Tables: Quantitative Aptitude Notes for Odisha Patwari / Lekhpal

📚 Odisha Patwari / Lekhpal – Quantitative Aptitude

Topic: Tables

Tables are a systematic arrangement of data in rows and columns.
In aptitude, they usually represent a set of numbers that follow a hidden rule (arithmetic, geometric, quadratic, etc.) or a pre‑calculated list (powers, factorials, triangular numbers).

1. Simple Explanation

Purpose	How It Helps
Pattern Recognition	Spot the rule that generates the numbers.
Data Storage	Keep a reference list (e.g., 5th powers, 7th powers).
Interpolation/Extrapolation	Estimate missing values using the pattern.
Cross‑Referencing	Quickly match two related quantities (e.g., x ↔ f(x)).

Key Idea: If you can spot the rule, you can fill any missing entry or compute any requested value without lengthy calculations.

2. Key Points to Remember

#	Concept	Why It Matters
1	Identify the Sequence Type	- Arithmetic Progression (AP) → constant difference - Geometric Progression (GP) → constant ratio - Quadratic / Polynomial → second‑order differences become constant
2	Use Difference Tables	Compute successive differences until the pattern stabilises.
3	Check Symmetry & Mirror Properties	Many tables are symmetric around the centre (e.g., Pascal’s Triangle).
4	Use Pre‑calculated Tables	Memorise small tables (1–12 multiplications, squares, cubes, factorials up to 10).
5	Interpolation / Extrapolation	If the table is linear, use the slope to predict missing values.
6	Cross‑Reference Columns	When two columns are interdependent (e.g., `n` and `n²`), verify consistency.
7	Check Units / Context	In Patwari problems, tables often involve land area, revenue, or time. Context helps choose the right pattern.

3. Worked Example

Problem (Typical Patwari Question)
A table gives the number of acres (A) and the corresponding revenue (R) in rupees per annum for a farmer:

Acres (`A`)	Revenue (`R`)
10	500
20	900
30	1300
40	1700
50	2100
?	2900

Find the missing number of acres.

Step‑by‑Step Solution

Look for a pattern in R vs. A.
Compute differences in R when A increases by 10 acres.

A R ΔR

10 500 –

20 900 400

30 1300 400

40 1700 400

50 2100 400

The revenue increases by 400 rupees for every additional 10 acres.
→ Linear relationship: ΔR / ΔA = 400 / 10 = 40 rupees per acre.
Determine the missing A.
The revenue for the unknown entry is 2900 rupees.
Find how many 400‑rupee increments above 2100 rupees:
```
2900 – 2100 = 800
800 / 400 = 2 increments
```
Each increment corresponds to 10 acres → 2 × 10 = 20 acres.
Add to the last known acreage.
50 acres + 20 acres = 70 acres.

`A`	`R`	Δ`R`
10	500	–
20	900	400
30	1300	400
40	1700	400
50	2100	400

Answer: The missing number of acres is 70 acres.
(Check: 70 acres → 2100 + 2×400 = 2900 rupees.)

Quick Checks

Verify linearity by computing R / A:
500/10 = 50, 900/20 = 45, 1300/30 ≈ 43.3, ... → Slightly decreasing, but the difference method is reliable.
Alternative: Use slope ΔR/ΔA = 40 → R = 40A + 100 (since 10*40+100=500).
Plug A = 70: R = 40*70+100 = 2900.

4. Quick Revision Summary

Topic	Take‑away
Table Types	AP, GP, Quadratic, Powers, Factorials, Triangular numbers.
Pattern Detection	Constant difference → AP; constant ratio → GP; constant second difference → Quadratic.
Difference Table	Build until a row becomes constant → that row shows the degree of the polynomial.
Interpolation	For linear tables, use slope: `Δy/Δx`.
Extrapolation	Extend the pattern beyond given data.
Memorisation	Keep handy tables up to 12×12, squares up to 20², cubes up to