The number that does not belong — Aptitude Question
The number that does not belong: Which number does not belong in this series? 8, 27, 64, 100, 125, 216 Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Easy
- Time target: 40 seconds
Question
Which number does not belong in this series?
8, 27, 64, 100, 125, 216
Options
- 27
- 64
- 100
- 216
Show the answer and the worked solution
Correct answer: C. 100
Worked solution
- 8 = 2³, 27 = 3³, 64 = 4³, 125 = 5³, 216 = 6³.
- 100 is not a cube (it is 10²), so 100 does not belong.
Answer: 100.
The idea
Test the small perfect powers first: squares up to 225 and cubes up to 216 cover most such questions.
Shortcut. The run is 2³ to 6³ with 100 wedged between 4³ and 5³; a cube between 64 and 125 would need a whole number between 4 and 5, and none exists.
Common trap. 64 — it is also a square (8²), so a candidate hunting for the 'square' may pick it; but 64 = 4³ fits the cube run, while 100 is only a square.