Q. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?
(a) 5
(b) 11
(c) 12
(d) 13
Correct Answer: (c) 12
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Integers between 1 and 100 which have 4 as a digit are:
To determine how many integers between 1 and 100 contain the digit 4 but are NOT divisible by 4, follow these steps:
1. Identify Numbers Containing the Digit 4:
Single-digit: 4
Two-digit: 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94
Total numbers with the digit 4: 19
2. Identify Numbers Divisible by 4 Among Them:
4 ÷ 4 = 1 → 4
24 ÷ 4 = 6 → 24
40 ÷ 4 = 10 → 40
44 ÷ 4 = 11 → 44
48 ÷ 4 = 12 → 48
64 ÷ 4 = 16 → 64
84 ÷ 4 = 21 → 84
Total numbers divisible by 4: 7
3. Calculate Numbers with Digit 4 but Not Divisible by 4:
19 (total with digit 4) – 7 (divisible by 4) = 12
Answer: 12
