Q1. In the above poster how are you saying "this statement is true if a = 4 and b = 8"? as I understand a <4> is not a multiple of b <8>
statement (1) is true for those values. since we're considering the sufficiency of statement (1), we need to select only values that satisfy that particular statement.
a = 4, b = 8, satisfy statement (1), but give a NO to the prompt question.
a = 8, b = 4, also satisfy statement (1), but give a YES to the prompt question.
therefore, statement (1) is insufficient.
don't confuse "statement" with "prompt / question". we will NEVER use "statement" to refer to the question.
Q2. What are the prime factors of 12? As I understand, Prime factors of 12 are 2, 2, 3. So if 12 is "a" as in the above question and and 6 is "b" as in the above question, I think it will always be true that all prime factors of "b" (2,3) will be prime factors of "a" and hence a will always be a multiple of b?
i don't really see what you're trying to say here. however, your example is a = 12, b = 6, which is functionally identical to my example of a = 8, b = 4.
...but i'm a bit troubled by this: and hence a will always be a multiple of b?
so wait - do you think that one example
proves that something is ALWAYS true? if so, that's going to be a big problem.