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Tricky DS Problem... from MGMAT Number Properties, CH 8

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by mikeyyJ » Tue Aug 16, 2011 6:20 am
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!
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Source: — Data Sufficiency |

by kmittal82 » Tue Aug 16, 2011 6:29 am
>is 0 divisible by 4?

Last time I checked, 0/4 = 0, so yes, 0 is divisible by 4 (or by any other number (except 0) for that matter)
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by Brent@GMATPrepNow » Tue Aug 16, 2011 7:50 am
mikeyyJ wrote: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!
In general, we can say: If k and d are integers and k/d is an integer, then k is divisible by d.

So, since 0/4 is an integer, 0 is divisible by 4.

Cheers,
Brent

Aside: You will find that the vast majority of divisibility questions on the GMAT involve positive (i.e., non-zero) integers.
Brent Hanneson - Creator of GMATPrepNow.com
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by saketk » Wed Aug 17, 2011 8:35 am
yeah, 0 is divisible by 4.

both statements are sufficient.
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