There are 22 integers between 1 and 22.
Half of these are divisible by 2 --> 22/2 = 11 numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22)
One-fifth of these are divisible by 5 --> 22/5 = 4 numbers (5, 10, 15, 20)
But we can't just subtract 11 and 4. There are some numbers that are both divisible by 2 and 5. Those are the numbers divisible by 10. We need to add them back in because they are counted twice.
One-tenth of these are divisible by 10 --> 22/10 = 2 numbers (10, 20)
22 - 11 - 4 + 2
= 9 numbers
Answer:
9 numbers (1, 3, 7, 9, 11, 13, 17, 19, 21)