II wrote:If x is a positive integer, is x – 1 a factor of 104?
(1) x is divisible by 3.
(2) 27 is divisible by x.
Statement 2 gives us more direct info, so let's start there.
(2) 27 is divisible by x; in other words, x is a factor of 27.
So, x = 1, 3, 9 or 27
If we pick x=3, we get "is 2 a factor of 104?" yes!
If we pick x=9, we get "is 8 a factor of 104?" yes!
If we pick x=27, we get "is 26 a factor of 104?" yes!
If we pick x=1, we get "is 0 a factor of 104?" Doh! no!
[fun math fact: 0 is a multiple of every integer but a factor of no integer.]
So (2) is insufficient.
(1) x is divisible by 3; in other words, x is a multiple of 3.
If we pick x=3, we get "is 2 a factor of 104"? yes!
If we pick x=300, we get "is 299 a factor of 104?" no!
So (1) is insufficient.
When we combine (2) and (1), the only possible values for x are 3, 9 and 27. From our work with statement (2) we already know that all 3 of these give us "yes" answers to the original question. Combined, the statements are sufficient: choose (c).
