If x is a positive integer, is x^3 - 3x^2 + 2x divisible by 4?
(i) x = 4y + 4
(ii) x = 2z + 2
This comes from p98 of the fourth edition of Manhattan Gmat's Number Properties Guide
(i) tells us that x is divisible by 4 - Sufficient
(ii) tells us that x is divisible by 2 - claims to be sufficient, but I'm not sure I totally agree... as explained by the book, x just has to be even, because the question is asking if the product of a set of 3 numbers (x-2, x-1, and x) is divisible by 4. What if x = 2? Then the question is, is 0 divisible by 4? Not too sure myself, so please explain. Thanks!
(i) x = 4y + 4
(ii) x = 2z + 2
This comes from p98 of the fourth edition of Manhattan Gmat's Number Properties Guide
(i) tells us that x is divisible by 4 - Sufficient
(ii) tells us that x is divisible by 2 - claims to be sufficient, but I'm not sure I totally agree... as explained by the book, x just has to be even, because the question is asking if the product of a set of 3 numbers (x-2, x-1, and x) is divisible by 4. What if x = 2? Then the question is, is 0 divisible by 4? Not too sure myself, so please explain. Thanks!
