BITSAT Logical Reasoning – Pie Charts & Line Graphs
Target: Quickly understand, interpret and solve questions on pie charts and line graphs, which frequently appear in the BITSAT Logical Reasoning section.
1. Simple Explanation
| Chart | What it shows | How it’s read |
|---|---|---|
| Pie Chart | Distribution of a whole into parts (percentages). | 1. Each slice’s angle (or area) ∝ its percentage. 2. All slices together = 100 %. |
| Line Graph | Change of a quantity over a period (time, distance, etc.). | 1. X‑axis: independent variable (e.g., time). 2. Y‑axis: dependent variable (e.g., temperature). 3. Slope = rate of change. |
2. Key Points & Tips
| Chart | Key Points | Tip |
|---|---|---|
| Pie Chart | • All slices add up to 100 %. • A slice of x % of the whole = x/100 × Total. • Missing slice = 100 % – sum of known slices. |
Check the “whole” first (often “100 %” or a given total). |
| Line Graph | • Slope = (Δy)/(Δx). • Average rate = (final value – initial value) ÷ (final time – initial time). • Trend: ↑ = increasing, ↓ = decreasing, ↔ = stable. • Extrapolate by extending the line if it’s linear. |
Look for linearity – BITSAT usually gives a straight‑line graph. |
| Both | • Units must be consistent (e.g., all percentages, or all days). • Check for missing points or missing slices. • Verify calculations with a quick sanity check (e.g., percentages should not exceed 100 %). |
Mark the key numbers (e.g., 30 % of 200 = 60). |
3. Worked Example
3.1 Pie Chart Example
Problem (BITSAT‑style)
A pie chart represents the distribution of students across 4 departments in a college. The chart shows:
| Department | Percentage |
|---|---|
| Computer Science (CS) | 35 % |
| Electronics (EL) | 25 % |
| Mechanical (ME) | 20 % |
| Others | ? |
The total number of students is 400.
Solution
-
Find missing percentage
( \text{Missing} = 100% - (35% + 25% + 20%) = 100% - 80% = 20% ) -
Convert to number of students
( 20% \text{ of } 400 = \frac{20}{100} \times 400 = 80 )
Answer: 80 students belong to “Others”.
3.2 Line Graph Example
Problem (BITSAT‑style)
A line graph shows the monthly average temperature (°C) for a city from January (month 1) to March (month 3).
| Month | Temperature (°C) |
|---|---|
| Jan (1) | 12 |
| Feb (2) | 15 |
| Mar (3) | 20 |
Questions:
- What is the average rate of temperature increase per month between Jan and Mar?
- Estimate the temperature in April (month 4) assuming the trend continues linearly.
Solution
-
Average rate
[ \text{Rate} = \frac{20 - 12}{3 - 1} = \frac{8}{2} = 4,^\circ\text{C per month} ] -
Estimate April
[ \text{Temp}_{\text{Apr}} = 20 + 4 = 24^\circ\text{C} ]
Answer:
- Average rate = 4 °C/month.
- Estimated April temperature = 24 °C.
4. Quick Revision Summary
| Item | What to check | Quick Formula |
|---|---|---|
| Pie Chart | • Percentages add to 100 %. • Missing slice = 100 % – sum of known slices. • Convert % to numbers: ( \frac{%}{100} \times \text{Total} ). |
( \text{Missing %} = 100 - \sum \text{known %} ) |
| Line Graph | • Identify X‑ and Y‑axes. • Compute Δy / Δx for slope. • Extrapolate if line is straight. |
( \text{Slope} = \frac{\Delta y}{\Delta x} ) |
| Common Mistakes | • Forgetting to use the right base (total students vs 100 %). • Mixing units (days vs months). • Assuming non‑linear trend when the graph is straight. |
- |
| Practice Tip | Solve 2–3 BITSAT sample questions each week. Focus on quick mental math for percentages and slopes. | - |
Final Thought:
In BITSAT, diagrams are designed to test interpretation speed. Keep your calculations simple, double‑check sums, and remember that most line graphs are linear unless stated otherwise. Happy studying!