mt10087 wrote:I'm still very confused on this really straightforward concept. Even with reduced numbers it still doesn't make sense to me.
is x divisible by 24?
If x is divisible by 6....(3, 2)...It seems divisible to 24.
24/6= 4
24/3= 8
24/2= 12
If x is divisible by 4...(2,2)...It seems divisible by 24
24/4 = 8
24/2 = 12
Could anyone explain where my thought process has gone wrong?
You're answering the opposite question to what's being asked. You're (correctly) answering the question:
Is positive integer x a divisor of 24?
1. x is a divisor of 4
2. x is a divisor of 6
In this case, each Statement is sufficient - from Statement 1, x can only be 1, 2 or 4, and from Statement 2 x can only be 1, 2, 3 or 6, all of which are divisors of 24.
In the original question, the statements tell us the opposite of what the statements tell us in the question I invented above. In the original question, Statement 1 tells us that x is
divisible by 4. That means that 4 is a divisor of x, not that x is a divisor of 4. That is, x is a multiple of 4: x could be 4, 8, 12, 16, 20, 24, and so on. All we know for sure is that 2^2 is a factor of x. That's not enough to tell us if x is a multiple of 24 - it might be, because x could be equal to 24, or 48, or 72, but it might not be, because x could be equal to 8, or 28, or 100, for example.
Statement 2 is not sufficient for the same reason, and even combined, the Statements are not sufficient, since x could be equal to 12 or 36, etc, in which case x is not divisible by 24, or x could be equal to 24, or 48, etc, in which case x is divisible by 24.
