Tables: Quantitative Aptitude Notes for GMAT

GMAT Quantitative – Tables

Study Notes (Markdown)

1. Simple Explanation

Tables are a compact way of presenting data. In GMAT Quantitative you’ll encounter tables that:

| • | Frequency tables – show how many times each value appears.
| • | Cumulative tables – show the running total up to each value.
| • | Cross‑tab tables – show two sets of categories and the number that fall into each intersection.
| • | Special tables – percentages, ratios, or “unknowns” that must be solved for.

The goal: interpret the information, set up the right equations, and solve for the missing value(s).

2. Key Points

#	Concept	Why It Matters	Quick Tip
1	Read the header carefully	Identifies what each column/row represents.	Write it out in plain words.
2	Check the units	Consistency (e.g., dollars, people, percentages).	Convert if necessary.
3	Identify totals	Total frequency or total percentage often given.	Use it to find missing values.
4	Cumulative vs. non‑cumulative	Cumulative adds up; non‑cumulative lists raw counts.	Subtract adjacent rows to get raw counts.
5	Cross‑tab relationships	Rows × Columns = Total.	Verify that the sum of a row/column equals the reported total.
6	Use algebra	Set up equations for unknowns.	Treat each variable as `x`, `y`, etc.
7	Check for consistency	Negative numbers or totals that don’t add up = error.	Re‑examine the problem.
8	Work backwards	Start with totals or known percentages.	Often easier than forward calculation.
9	Simplify fractions	Reduces arithmetic.	Reduce before multiplying/dividing.
10	Round only at the end	GMAT expects exact integers or fractions.	Keep decimals in calculations.

3. Worked Example

Problem

A company surveyed 100 customers. The table below shows the number of customers who purchased Product A and Product B. Some customers bought both products. Determine how many customers bought only Product A.

	Purchased Product B	Did Not Purchase Product B	Total
Purchased Product A	15	?	30
Did Not Purchase Product A	20	45	65
Total	35	90	100

Solution

Understand the layout
- Row = “Purchased Product A” or “Did Not Purchase Product A”.
- Column = “Purchased Product B” or “Did Not Purchase Product B”.
Identify the missing value
- Cell (Purchased A, Did Not B) = ?.
Use row totals
- Row “Purchased Product A” total = 30.
- Already known cell (Purchased A, Purchased B) = 15.
- So, ? = 30 – 15 = 15.
Cross‑check with column totals
- Column “Did Not Purchase B” total = 90.
- Known cell (Did Not A, Did Not B) = 45.
- So, ? = 90 – 45 = 45.
- These two missing cells must satisfy both row and column totals simultaneously.
- Indeed, 45 (Did Not A, Did Not B) + 15 (Purchased A, Did Not B) = 60, which equals the column total for “Did Not Purchase B”?
  Wait, column total is 90 – sorry mis‑calc. Let’s recompute:
  Column “Did Not B” total = 90.
  Known cells:
  - (Purchased A, Did Not B) = 15 (we found).
  - (Did Not A, Did Not B) = 45.
    Sum = 15 + 45 = 60, not 90.
- Therefore, we mis‑read the table: The column totals must match the given totals.
- Actually the table totals are:
  - Row “Did Not Purchase Product A” total = 65.
  - Column “Did Not Purchase Product B” total = 90.
  - The sum of all cells should be 100.
- Re‑calculate:
  - Row “Did Not Purchase A” totals: 20 (Purchased B) + 45 (Did Not B) = 65 ✔️
  - Row “Purchased A” totals: 15 + 15 = 30 ✔️
  - Column “Purchased B” totals: 15 + 20 = 35 ✔️
  - Column “Did Not B” totals: 15 + 45 = 60 ❌
Oops! The column totals don’t sum to 100. The table must be corrected.

Correct interpretation: The column totals given (35 and 90) actually sum to 125, not 100. That indicates a typo in the problem statement.

Fix: Assume the column totals are 35 (Purchased B) and 65 (Did Not B). Then the totals sum to 100.
- Column “Did Not B” total = 65.
- Known cells: (Purchased A, Did Not B) = 15 (found).
- (Did Not A, Did Not B) = 45.
- Sum = 15 + 45 = 60, still not 65.
Conclusion: Without a consistent table, we can’t solve.

Lesson: Always verify that the totals in a table add up to the grand total. If they don’t, re‑read the problem for mis‑prints or missing numbers.

Corrected Example

Let’s use a coherent table: