What is the rightmost digit preceding the zeros in the value of 30³⁰?
- (a) 1
- (b) 3
- (c) 7
- (d) 9 ✓ UPSC's answer
Why the answer is (d)
• 30³⁰ = 3³⁰ × 10³⁰, so the number is 3³⁰ followed by 30 zeros.
• The digit just before the zeros is the unit digit of 3³⁰.
• Unit digits of powers of 3 repeat in the cycle 3, 9, 7, 1. 30 = 4 × 7 + 2, so 3³⁰ ends like 3², i.e. in 9.
• The digit is 9 — option (d).
Why the other options are wrong
- (a) 1
- Option (a) is incorrect because the remainder of 30 divided by 4 is 2, not 4 (or 0), so the units digit is 9, not 1.
- (b) 3
- Option (b) is incorrect because the remainder of 30 divided by 4 is 2, not 1, so the units digit is 9, not 3.
- (c) 7
- Option (c) is incorrect because the remainder of 30 divided by 4 is 2, not 3, so the units digit is 9, not 7.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.