Quantitative Aptitude – Tables
(For Andhra Pradesh Patwari / Lekhpal Examination)
1. Simple Explanation
In quantitative aptitude, a table is a systematic arrangement of numbers or data in rows and columns. Tables help you:
- Organise data for easier comparison.
- Find missing values by using relationships between rows, columns, or the whole table.
- Perform calculations (addition, subtraction, multiplication, division) quickly.
- Interpret patterns (increasing, decreasing, ratios, proportions, etc.).
When a problem says “fill in the missing value” or “compare the two tables”, you’re expected to use the logic of tables.
2. Key Points to Master
| # | Concept | What to Look For | Quick Tip |
|---|---|---|---|
| 1 | Row & Column Relationships | Sum, product, or ratio of rows/columns. | Check if a row/column is half of, twice, or adds to another. |
| 2 | Diagonal/Total | Often the missing number is the sum of a row/column or the total of the table. | Compute totals first; missing entry often balances the total. |
| 3 | Progressions | Arithmetic progression (AP) or geometric progression (GP) across rows/columns. | Use common difference/ratio to fill gaps. |
| 4 | Cross‑Multiplication | For tables with ratios (e.g., 2:3). | a/b = c/d → a*d = b*c. |
| 5 | Percentage / Fraction | Tables with percentages of a whole or fractions of a number. | Convert to a common base before comparing. |
| 6 | Comparative Tables | Two tables are equivalent after a transformation (e.g., scaling). | Verify by dividing corresponding elements. |
| 7 | Sequence Completion | Tables that follow a simple arithmetic or geometric rule. | Identify first term and common difference/ratio. |
| 8 | Cumulative / Running Totals | Running sum across a column or row. | Add previous total to current entry. |
| 9 | Missing Value in a Matrix | Often the value that completes a property (e.g., area, perimeter). | Use geometry facts or algebraic equations. |
| 10 | Symmetry / Pattern Recognition | Mirror or rotational symmetry in tables. | Draw a line of symmetry to spot patterns. |
3. Worked Example
Problem (Typical for Patwari Exam)
In the following table, the missing entry is represented by X.
| 2 | 4 | 6 | 8 | | 3 | 6 | 9 | 12 | | 4 | 8 | 12 | X |Find X.
Step‑by‑Step Solution
-
Identify the pattern
- Columns: 2, 4, 6, 8 – each is 2×(column number).
- Rows: 2, 3, 4 – each is row number × column number.
-
Apply the pattern to the missing cell
- Row 3, Column 4 →
3 × 4 = 12.
- Row 3, Column 4 →
-
Answer
- X = 12
Alternative Quick Check
Sum of third row: 4 + 8 + 12 = 24.
If the row should be a multiple of the row number × sum of column numbers:
- Row number (3) × sum of first three columns (2+4+6=12) = 36.
- The missing entry should bring the row sum to 36 → 36 – 24 = 12.
- Confirms X = 12.
4. Quick Revision Summary
| Topic | What to Remember | Quick Question |
|---|---|---|
| Row/Column Relations | Check if rows or columns follow a simple arithmetic or geometric rule. | If row 2 is double row 1, what is row 3? |
| Totals | Missing numbers often balance the total of a row/column. | Sum of row = 50, known entries = 30 → missing = 20. |
| Progressions | Identify AP or GP across the table. | 5, 10, 20, X → X = 40 (GP, ratio 2). |
| Cross‑Multiplication | Use for ratio tables. | 2/3 = 4/?. |
| Percentages | Convert to common base before comparison. | 20% of 200 = 40. |
| Symmetry | Look for mirror or rotational patterns. | Does the table remain the same if rows and columns are swapped? |
| Missing Value in a Matrix | Use algebra or geometry. | 3x3 grid where sum of each row = 30 → find X. |
Quick Practice Questions (Answer Below)
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| 10 | 20 | 30 | | 15 | 30 | 45 | | 20 | X | 60 |Find X.
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| 1 | 2 | 3 | 4 | | 2 | 4 | 6 | 8 | | 3 | 6 | 9 | 12 | | 4 | 8 | 12 | X |Find X.
-
A table of monthly sales (in ₹) shows the following:
- Jan: 5,000
- Feb: 7,500
- Mar: 9,000
- Apr: X
The sales increased by the same amount each month. Find X.
Answers
X = 50(Row sum equals 30, 20 + 30 = 50).X = 16(Row