What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × ... × 999 ?
- (a) 1
- (b) 3
- (c) 5 ✓ UPSC's answer
- (d) 9
Why the answer is (c)
• The product 1 × 3 × 5 × … × 999 contains the factor 5, so it is a multiple of 5.
• Every factor is odd, so the product is odd and cannot be a multiple of 10.
• An odd multiple of 5 always ends in 5.
• So the unit digit is 5, option (c).
Why the other options are wrong
- (a) 1
- The unit digit cannot be 1 because the product includes the factor 5, and multiplying 5 by any odd number greater than 1 results in a unit digit of 5, not 1.
- (b) 3
- The unit digit cannot be 3 because the product includes the factor 5, and 5 multiplied by any odd number results in a unit digit of 5, not 3.
- (d) 9
- The unit digit cannot be 9 because the product includes the factor 5, and 5 multiplied by any odd number results in a unit digit of 5, not 9.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.