Question Statement:
40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to
represent this as a slice of a pie chart is
Options:
-
(A) 120
-
(B) 144
°
-
(C) 160
-
(D) 212
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2017 Q.59)**
**1. Governing Concept & Question Classification**:
- **Section**: General Aptitude (GA)
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Data Interpretation (Pie Chart Sector Angles)
**2. Detailed Step-by-Step Derivation**:
- A complete pie chart represents $100\%$ of data distributed over a full circular angle of $360^\circ$.
- The central angle $\theta$ corresponding to a sector of percentage $P$ is calculated as:
$\theta = \left(\frac{P}{100}\right) \times 360^\circ$
- Given $P = 40\%$:
$\theta = \left(\frac{40}{100}\right) \times 360^\circ = 0.40 \times 360^\circ = 144^\circ$
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: $120^\circ$ corresponds to $33.33\%$.
- **Option (B) [CORRECT]**: $144^\circ$ is the exact sector angle corresponding to $40\%$ of $360^\circ$.
- **Option (C) [INCORRECT]**: $160^\circ$ corresponds to $44.44\%$.
- **Option (D) [INCORRECT]**: $212^\circ$ corresponds to $58.89\%$.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test