13.4 Table Analysis: Evaluating Binary Statements (True/False, Yes/No)

13.4 Table Analysis: Evaluating Binary Statements (True/False, Yes/No)

Quick Summary: The final challenge of Table Analysis on the GMAT Focus Edition is executing three consecutive binary evaluations (Yes/No or True/False) under strict all-or-nothing scoring. Rather than testing basic arithmetic, these statements test your command of formal logic and quantitative reasoning: evaluating conditional claims with precise subset filtering, distinguishing absolute changes from percentage growth rates, executing rapid ratio comparisons without manual division, and avoiding aggregation errors such as the weighted average fallacy. Mastering these four core statement archetypes ensures complete accuracy across all three parts.

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The Logic of Conditional Statements in Table Analysis

One of the most frequent statement formats in Table Analysis is the conditional claim:

$\text{"If } P, \text{ then } Q\text{" } \quad (P \implies Q)$

Examples include:

• "If a hospital has more than 300 beds, its patient readmission rate is below 8.0%."
• "Any tech startup founded after 2020 that secured Series B funding achieved profitability by 2024."

The Scope Filter Protocol

When evaluating $P \implies Q$, you must apply the Scope Filter:

1. Filter Strictly for P (The Antecedent): Sort the table to isolate only the rows where condition P is True. In the hospital example, you isolate only hospitals with > 300 beds.
2. Test for Q (The Consequent) Exclusively within that Subgroup: Inspect condition Q (readmission rate < 8.0%) among those filtered rows.
   • If every single row in the filtered subset satisfies Q, the statement is Yes (True).
   • If even one row in the filtered subset fails Q (e.g., a 350-bed hospital has an 8.2% readmission rate), the statement is No (False).
3. Ignore Non-P Rows Completely: Rows where P is False (hospitals with <= 300 beds) are wholly irrelevant. A 150-bed hospital with a 12% readmission rate does NOT invalidate the statement!

The Trap of Affirming the Consequent

A classic trap occurs when test-takers look at rows where Q is true and assume the statement requires P to be true.
Example: Finding an 80-bed hospital with a 6.5% readmission rate does not violate "If beds > 300, then readmission < 8.0%". The statement never claimed that only large hospitals have low readmission rates (Q implies P). Do not confuse a conditional statement with its converse.

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Absolute Change vs. Percentage Change

Table Analysis statements frequently exploit the mathematical distinction between absolute differences and relative percentage changes.

$\text{Absolute Change} = Y_{\text{final}} - Y_{\text{initial}}$

$\text{Percentage Change} = \left( \frac{Y_{\text{final}} - Y_{\text{initial}}}{Y_{\text{initial}}} \right) \times 100\%$

The Base-Value Distortion

Consider two companies in a table over a three-year period:

Notice the opposing outcomes:

• Titan Corp achieved by far the greatest absolute revenue gain (+$150M vs +$15M).
• Venture Inc achieved by far the greatest percentage revenue growth (+150% vs +30%).

When a Table Analysis statement uses words like "grew by the largest amount", "greatest increase", or "largest difference", it specifies absolute change. When it uses words like "highest growth rate", "greatest percentage increase", or "expanded most rapidly", it specifies percentage change. Never substitute one for the other.

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Ratio Comparisons: The Cross-Multiplication Principle

When a statement asks you to compare ratios across different rows (e.g., "The ratio of R&D expenditure to operating profit was higher for Firm A than for Firm B"), test-takers often open the on-screen calculator and perform two separate long divisions, rounding decimals and wasting time.

Instead, use the fundamental algebraic property of fractions for positive numbers:

$\frac{a}{b} > \frac{c}{d} \iff a \times d > b \times c$

Application

Suppose Firm A has R&D of $42M and Profit of $130M. Firm B has R&D of $31M and Profit of $98M. Is (42 / 130) > (31 / 98)?

• Rather than dividing 42 / 130 ≈ 0.3230 and 31 / 98 ≈ 0.3163, cross-multiply: $42 \times 98 = 4,116$ $130 \times 31 = 4,030$
• Because 4,116 > 4,030, the inequality (42 / 130) > (31 / 98) is proven immediately with two simple multiplications on the on-screen calculator.

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Aggregation Traps and the Weighted Average Fallacy

A pervasive trap in Table Analysis involves statements that claim to deduce an overall aggregate mean from individual subgroup averages.

$\text{True Population Mean} = \frac{\sum (w_i \times \bar{x}_i)}{\sum w_i} \neq \frac{\sum \bar{x}_i}{k}$

If a table lists the average employee salary for 5 regional divisions, you cannot compute the company-wide average salary by simply summing the 5 regional averages and dividing by 5, unless each division has the exact same number of employees.

If the statement claims "The average salary of all employees across the 5 divisions is $72,000", but the table provides only the divisional averages without the employee headcount per division, the statement cannot be inferred. You must select No because the weights are unknown.

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Comprehensive Worked Example: Renewable Energy Infrastructure

Let us analyze a comprehensive Table Analysis dataset containing 12 renewable power generation assets.

Contextual Narrative

The table displays operational and financial metrics for 12 utility-scale renewable energy facilities commissioned between 2021 and 2024. Capital Expenditure (CapEx) represents total upfront installation costs in millions of dollars. Annual Generation is reported in gigawatt-hours (GWh) for the year 2025. Capacity Factor is the ratio of actual energy produced to the maximum possible electrical output if operated continuously at full nameplate capacity throughout the entire year. Levelized Cost of Energy (LCOE) is the estimated net present cost of electricity generation over the facility lifetime, expressed in dollars per megawatt-hour ($/MWh).

