If 3²⁰¹⁹ is divided by 10, then what is the remainder ?
- (a) 1
- (b) 3
- (c) 7 ✓ UPSC's answer
- (d) 9
Why the answer is (c)
• The last digit of powers of 3 repeats in a cycle of 4: 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, then 3, 9, 7, 1 again.
• 2019 = 4 × 504 + 3, so 3²⁰¹⁹ ends in the same digit as 3³, which is 7.
• The remainder on division by 10 is the last digit, 7 — option (c).
Why the other options are wrong
- (a) 1
- 1 is the last digit of 3⁴ⁿ; 2019 leaves remainder 3 on division by 4, not 0.
- (b) 3
- 3 is the last digit of 3⁴ⁿ⁺¹; 2019 leaves remainder 3 on division by 4, not 1.
- (d) 9
- 9 is the last digit of 3⁴ⁿ⁺²; 2019 leaves remainder 3 on division by 4, not 2.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.