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OG - DS #63

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jenwindy
 Post subject: OG - DS #63
 Post Posted: Mon Oct 29, 2007 9:53 pm 
I am not clear with the answer explanation to the following problem:


If y is an integer, is y^3 divisible by 9?

(1) y is divisible by 4
(2) y is divisible by 6



Answer explanation:
In order for y^3 to be divisible by 9, the integer y must also be divisible by 3. WHY IS THIS? Can anybody help clarify?

(1) Not all multiples of 4 are divisible by 3 (e.g. y=12 is divisible by 3 but y=16 is not divisible by 3; NOT sufficient)
(2) Any number divisible by 6 is also divisible by 3; SUFFICIENT.

The correct answer is B; statement 2 along is sufficient.


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StaceyKoprince
 Post subject:
 Post Posted: Thu Nov 01, 2007 11:08 am 
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ManhattanGMAT Staff


Posts: 6077
Location: San Francisco
y^3 = y*y*y

In order for y^3 to be divisible by any number, the components of that number must be contained in those three y's. To check if something is divisible by 9, I first break that down into its prime factors, 3*3. So I need two factors of 3 to be contained in those three y's (if it is divisible by 9).

I can't break 3 down any further because it's already prime. So, if one y contains a 3, that will guarantee me the two factors of 3 I need to say that y*y*y is divisible by 9 (and, actually, it will end up giving me three factors of 3, since each y contains a 3).

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Stacey Koprince
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jenwindy
 Post subject:
 Post Posted: Mon Nov 05, 2007 2:34 pm 
I understand it now! Thanks Stacey!!
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RonPurewal
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 Post Posted: Tue Nov 06, 2007 4:35 am 
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ManhattanGMAT Staff


Posts: 7146


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