GMAT Review: Table Analysis (Sortable Tables, Yes/No/True/False Statements)

GMAT – Table Analysis (Sortable Tables, Yes/No/True/False Statements)

GMAT Study Guide – Table Analysis (Sortable Tables, Yes/No/True/False Statements)

What This Is

Table‑analysis questions present a sortable (grid‑style) table of data and ask you to evaluate Yes/No/True/False statements, often with “must be true,” “could be true,” or “cannot be true” qualifiers. They appear on the Quantitative (Data Sufficiency) and Verbal (Critical Reasoning) sections. The key is to read the table, spot the logical relationship the statement is testing, and decide whether the statement holds for all rows (or a specific subset) without doing unnecessary arithmetic.

Typical example:
A table lists the number of projects each of four teams (A‑D) completes in three months (Jan‑Mar). Statement: “Team C completed more projects in March than Team A did in January.” Decide if the statement is True, False, or Cannot be determined.

Key Terms & Rules

• Sortable Table: A grid where rows and columns can be mentally reordered; treat each cell as an independent data point unless the question links rows/columns.
• Yes/No/True/False (Y/N/T/F) Statement: The stem asks whether a proposition is always true, always false, or undetermined given the table.
• Must Be True: The statement must hold for every possible configuration that satisfies the table’s constraints.
• Could Be True: At least one valid configuration of the table makes the statement true.
• Cannot Be True: No valid configuration can satisfy the statement.
• Implicit Constraint: Any condition not explicitly stated in the table (e.g., “all numbers are positive”) cannot be assumed unless the stem says so.
• Row‑wise vs. Column‑wise Reasoning: Decide whether the statement compares values within a single row (same entity) or across columns (different entities).
• Boundary Test: Check the extreme (minimum/maximum) values allowed by the table to see if a statement can be forced true or false.
• Elimination by Contradiction: Assume the statement is true; if it forces a violation of the table’s given numbers, the statement is False.
• Data Sufficiency (DS) Format: When the question is DS, you’ll have two statements (S1, S2). Use the standard A‑E answer key to decide if one or both statements together are sufficient.
• “Exactly One” / “At Least One” Language: Treat these as exclusive or inclusive logical operators; they change the set of rows you must examine.

Step‑by‑Step Process Flow

1. Read the Table Carefully – Note the headings, any totals, and the units. Jot down any given relationships (e.g., “Row 2 total = 30”).
2. Identify the Claim Type – Is the stem asking “must be true,” “could be true,” or “cannot be true”? Mark the logical quantifier (∀ vs. ∃).
3. Locate the Relevant Cells – Highlight the rows/columns the statement references. If the claim spans multiple rows, list the minimum/maximum values that could appear in those cells.
4. Apply Boundary Testing – Push the highlighted cells to their extreme permissible values (e.g., smallest possible number, largest possible number) while keeping the rest of the table consistent.
5. Decide –
6. If the claim holds under all boundary scenarios → True (or “must be true”).
7. If a single boundary scenario violates the claim → False (or “cannot be true”).
8. If both a satisfying and a violating scenario exist → Cannot be determined (or “could be true”).
9. (DS only) Evaluate Statements Separately – Run steps 1‑5 for S1 and S2, then for the combination, and select the appropriate A‑E choice.

Common Mistakes

• Mistake: Assuming the table’s numbers are ordered (e.g., “Row 1 always has the smallest value”).
  Correction: Treat the table as a set of independent facts; only use the explicit ordering given in the stem.

• Mistake: Forgetting the “must be true” quantifier means every row must satisfy the condition.
  Correction: Test the worst‑case row; if any row can violate the statement, the answer is False.

• Mistake: Using arithmetic that isn’t needed (e.g., adding unrelated columns).
  Correction: Focus only on the cells directly referenced; extraneous calculations waste time and can introduce errors.

• Mistake: In DS questions, treating S1 and S2 as independent when the stem actually links them (e.g., “If S1 is true, then S2 is automatically true”).
  Correction: Look for logical connectors (“and,” “or,” “if…then”) that create dependencies; evaluate the combined effect accordingly.

• Mistake: Over‑generalizing “cannot be true” when a single hidden configuration could make the statement true.
  Correction: Perform a quick constructive check: assign the extreme values that would satisfy the claim; if they fit the table, the answer is “could be true.”

Exam Insights

1. Most‑tested concept: Boundary testing – the GMAT loves to ask whether a statement holds at the extreme ends of the allowed range.
2. Trap: The phrase “exactly one” often forces you to consider both the existence of a single qualifying row and the impossibility of a second one.
3. Distinction: “Could be true” ≠ “May be true.” The former requires at least one viable configuration; the latter is ambiguous and never appears on the GMAT.
4. Data‑sufficiency nuance: Even if S1 alone seems sufficient, the GMAT may still require S2 because the table contains hidden inter‑row constraints (e.g., totals that involve both rows).

Quick Check Questions

1. Table:
   | Team | Jan | Feb | Mar | Total | |------|-----|-----|-----|-------| | A | 5 | 7 | 6 | 18 | | B | 4 | 8 | 6 | 18 | | C | 6 | 5 | 7 | 18 | | D | 7 | 6 | 5 | 18 |

Statement: “Team D completed more projects in January than Team A did in March.”
Answer: True – 7 > 6; the numbers are fixed, no alternative values exist.

1. DS Question:
   
   Table shows the ages (in years) of four siblings:

S1: “Sibling 2 is older than sibling 1.”
S2: “Sibling 3 is older than sibling 2.”

Answer: A – Each statement alone is sufficient to answer the question “Is sibling 2 older than sibling 1?” (S1 directly answers; S2 is irrelevant).

1. Y/N/T/F:
   
   Table of five products with profit margins (in %):

Statement: “All products have a higher profit margin in Q2 than in Q1.”
Answer: False – Product Z shows 14 % in Q2, which is lower than its Q1 margin of 15 %.

Last‑Minute Cram Sheet (10 One‑Liners)

1. ⚠️ Boundary Test: Always push a cell to its minimum or maximum allowed value to test “must be true.”
2. ∀ (All) vs. ∃ (Some): “Must be true” = ∀ rows; “Could be true” = ∃ at least one row.
3. Exact‑One Rule: Verify both existence of one qualifying row and non‑existence of a second.
4. Row‑wise Comparison: When a statement compares two cells in the same row, ignore other rows completely.
5. Column‑wise Comparison: When comparing across columns, treat each column as a separate variable; don’t mix rows unless the stem says so.
6. Implicit Constraint = No: Never assume positivity, uniqueness, or ordering unless explicitly given.
7. DS Shortcut: If S1 alone answers the question, answer A; if S2 alone answers, answer B; if both together are needed, answer C.
8. Contradiction Method: Assume the statement true → derive a numeric conflict → label it False.
9. “At Least One” = ∃: Look for a single feasible configuration; if you can construct one, the answer is “could be true.”
10. Quick Elimination: Cross out any answer that requires a value outside the given range (e.g., > total, < 0).

Good luck—master the table, master the GMAT!