What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × ... × 999?

Answer: (c) 5

The product of all odd numbers up to 999 is odd and contains 5 as a factor. An odd multiple of 5 always ends in 5.

1. The product contains the factor 5, so it is a multiple of 5 and its unit digit is 0 or 5.
2. Every factor is odd, so the product is odd and cannot end in 0.
3. Hence the unit digit is 5.
4. Check: 1 × 3 × 5 = 15 already ends in 5, and multiplying any number ending in 5 by an odd number keeps the last digit 5.

Remember · Odd × 5 ends in 5; an even number times 5 ends in 0. Spot a factor of 5 before multiplying anything.

Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error