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UPSC Prelims 2026 CSAT, question 49

Topic: Number system

Q49

How many times does 5 appear in all two-digit positive integers?

  1. (a) 18
  2. (b) 19Correct answer
  3. (c) 20
  4. (d) 21

Solution.

Answer: (b) 19

  1. Among two-digit integers (1010 to 9999), the digit 55 appears in the units place 99 times (15,25,35,45,55,65,75,85,9515, 25, 35, 45, 55, 65, 75, 85, 95).
  2. The digit 55 appears in the tens place 1010 times (50,51,52,53,54,55,56,57,58,5950, 51, 52, 53, 54, 55, 56, 57, 58, 59).
  3. Therefore, the digit 55 appears 9+10=199 + 10 = 19 times in total (with 5555 contributing two 55's).

Trap: Do not subtract 1 for 55: the question asks how many times the digit 5 appears, not how many two-digit numbers contain the digit 5 (which would be 18).