respectively. Because every single one of these values exceeds 7.0, the statement is True.

Step-by-Step Solution

1

Filter the dataset based on the volume condition.

Identified four hospitals with annual volume > 50k: Metro Central (85), Valley General (62), University Health (92), and Riverside Care (54).

The statement specifies a condition that applies only to hospitals with patient volume over 50 thousand.

2

Calculate the ratio of Median Wait Time (minutes) to Mean Treatment Duration (hours) for each qualifying hospital.

Metro Central = 8.75; Valley General = 7.50; University Health ≈ 9.23; Riverside Care ≈ 7.37.

Determines the exact numerical value of the ratio for each qualifying row.

3

Compare each calculated ratio to the threshold value of 7.0.

All four calculated ratios are strictly greater than 7.0.

Verifies whether the universal claim ('for every hospital...') holds true.

Key Concept

Multi-Statement Boolean Evaluation via Conditional Data Filtering and Ratio Analysis

Question 15Question →

The table below displays Q2 2026 performance data for seven autonomous cargo drone fleets operated by a logistics provider:

Fleet ID	Total Flight Hours	On-Time Delivery Rate (%)	Payload Capacity (kg)	Operating Cost per Km ($)
Alpha-1	420	94.5%	150	12.40
Beta-2	550	91.0%	200	15.80
Gamma-3	310	96.0%	120	10.50
Delta-4	600	88.5%	250	18.20
Epsilon-5	480	93.0%	180	14.10
Zeta-6	390	97.5%	140	11.80
Eta-7	510	89.0%	220	16.50

Consider the following three statements:

I. The median Operating Cost per Km among fleets with a Payload Capacity of at least 150 kg is greater than $15.00.
II. Among fleets with an On-Time Delivery Rate above 92.0%, the fleet with the lowest Total Flight Hours also has the lowest Operating Cost per Km.
III. The mean Total Flight Hours for fleets with a Payload Capacity under 180 kg is greater than 400 hours.

Which of the statements evaluate to True based on the table?

Only Statement I is true

Only Statement II is true

Exactly Statements I and II are true

Exactly Statements II and III are true

All three statements (I, II, and III) are true

Show answer & explanation

Answer: Exactly Statements I and II are true

Answer

Statements I and II are True, while Statement III is False.

Evaluating each statement systematically shows that Statement I is True because the sorted costs for eligible fleets are

12.40,

14.10,

15.80,

16.50,

18.20, giving a median of

15.80 (which exceeds

15.00). Statement II is True because Gamma-3 meets the delivery rate threshold (> 92.0%) and holds both the minimum flight hours (310) and minimum operating cost (

10.50) among those fleets. Statement III is False because the filtered fleets (Alpha-1, Gamma-3, Zeta-6) have a mean flight hour of 373.33 hours, which is less than 400 hours. Thus, exactly Statements I and II are true.

Step-by-Step Solution

1

Evaluate Statement I by filtering and sorting Operating Cost per Km for fleets with Payload Capacity

\ge 150\text{ kg}

.

Fleets meeting the condition are Alpha-1 (150 kg), Beta-2 (200 kg), Delta-4 (250 kg), Epsilon-5 (180 kg), and Eta-7 (220 kg). Their operating costs sorted from lowest to highest are

12.40,

14.10,

15.80,

16.50,

18.20. The median of these 5 values is the 3rd value, which is

15.80. Since

15.80 >

15.00, Statement I is TRUE.

Finding the median of an odd number of items requires ordering the subset values and taking the middle element.

2

Evaluate Statement II by filtering fleets with On-Time Delivery Rate

> 92.0\%

.

Fleets meeting the condition are Alpha-1 (94.5%), Gamma-3 (96.0%), Epsilon-5 (93.0%), and Zeta-6 (97.5%). Among these 4 fleets, Gamma-3 has the lowest Total Flight Hours (310 hours) and also the lowest Operating Cost per Km ($10.50). Therefore, Statement II is TRUE.

Cross-column multi-condition filtering verifies both the minimum flight hours and minimum operating cost within the subset.

3

Evaluate Statement III by calculating the mean Total Flight Hours for fleets with Payload Capacity

< 180\text{ kg}

.

Fleets with Payload Capacity strictly less than 180 kg are Gamma-3 (120 kg), Zeta-6 (140 kg), and Alpha-1 (150 kg). (Epsilon-5 is excluded as its payload is exactly 180 kg). Their flight hours are 310, 390, and 420. Mean =

\frac{310 + 390 + 420}{3} = \frac{1120}{3} \approx 373.33\text{ hours}

. Since

373.33 < 400

, Statement III is FALSE.

Computing the arithmetic mean of the correctly filtered subset shows it is below the threshold of 400 hours.

Key Concept

Multi-Statement Boolean Evaluation on structured tables involving subset filtering, median calculation, and conditional verification.

Estimated Time:2m 0s

Multi-Statement Boolean Evaluation

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