Scaling every number — Averages Aptitude Question
Scaling every number: The average of 8 numbers is 20. If each number is multiplied by 3, what is the new average? Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
The average of 8 numbers is 20. If each number is multiplied by 3, what is the new average?
Options
- 20
- 23
- 40
- 60
Show the answer and the worked solution
Correct answer: D. 60
Worked solution
- Every number triples, so the total triples.
- The count is unchanged, so the average triples: 20 × 3 = 60.
Answer: 60.
The idea
Multiplying all values by k multiplies the average by k; adding k to all values adds k to the average. Confusing the two gives 23, which is offered.
Shortcut. Picture all eight numbers equal to 20; tripled, every one becomes 60, so the average is 60.
Common trap. "23" — adding 3 to the average; multiplying every value multiplies the average, and only adding a constant adds to it.