Unit digit of 4⁵⁴ — Number System Aptitude Question
Unit digit of 4⁵⁴: What is the unit digit of 4⁵⁴? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
What is the unit digit of 4⁵⁴?
Options
- 2
- 4
- 6
- 8
Show the answer and the worked solution
Correct answer: C. 6
Worked solution
- Unit digits of 4ⁿ alternate: 4, 6, 4, 6, …
- Odd powers end in 4, even powers end in 6.
- 54 is even, so the unit digit is 6.
Answer: 6.
The idea
Bases 4 and 9 have a cycle of length 2, not 4: odd power keeps the base's digit, even power gives 6 and 1 respectively. Recognising the short cycles saves time.
Shortcut. 4⁵⁴ = 16²⁷, and every power of 16 ends in 6.
Common trap. 4 — assuming the power keeps the base's unit digit, which is true for 4 only at odd exponents.