📊 Study Notes – Tables in Quantitative Aptitude
(For the Village Development Officer – VDO Program)
1. Simple Explanation
A table is a systematic arrangement of data in rows and columns. In quantitative aptitude, tables are used to:
- Organise information (e.g., population, sales, test scores).
- Make comparisons (between two or more items).
- Find missing values (using patterns, ratios, or averages).
- Answer questions quickly by reading off the required cell.
Typical types of tables you’ll encounter:
| Type | Example |
|---|---|
| Simple Data Table | Student marks across subjects |
| Frequency Table | Number of people in age groups |
| Comparison Table | Population of villages vs. towns |
| Relationship Table | Production vs. cost |
2. Key Points & Tips
| # | Point | Why It Matters | Quick Tip |
|---|---|---|---|
| 1 | Read the header first | It tells you what each column/row represents. | Skim the header row & column before diving in. |
| 2 | Identify the problem type | Are you asked for a value, average, ratio, or difference? | Write the question down in one line. |
| 3 | Use the “index” (row/column label) | Some questions ask for “the 4th row in the 2nd column”. | Memorise the labeling convention (e.g., R1C2). |
| 4 | Check for hidden patterns | Many tables hide sequences (arithmetic, geometric, factorial). | Look for increments between successive cells. |
| 5 | Apply arithmetic & algebra | Often you’ll need to solve for a missing number or compute a ratio. | Treat the table as a set of equations. |
| 6 | Cross‑check totals | Totals or averages can be used to verify your answer. | If the sum of rows ≠ total, double‑check calculations. |
| 7 | Use short‑cuts for large tables | For big tables, look for “quick” calculations (like average of averages). | Compute partial sums first, then fill in gaps. |
| 8 | Always write units | Prevents unit‑mixing errors (e.g., km vs. m). | Add a units column if necessary. |
| 9 | Leverage proportion | For percentage changes, ratios, or scaling. | “If 1/4 of the table is 25, then 3/4 is 75.” |
| 10 | Practice mental math for simple tables | Reduces time during exams. | Practice reading small tables quickly. |
3. Worked Example
Problem
A VDO receives a table of the number of households in four villages (A, B, C, D) and the total income (in ₹) generated by each village in a month. The table is partially filled:
| Village | Households | Income (₹) |
|---|---|---|
| A | 50 | 250,000 |
| B | ? | 300,000 |
| C | 40 | ? |
| D | 30 | 180,000 |
Additional information:
- The average income per household across all four villages is ₹6,200.
- Village C has 10% more households than Village D.
Find:
- Number of households in Village B.
- Income of Village C.
Step‑by‑Step Solution
| Step | What to do | Calculation |
|---|---|---|
| 1 | Compute total households from the average income. | (\text{Avg Income} = \frac{\text{Total Income}}{\text{Total Households}}) (6,200 = \frac{1,030,000}{\text{Total Households}}) (\text{Total Households} = \frac{1,030,000}{6,200} \approx 166) |
| 2 | Sum known households | (50 + 40 + 30 = 120) |
| 3 | Find households in B | (166 - 120 = 46) |
| 4 | Determine households in C using the 10% relation | Households in D = 30 → C = (30 \times 1.10 = 33) |
| 5 | Check total households | (50 + 46 + 33 + 30 = 159) → Mismatch! Why? Because we mis‑applied the average. Re‑compute total households from income: ( \text{Total Income} = 250,000 + 300,000 + \text{?} + 180,000 = 730,000 + \text{?}) |
| 6 | Re‑compute using total income | Let income of C = X. Sum incomes = (250,000 + 300,000 + X + 180,000 = 730,000 + X). Total households = 50 + 46 + 33 + 30 = 159 (from step 3 & 4). Average income = (\frac{730,000 + X}{159} = 6,200). |
| 7 | Solve for X | (730,000 + X = 6,200 \times 159 = 985,800). (X = 985,800 - 730,000 = 255,800). |