Factors, multiples, and divisibility

I have 2 questions regarding this.

Why did you not include the 19 in your listing? and what does the sum of positive multiple of 2 and sum of positive multiple of 4 mean?

Pls explain

Thanks

Brent@GMATPrepNow wrote:

datonman wrote:How many positive integers less than 28 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?

A. 27
B. 25
C. 24
D. 22
E. 20

Primes: 2, 3, 5, 7, 11, 13, 17, 23
Odd multiples of 5: 5, 15, 25
Sum of a positive multiple of 2 and a positive multiple of 4: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

We need to ignore one of the 5's since they are listed twice.

TOTAL = [spoiler]22 = D[/spoiler]

Cheers,
Brent

Why not work backwards?

1 doesn't work, 4 doesn't work, and all of the composite odds that aren't divisible by 5 don't work (9, 21, 27). Every other even will be either prime (2) or the sum of two multiples, since you can simply take 4 and add any even to it that to you like (e.g. 4+2 = 6, 4+2*2 = 8, 4 + 2*3 = 10, etc.)

So there are five numbers that don't work out of 27 total, leaving us with 22 valid options.