Marks across three papers — Caselets Aptitude Question
Marks across three papers: A candidate scored 72, 84 and 90 in three papers, each marked out of 100. Answer and worked solution on CodeKairo.
- Topic: Caselets
- Section: Data Interpretation
- Difficulty: Hard
- Time target: 90 seconds
Question
A candidate scored 72, 84 and 90 in three papers, each marked out of 100. The papers carry weights of 2, 3 and 5 respectively.
What is the weighted average?
Options
- 82.0
- 84.6
- 85.2
- 86.0
Show the answer and the worked solution
Correct answer: B. 84.6
Worked solution
- Weighted total = 72 × 2 + 84 × 3 + 90 × 5 = 144 + 252 + 450 = 846.
- Total weight = 10.
- Weighted average = 846 ÷ 10 = 84.6.
Answer: 84.6.
The idea
Multiply, add, then divide by the sum of the weights. The plain mean of 82 is offered for anyone who ignores the weighting.
Shortcut. Work in deviations from 84: −12 × 2 + 0 × 3 + 6 × 5 = +6, spread over a total weight of 10, gives 84 + 0.6 = 84.6.
Common trap. "82.0" — taking the plain mean (72 + 84 + 90) ÷ 3 and ignoring that the 90 carries half the total weight.