In set of 30 different positive integers, every number is even and/or a multiple of 3. If 22 of these numbers are even and 15 are multiple of 3, then how many of these numbers are multiple of 6?

Answer 1

all multiples of 6 are even and multiples of 3

Venn diagram (intersection is mult of 6)
n are multiples of 6
22 - n are even only
15 - n are 3 only

(22- n) + n + (15-n) = 30

37 - n = 30

n = 7