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11 Nov 2019, 04:53
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Difficulty:
95%
(hard)
Question Stats:
31% (01:35) correct
69%
(02:10)
wrong
based on 150
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) \(x + y + z = 0\)
Are You Up For the Challenge: 700 Level Questions
(1) \(x^2 + y^2 + z^2=xy + yz + xz\)
(2) \(x + y + z = 0\)
Are You Up For the Challenge: 700 Level Questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
11 Nov 2019, 08:55
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If \(xyz ≠ 0\), is \(x^3 + y^3 + z^3 = 0\)?
You should know the formula..\(x^3 + y^3 + z^3 -3xyz=(x+y+z)(x^2 + y^2 + z^2-(xy + yz + xz))\)
(1) \(x^2 + y^2 + z^2=xy + yz + xz\)
\(x^2 + y^2 + z^2=xy + yz + xz.......\)\(x^2 + y^2 + z^2-(xy + yz + xz)=0\)...
\(x^3 + y^3 + z^3 -3xyz=(x+y+z)(x^2 + y^2 + z^2-(xy + yz + xz))=(x+y+z)*0=0.....x^3+y^3+z^3=3xyz\neq{0}\)
(2) \(x + y + z = 0\)
\(x^3 + y^3 + z^3 -3xyz=(x+y+z)(x^2 + y^2 + z^2-(xy + yz + xz))=(0)(x^2 + y^2 + z^2-(xy + yz + xz))=0.....x^3+y^3+z^3=3xyz\neq{0}\)
D
You should know the formula..\(x^3 + y^3 + z^3 -3xyz=(x+y+z)(x^2 + y^2 + z^2-(xy + yz + xz))\)
(1) \(x^2 + y^2 + z^2=xy + yz + xz\)
\(x^2 + y^2 + z^2=xy + yz + xz.......\)\(x^2 + y^2 + z^2-(xy + yz + xz)=0\)...
\(x^3 + y^3 + z^3 -3xyz=(x+y+z)(x^2 + y^2 + z^2-(xy + yz + xz))=(x+y+z)*0=0.....x^3+y^3+z^3=3xyz\neq{0}\)
(2) \(x + y + z = 0\)
\(x^3 + y^3 + z^3 -3xyz=(x+y+z)(x^2 + y^2 + z^2-(xy + yz + xz))=(0)(x^2 + y^2 + z^2-(xy + yz + xz))=0.....x^3+y^3+z^3=3xyz\neq{0}\)
D
18 Apr 2022, 12:34
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