Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 18

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?

  1. 8
  2. 12
  3. 16
  4. 24

Answer

12

  • Key fact: Odd digits are 1, 3, 5, 7, 9. For divisibility by 5, the last digit must be 5.
  • Hundreds place: Can be any of 1, 3, 7, 9 → 4 choices.
  • Tens place: After fixing the hundreds digit and 5 at the units place, remaining odd digits available = 3 choices.
  • Total numbers: 4 × 3 = 12.
  • Verdict on options: (a) 8 ❌, (b) 12 ✅, (c) 16 ❌, (d) 24 ❌.
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