I am currently studying for the GMAT, and I have run into a problem that confuses me because the correct answer explanation is somewhat vague.

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

The correct answer is D, 22

This is how I am solving the problem.

Step 1: Write out all of the numbers and circle all of the prime numbers. This leaves me with 1, 3, 5, 7, 11, 13, 17, 19, 23, and 27 (10 terms)

Step 2: Include all odd multiples of 5 that are not already prime, which was 15 and 25 (12 terms so far)

Step 3:???

My book's explanation says that a positive sum of a multiple of 2 and 4 just means to include all even numbers after 4. However, I do not understand the logic. For example, how does 6 contain a multiple of 4 AND a multiple of 2? etc.