How many times does 5 appear in all two-digit positive integers?
- (a) 18
- (b) 19 ✓ UPSC's answer
- (c) 20
- (d) 21
Why the answer is (b)
• Two-digit numbers run from 10 to 99.
• 5 in the tens place: 50 to 59, i.e. 10 times.
• 5 in the units place: 15, 25, …, 95, i.e. 9 times (55 is already counted once in the tens place and again here, correctly, since it has two 5s).
• Total 10 + 9 = 19: (b).
Why the other options are wrong
- (a) 18
- 18 counts 55 only once, though it contains two 5s.
- (c) 20
- 20 wrongly counts 05, which is not a two-digit number.
- (d) 21
- 21 overcounts.
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.