QB_PH_GA_018: Quantitative Aptitude

A student scores 65, 72, 80, and 83 marks in four physics tests. What score must the student achieve in the fifth test to attain an overall average score of 80 marks?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Arithmetic Mean Formula**: $\bar{x} = \frac{\sum_{i=1}^5 x_i}{5} = 80$ 2. **Total Marks Required Across 5 Tests**: $\sum_{i=1}^5 x_i = 5 \times 80 = 400$ 3. **Sum of Existing Scores**: $x_1 + x_2 + x_3 + x_4 = 65 + 72 + 80 + 83 = 300$ 4. **Fifth Test Score Calculation**: $x_5 = 400 - 300 = 100$ 5. **Official Answer**: 100.