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# If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?

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If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?  [#permalink]

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21 Aug 2017, 15:01
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Difficulty:

95% (hard)

Question Stats:

21% (02:39) correct 79% (01:52) wrong based on 41 sessions

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If $$xyz ≠ 0$$, is $$x^3 + y^3 + z^3 = 0$$?

(1) $$x^2 + y^2 + z^2=xy + yz + xz$$
(2) $$x + y + z = 0$$

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Math Expert
Joined: 02 Aug 2009
Posts: 7989
If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?  [#permalink]

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22 Aug 2017, 07:30
1
septwibowo wrote:
chetan2u wrote:
Gnpth wrote:
If $$xyz ≠ 0$$, is $$x^3 + y^3 + z^3 = 0$$?

(1) $$x^2 + y^2 + z^2=xy + yz + xz$$
(2) $$x + y + z = 0$$

Hi..
I cannot say if such a equation would be in real GMAT. But T formula that is required here is..
$$x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)+3xyz$$
Let's see the statements..
1..
$$x^2+y^2+z^2=xy+cz+yz$$..
Substitute in main formula..
So $$x^3+y^3+z^3=0+3xyz$$
But xyz is not 0..
Ans is NO
Sufficient
II
X+y+z=0..
Again same as above
Sufficient

D

Dear chetan2u , can u please explain the one I highlighted?

Thanks!

hi..

thats a formula sometimes seen on IIM CAT in india..
$$(x+y+z)(x^2+y^2+z^2-xy-xz-yz)+3xyz = x^3+xy^2+xz^2-x^2y-x^2z-xyz + y^3+x^2y+yz^2-xy^2-xyz-y^2z +$$.
$$x^2z+zy^2+z^3-xyz-xz^2-yz^2+3xyz =x^3+y^3+z^3$$

All other terms cancel out
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Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?  [#permalink]

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21 Aug 2017, 21:25
Gnpth wrote:
If $$xyz ≠ 0$$, is $$x^3 + y^3 + z^3 = 0$$?

(1) $$x^2 + y^2 + z^2=xy + yz + xz$$
(2) $$x + y + z = 0$$

Hi..
I cannot say if such a equation would be in real GMAT. But T formula that is required here is..
$$x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)+3xyz$$

Let's see the statements..
1..
$$x^2+y^2+z^2=xy+cz+yz$$..
Substitute in main formula..
So $$x^3+y^3+z^3=0+3xyz$$
But xyz is not 0..
Ans is NO
Sufficient
II
X+y+z=0..
Again same as above
Sufficient

D
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Joined: 27 Dec 2016
Posts: 227
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?  [#permalink]

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22 Aug 2017, 07:22
chetan2u wrote:
Gnpth wrote:
If $$xyz ≠ 0$$, is $$x^3 + y^3 + z^3 = 0$$?

(1) $$x^2 + y^2 + z^2=xy + yz + xz$$
(2) $$x + y + z = 0$$

Hi..
I cannot say if such a equation would be in real GMAT. But T formula that is required here is..
$$x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)+3xyz$$
Let's see the statements..
1..
$$x^2+y^2+z^2=xy+cz+yz$$..
Substitute in main formula..
So $$x^3+y^3+z^3=0+3xyz$$
But xyz is not 0..
Ans is NO
Sufficient
II
X+y+z=0..
Again same as above
Sufficient

D

Dear chetan2u , can u please explain the one I highlighted?

Thanks!
_________________
There's an app for that - Steve Jobs.
Manager
Joined: 27 Dec 2016
Posts: 227
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?  [#permalink]

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22 Aug 2017, 07:34
chetan2u wrote:
hi..

thats a formula sometimes seen on IIM CAT in india..
$$(x+y+z)(x^2+y^2+z^2-xy-xz-yz)+3xyz = x^3+xy^2+xz^2-x^2y-x^2z-xyz + y^3+x^2y+yz^2-xy^2-xyz-y^2z +$$.
$$x^2z+zy^2+z^3-xyz-xz^2-yz^2+3xyz =x^3+y^3+z^3$$

All other terms cancel out

Wow
That's why you doubted that this is not a typical GMAT equation?

Thanks anyway.
_________________
There's an app for that - Steve Jobs.
Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?   [#permalink] 22 Aug 2017, 07:34
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