If 3^2019 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)
• To find the remainder when $3^{2019}$ is divided by 10, we examine the pattern of the last digit of powers of 3.
• The last digits of $3^n$ for $n=1, 2, 3, 4, \dots$ are 3, 9, 7, 1, repeating in a cycle of 4.
• We divide the exponent 2019 by the cycle length 4: $2019 \div 4 = 504$ with a remainder of 3.
• A remainder of 3 indicates the last digit corresponds to the 3rd term in the cycle, which is 7.
• Therefore, the remainder when $3^{2019}$ is divided by 10 is 7, matching option (c).
Why the other options are wrong
- (a) 1
- Option (a) is incorrect because the last digit of $3^{2019}$ is 7, not 1.
- (b) 3
- Option (b) is incorrect because the last digit of $3^{2019}$ is 7, not 3.
- (d) 9
- Option (d) is incorrect because the last digit of $3^{2019}$ is 7, not 9.
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.