The digit in the unit place of the number 6¹²⁹ × 7³⁰⁷ is
- (a) 2
- (b) 4
- (c) 8 ✓ UPSC's answer
- (d) 6
Why the answer is (c)
• Any power of 6 ends in 6.
• Powers of 7 end in the cycle 7, 9, 3, 1. 307 ÷ 4 leaves 3, so 7³⁰⁷ ends in 3.
• 6 × 3 = 18, so the unit digit is 8: (c).
Why the other options are wrong
- (a) 2
- 2 would need 7³⁰⁷ to end in 7 (6 × 7 = 42), but it ends in 3.
- (b) 4
- 4 would need 7³⁰⁷ to end in 9 (6 × 9 = 54), but it ends in 3.
- (d) 6
- 6 would need 7³⁰⁷ to end in 1, but it ends in 3.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.