How many positive integers less than 26 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?  Options
A) 27
B) 21
C) 24
D) 22
E) 20

Rationale: 9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 10 - 1 = 21 . answer : b .
Answer: B