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If x,y, and z are three non-zero numbers
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26 Apr 2021, 10:20
26 Apr 2021, 10:20
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If x,y, and z are three non-zero numbers and \(xy>0\) and \(yz<0\), which of the following must be negative?
A. \(xyz\)
B. \(xyz^2\)
C. \(xy^2z\)
D. \(xy^2z^2\)
E. \(x^2y^2z^2\)
F. \(x^2yz\)
G. \(-(x^2y^2z^2)\)
H. \(x^2yz^2\)
I. \(x(-y)z^2\)
J. \(-(xyz^2)\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(xyz\)
B. \(xyz^2\)
C. \(xy^2z\)
D. \(xy^2z^2\)
E. \(x^2y^2z^2\)
F. \(x^2yz\)
G. \(-(x^2y^2z^2)\)
H. \(x^2yz^2\)
I. \(x(-y)z^2\)
J. \(-(xyz^2)\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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C,F,G,I,J
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Re: If x,y, and z are three non-zero numbers
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27 Apr 2021, 07:38
27 Apr 2021, 07:38
1
Carcass wrote:
If x,y, and z are three non-zero numbers and \(xy>0\) and \(yz<0\), which of the following must be negative?
A. \(xyz\)
B. \(xyz^2\)
C. \(xy^2z\)
D. \(xy^2z^2\)
E. \(x^2y^2z^2\)
F. \(x^2yz\)
G. \(-(x^2y^2z^2)\)
H. \(x^2yz^2\)
I. \(x(-y)z^2\)
J. \(-(xyz^2)\)
A. \(xyz\)
B. \(xyz^2\)
C. \(xy^2z\)
D. \(xy^2z^2\)
E. \(x^2y^2z^2\)
F. \(x^2yz\)
G. \(-(x^2y^2z^2)\)
H. \(x^2yz^2\)
I. \(x(-y)z^2\)
J. \(-(xyz^2)\)
Given: \(xy > 0\) and \(yz < 0\)
We can have two cases;
Case I: when \(x\) is +ve, \(y\) is +ve and \(z\) is -ve
Case II: when \(x\) is -ve, \(y\) is -ve and \(z\) is +ve
A. \(xyz < 0\)
Case I: Yes
Case II: No
B. \(xyz^2 < 0\)
Case I: No
Case II: No
C. \(xy^2z < 0\)
Case I: Yes
Case II: Yes
D. \(xy^2z^2 < 0\)
Case I: No
Case II: Yes
E. \(x^2y^2z^2 < 0\)
Case I: No
Case II: No
F. \(x^2yz < 0\)
Case I: Yes
Case II: Yes
G. \(-(x^2y^2z^2) < 0\)
Case I: Yes
Case II: Yes
H. \(x^2yz^2 < 0\)
Case I: No
Case II: Yes
I. \(x(-y)z^2 < 0\)
Case I: Yes
Case II: Yes
J. \(-(xyz^2) < 0\)[/quote]
Case I: Yes
Case II: Yes
Hence, option C, F, G, I, and J
gmatclubot
Re: If x,y, and z are three non-zero numbers [#permalink]
27 Apr 2021, 07:38
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