Table: Utility-Scale Renewable Energy Projects

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Step-by-Step Problem Walkthrough

Task: For each of the following statements, select Yes if the statement can be reasonably inferred from the table. Otherwise, select No.

1. If a project has an LCOE of less than $45.0/MWh, its Capacity Factor is less than 40.0%.
2. The project with the highest ratio of Annual Generation to CapEx is a Solar PV facility.
3. The mean CapEx of the three facilities with the highest Capacity Factors exceeds $300 million.

Analytical Deconstruction

Statement 1: Conditional Claim with Scope Filter

1. Identify the Condition (P implies Q):
   P: Project has LCOE < $45.0/MWh.
   Q: Capacity Factor is < 40.0%.
2. Apply the Scope Filter: Isolate all projects where LCOE < 45.0:
   • PRJ-102 (Solar PV): LCOE = 41.5, Capacity Factor = 24.0%
   • PRJ-103 (Onshore Wind): LCOE = 44.0, Capacity Factor = 36.5%
   • PRJ-105 (Solar PV): LCOE = 39.0, Capacity Factor = 25.5%
   • PRJ-109 (Solar PV): LCOE = 37.5, Capacity Factor = 26.0%
   • PRJ-112 (Onshore Wind): LCOE = 42.0, Capacity Factor = 38.0%
3. Test Condition Q across all filtered projects:
   • Capacity Factors: 24.0%, 36.5%, 25.5%, 26.0%, 38.0%.
   • The maximum Capacity Factor in this subset is 38.0%, which is strictly less than 40.0%.
4. Check Irrelevant Rows: Note that other projects have Capacity Factors > 40% (e.g., Geothermal, Hydroelectric, Offshore Wind), but their LCOE values are all >= $49.0/MWh, meaning they fall outside the conditional antecedent. Every single project meeting the 'if' condition satisfies the 'then' condition.
5. Verdict for Statement 1: Yes.

Statement 2: Ratio Comparison across Technologies

1. Identify Target Ratio: Generation / CapEx = Annual Generation (GWh) / CapEx ($M).
2. Scan Promising Candidates:
   • Solar PV projects:
     • PRJ-102: 380 / 180 ≈ 2.111 GWh/$M
     • PRJ-105: 310 / 140 ≈ 2.214 GWh/$M
     • PRJ-109: 490 / 210 = 7 / 3 ≈ 2.333 GWh/$M
   • Onshore Wind projects:
     • PRJ-103: 620 / 220 ≈ 2.818 GWh/$M
     • PRJ-108: 540 / 190 ≈ 2.842 GWh/$M
     • PRJ-112: 690 / 250 = 2.760 GWh/$M
   • Offshore Wind and Hydro:
     • PRJ-101: 1,200 / 450 ≈ 2.667
     • PRJ-106: 1,450 / 520 ≈ 2.788
     • PRJ-110: 1,850 / 680 ≈ 2.721
3. Compare Maxima:
   • The highest Solar PV ratio is PRJ-109 at 490 / 210 ≈ 2.333.
   • But Onshore Wind facility PRJ-108 achieves 540 / 190 ≈ 2.842.
   • Cross-multiplication verification between PRJ-108 (Wind) and PRJ-109 (Solar):
     $540 \times 210 = 113,400 \quad \text{vs} \quad 190 \times 490 = 93,100$
   • Because 113,400 > 93,100, PRJ-108 has a strictly higher generation-to-CapEx ratio than PRJ-109.
4. Verdict: The project with the highest ratio is PRJ-108 (an Onshore Wind facility), NOT a Solar PV facility.
5. Verdict for Statement 2: No.

Statement 3: Mean of Top 3 Capacity Factors

1. Operation: Sort by Capacity Factor (%) descending.
2. Isolate Top 3 Rows:
   • Rank 1: PRJ-104 (Geothermal) — Capacity Factor = 88.0%, CapEx = $310M
   • Rank 2: PRJ-111 (Geothermal) — Capacity Factor = 85.0%, CapEx = $280M
   • Rank 3: PRJ-107 (Biomass) — Capacity Factor = 76.0%, CapEx = $160M
3. Compute Mean CapEx of these three projects:
   $\text{Sum of CapEx} = 310 + 280 + 160 = 750$ $\text{Mean CapEx} = \frac{750}{3} = \$250 \text{ million}$
4. Evaluate Value: The statement claims the mean CapEx exceeds $300 million. Because $250M is not greater than $300M, the statement is false.
5. Verdict for Statement 3: No.

Final Correct Dichotomous Triplet: Statement 1 = Yes; Statement 2 = No; Statement 3 = No.

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Trap Catalog for Dichotomous Table Analysis

1. The Causation Fallacy: Inferring that a low LCOE was caused by a specific technology or region when the table merely documents numerical correlation.
2. Converse Statement Inversion: Assuming that because all projects with LCOE < 45 have Capacity Factor < 40%, all projects with Capacity Factor < 40% must have LCOE < 45.
3. The Unweighted Grand Mean Trap: Averaging the Capacity Factors of technologies with unequal project counts and treating it as the system-wide capacity factor.
4. Neglecting Column Units: Misinterpreting CapEx in millions ($M) versus generation in gigawatt-hours (GWh), resulting in decimal placement errors during manual calculation.