Unit digit of 7⁹⁵ − 3⁵⁸ — Number System Aptitude Question
Unit digit of 7⁹⁵ − 3⁵⁸: What is the unit digit of 7⁹⁵ − 3⁵⁸? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the unit digit of 7⁹⁵ − 3⁵⁸?
Options
- 0
- 2
- 4
- 6
Show the answer and the worked solution
Correct answer: C. 4
Worked solution
- Unit digits of 7ⁿ cycle 7, 9, 3, 1. 95 mod 4 = 3, so 7⁹⁵ ends in 3.
- Unit digits of 3ⁿ cycle 3, 9, 7, 1. 58 mod 4 = 2, so 3⁵⁸ ends in 9.
- 3 − 9 is negative, so borrow: 13 − 9 = 4.
Answer: 4.
The idea
Reduce each power to its unit digit with the mod-4 cycle, then do the arithmetic on those two digits alone. For a subtraction whose first digit is the smaller, borrow ten — this is the step that catches most candidates out.
Shortcut. Only the exponents mod 4 matter: 95 → 3 and 58 → 2, so compare 7³ = 343 with 3² = 9. 343 − 9 = 334 ends in 4, and since 7⁹⁵ is far larger than 3⁵⁸ the true difference ends in 4 too.
Common trap. 6 — subtracting the unit digits the wrong way round (9 − 3 = 6) instead of borrowing to get 13 − 9 = 4.