How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?

Answer: (c) 12

There are 19 numbers below 100 containing the digit 4: 4, 14, 24, 34, 40 to 49, and 54, 64, 74, 84, 94. Seven of them are multiples of 4, which leaves 12.

1. Units digit 4: 4, 14, 24, 34, 44, 54, 64, 74, 84, 94 = 10 numbers.
2. Tens digit 4 (other than 44): 40, 41, 42, 43, 45, 46, 47, 48, 49 = 9 numbers. Total = 19.
3. Multiples of 4 among them: 4, 24, 40, 44, 48, 64, 84 = 7.
4. Required count = 19 − 7 = 12.

Remember · Count the whole set first, then subtract the ones to exclude — fewer chances to miss a number.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error