Here is the question and the answer(explaination). The Answer is C, if 0 is not divisible by 3, else the answer should be E. My question is isnt 0 divisible by 3, because it leaves a reminder of 0. So shouldnt the answer be E.
Please advise.
Thanks in advance
If x is a positive integer, is x â€“ 1 a factor of 104?
(1) x is divisible by 3.
(2) 27 is divisible by x
The factors of 104 are {1, 2, 4, 8, 13, 26, 52, 104}. If x â€“ 1 is definitely one of these factors, OR if x â€“ 1 is definitely NOT one of these factors, then the statement is sufficient.
(1) INSUFFICIENT: x could be any one of the infinite multiples of 3. If x = 3, x â€“ 1 would equal 2, which is a factor of 104. If x = 6, x â€“ 1 would equal 5, which is not a factor of 104.
(2) INSUFFICIENT: The factors of 27 are {1, 3, 9, 27}. Subtracting 1 from each of these values yields the set {0, 2, 8, 26}. The nonzero values are all factors of 104, but 0 is not.
(1) AND (2) SUFFICIENT: Given that x is a factor of 27 and also divisible by 3, x must equal one of 3, 9 or 27. x â€“ 1 must therefore equal one of 2, 8, or 26  all factors of 104.
The correct answer is C.
