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# If y is an integer, is y^3 divisible by 8?

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Intern
Joined: 07 Sep 2012
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GMAT 1: 680 Q50 V32
GMAT 2: 700 Q49 V36
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Kudos [?]: 5 [0], given: 98

If y is an integer, is y^3 divisible by 8? [#permalink]  16 Sep 2012, 08:45
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78% (01:45) correct 22% (00:34) wrong based on 60 sessions
If y is an integer, is y^3 divisible by 8?

(1) y is even.
(2) y^3 - y is even.

[Reveal] Spoiler:
Shouldn't the answer be E because y could be 0 which is an even integer?
[Reveal] Spoiler: OA
Senior Manager
Joined: 28 Jun 2009
Posts: 454
Location: United States (MA)
Followers: 16

Kudos [?]: 131 [0], given: 46

Re: If y is an integer, is y(cube) divisible by 8? [#permalink]  16 Sep 2012, 08:57
I chose A.

(1) y^3 will always be divisible by 2^3 if y is even. Ex. y =2, 4, etc

Lets say y = 0 -> even integer
-> y^3 = 0
-> y^3/2^3 = 0/8
-> 0/8 = 0 [ 0/N = 0 for any N from -infinity to +infinity, except 0.]
Director
Joined: 22 Mar 2011
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Kudos [?]: 670 [1] , given: 43

Re: If y is an integer, is y(cube) divisible by 8? [#permalink]  16 Sep 2012, 09:08
1
KUDOS
crackmba2012 wrote:
If y is an integer, is y(cube) divisible by 8?
(1) y is even.
(2) y(cube)- y is even.

Shouldn't the answer be E because y could be 0 which is an even integer?

0 is even and it is divisible by 8. 0 is divisible by any non-zero integer.

(1) $$y=2k,$$ for some integer $$k,$$ then $$y^3=8k^3,$$ obviously divisible by 8.
Sufficient.

(2) Check for example for $$y=1$$ and $$y = 2.$$ You obtain 0 and 6. Both are even, but 6 is not divisible by 8.
Not sufficient.

Remark: $$y^3-y=y(y^2-1)=(y-1)y(y+1)$$ is the product of three consecutive integers, therefore it is always even.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 28 Jun 2009
Posts: 454
Location: United States (MA)
Followers: 16

Kudos [?]: 131 [0], given: 46

Re: If y is an integer, is y(cube) divisible by 8? [#permalink]  16 Sep 2012, 09:11
EvaJager wrote:

Remark: $$y^3-y=y(y^2-1)=(y-1)y(y+1)$$ is the product of three consecutive integers, therefore it is always even.

Awesome! I used a very long way to get here. Should have spotted this.
Re: If y is an integer, is y(cube) divisible by 8?   [#permalink] 16 Sep 2012, 09:11
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# If y is an integer, is y^3 divisible by 8?

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