Number Properties Strategy Guide- Divisibility DS question

[weich.sonja]

The explanation for the second statement of the Data Sufficiency practice problem on page 98 of the MGMAT Number Properties Strategy Guide doesn't make sense to me. Can someone please help? Here it is:

If x is a positive integer, is (X^3) - (3X^2) +(2x) divisible by 4?

1) x=4y+4, where y is an integer
2) x=2z+2, where z is an integer

Answer: D, both are sufficient
My answer: A

Start rephrasing the question by factoring: x(x-1)(x-2)

So I rephrased it as: Is X a multiple of 4? or is (X-1) a multiple of 4?

But MGMAT says that you rephrase it as: Is x even? or is (x-1) a multiple of 4.

I don't understand how "is x even?" is a proper rephrasing of the question because if x= 2, then X^3 - 3X^2 +2x = 8-12+4=0, which is not a multiple of 4. This is why I said that statement 2 is insufficient: if z=0, then x=2, and the function is equal to 0, but if z is any integer larger than zero, then the function is a multiple of 4.

Anyone have an explanation? The book's explanation doesn't do it for me....


THANK YOU!!!

[himanshu.m1986]

First of all, You need to move the post to Quant section..

0 is a multiple of every positive integer, and is divisible by every positive integer. That's true in real math, and in GMAT math as well, though almost every divisibility question on the GMAT is restricted to positive integers only

Since it is mentioned that X is a positive integer. Eq can be reduced to "is X is even". Because for divisible of 4 we need 2 even integers. so if X is even then (X-2) will be even, therefore the whole eq is divisible by 4. FYI "0 is an even number".

[StaceyKoprince]

himanshu is right! Please read (and follow!) forum guidelines before posting. If you would like to have a response from an instructor, please post in the appropriate folder.

himanshu, I appreciate that you want to help out a fellow student. Next time, though, can you do me a favor and not offer an explanation if the post is in the wrong folder? People who mistakenly post in the wrong folder will learn a lot faster to post in the right folder if they have to re-post and wait even longer to get an answer... ;)