How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?
Answer & explanation
Answer: (b) 12
A number divisible by 5 with an odd units digit must end in 5. The other two places are filled from 1, 3, 7, 9 without repetition: 4 × 3 = 12 numbers.
- Divisible by 5 means the units digit is 0 or 5; it must be odd, so it is 5.
- The hundreds digit can be any of the remaining odd digits 1, 3, 7, 9: 4 choices.
- The tens digit can be any of the 3 odd digits still unused: 3 choices.
- Total = 4 × 3 = 12.
Remember · Fill the restricted place first (here the units digit), then count the choices for the free places.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·