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# If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?

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

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21 Aug 2017, 14:01
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95% (hard)

Question Stats:

31% (01:19) correct 69% (01:58) wrong based on 39 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) $$x + y + z = 0$$
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5537
Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0? [#permalink]

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21 Aug 2017, 20:25
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Joined: 27 Dec 2016
Posts: 232
Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0? [#permalink]

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22 Aug 2017, 06:22
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.

Math Expert
Joined: 02 Aug 2009
Posts: 5537
If xyz ≠ 0, is x^3 + y^3 + z^3 = 0? [#permalink]

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22 Aug 2017, 06:30
1
KUDOS
Expert's post
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Manager
Joined: 27 Dec 2016
Posts: 232
Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0? [#permalink]

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22 Aug 2017, 06:34
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, 06:34
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