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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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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

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Kudos [?]: 1362 [0], given: 263

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

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

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New post 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!
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Kudos [?]: 32 [0], given: 188

Expert Post
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Math Forum Moderator
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P
Joined: 02 Aug 2009
Posts: 4912

Kudos [?]: 5248 [1], given: 112

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

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New post 22 Aug 2017, 07:30
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This post received
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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

Kudos [?]: 5248 [1], given: 112

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Joined: 27 Dec 2016
Posts: 139

Kudos [?]: 32 [0], given: 188

Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
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Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0? [#permalink]

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New post 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 :o :o :o
That's why you doubted that this is not a typical GMAT equation?

Thanks anyway.
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Re: If xyz ≠ 0, is x^3 + y^3 + z^3 = 0?   [#permalink] 22 Aug 2017, 07:34
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