Reasoning about an average — Aptitude Question
Reasoning about an average: A student's average across 4 tests is 80. What is the lowest possible score on any one… Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 105 seconds
Question
A student's average across 4 tests is 80. What is the lowest possible score on any one test, if each test is marked out of 100?
Options
- 20
- 40
- 60
- 80
Show the answer and the worked solution
Correct answer: A. 20
Worked solution
- Total across four tests = 4 × 80 = 320.
- To minimise one score, maximise the rest: 100 + 100 + 100 = 300.
- The lowest score = 320 − 300 = 20.
Answer: 20.
The idea
Extreme-value questions push every other quantity to its limit. Fix the total first, then push the others to their maximum.
Shortcut. Each of the other three tests can sit at most 20 above the average of 80, a surplus of 60, so the weakest can fall 60 below: 80 − 60 = 20.
Common trap. "60" — pushing only one other test to 100 so that the pair averages 80, instead of pushing all three others to 100.