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

Question

Aicharya · Accepted Answer

Integers from 1 to 100 having digit 4: 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94 — 19 numbers. Among these, those divisible by 4: 4, 24, 40, 44, 48, 64, 84 = 7. So numbers having digit 4 but not divisible by 4 = $19 - 7 = 12$.

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

Solution