Unit 2.2 (quantitative reasoning) includes data interpretation, data verification (sufficiency), matrix and date/calendar questions besides percentage, ratio, average and profit–loss, which have their own notes.
1. Data interpretation (तथ्याङ्क व्याख्या)
Data is given in a table, bar chart, line graph or pie chart, and you calculate totals, percentages, ratios, averages and changes.
- Percentage change = (new − old) ÷ old × 100.
- Pie chart: the whole circle = 360° = 100%, so 1% = 3.6°. A sector of 90° = 25%; 72° = 20%; 36° = 10%.
- Average = total ÷ number of items.
Example table – sales of a shop (in units):
| Year | Sales |
|---|---|
| 2079 | 120 |
| 2080 | 150 |
| 2081 | 180 |
- Increase from 2079 to 2080 = (150 − 120) ÷ 120 × 100 = 25%.
- Average sales = (120 + 150 + 180) ÷ 3 = 150.
- Tip: read the units and the question carefully; approximate when options are far apart.
2. Data sufficiency (तथ्याङ्क जाँच)
A question is followed by two statements, I and II. You do not need to find the answer, only whether the data is enough.
| Option | Meaning |
|---|---|
| a | Statement I alone is sufficient, II alone is not |
| b | Statement II alone is sufficient, I alone is not |
| c | Either I or II alone is sufficient |
| d | Both I and II together are needed |
| e | Even both together are not sufficient |
- Example: What is Ram’s age? I: Ram is 5 years older than Shyam. II: Shyam is 20. → Both together (d): Ram = 25.
- Example: What is the area of a square? I: Its side is 5 cm. II: Its diagonal is 5√2 cm. → Either alone (c).
3. Number matrix
Numbers are arranged in rows and columns with a rule (sum, difference, product, square). Find the rule in complete rows, then apply it.
| 2 | 3 | 6 |
| 4 | 5 | 20 |
| 3 | 7 | 21 |
Rule: first × second = third.
4. Calendar (date) problems
- Odd days: days left over after complete weeks.
- Ordinary year = 365 days = 52 weeks + 1 odd day. Leap year = 366 days = 2 odd days.
- Leap year rule: divisible by 4; a century year is a leap year only if divisible by 400 (2000 was leap; 1900 and 2100 are not).
- 100 years = 5 odd days; 200 years = 3; 300 years = 1; 400 years = 0.
- Day codes from odd days: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday.
- Example: Today is Monday. What day after 10 days? 10 ÷ 7 leaves 3, so Monday + 3 = Thursday.
- Example: 1 January 2025 was a Wednesday. 2025 is an ordinary year (1 odd day), so 1 January 2026 is a Thursday.
- Months with odd days: 31-day month = 3 odd days, 30-day month = 2, February = 0 (or 1 in a leap year).
5. Worked example
A district office received 400 applications in Shrawan, 500 in Bhadra and 600 in Asoj.
| Question | Working | Answer |
|---|---|---|
| Total applications | 400 + 500 + 600 | 1,500 |
| Average per month | 1,500 ÷ 3 | 500 |
| Increase from Shrawan to Asoj | (600 − 400) ÷ 400 × 100 | 50% |
| Share of Bhadra in total | 500 ÷ 1,500 × 100 | About 33.3% |
6. Tips
- Read the title, units and scale of the chart first.
- Round numbers to save time when options are far apart.
- Remember: percentage change = change ÷ original × 100.
7. How this topic is asked in the exam
Aptitude papers give a table, bar chart or pie chart and ask totals, averages, ratios and percentage changes. Practise quick mental arithmetic.
📌 Key points to remember
- Percentage change = change ÷ old × 100; pie chart 360° = 100%, 1% = 3.6°.
- Data sufficiency: decide if data is enough; options I alone, II alone, either, both, neither.
- Matrix: find the rule (sum, product, square) in complete rows and apply it.
- Ordinary year 1 odd day, leap year 2; century year is leap only if divisible by 400.
- 400 years have 0 odd days; add remainder of days ÷ 7 to find the day.
Test yourself: Data Interpretation, Data Sufficiency, Number Matrix and Calendar Problems
50 questions check what you read about Data interpretation (तथ्याङ्क व्याख्या), Number matrix and Calendar (date) problems. Each attempt picks 25 at random.