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 | 0.2

The table below details semiconductor fabrication performance metrics across eight product… — GMAT

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.

Answer: Answer

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

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.

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.

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.

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

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