How many 3-digit natural numbers are divisible by 9 but not divisible by 6?

3-digit numbers divisible by 9: Smallest 3-digit multiple of 9 = 108 Largest 3-digit multiple of 9 = 999 Count = (999 − 108)/9 + 1 = 891/9 + 1 = 99 + 1 = 100 numbers A number divisible by 9 is always divisible by 3. For it NOT to be divisible by 6, it must NOT be divisible by 2 (i.e., it must be odd). Multiples of 9: 108 (even), 117 (odd), 126 (even), 135 (odd), ... They alternate even, odd, even, odd... Out of 100 such numbers, exactly half are odd. So required count = 100 / 2 = 50