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16 Sep 2014, 00:40
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Official Solution:
Is \(x^3*y^2*z^2 > 0\)?
For \(x^3*y^2*z^2 > 0\) to be true, \(x\) must be positive, while \(y\) and \(z\) must be non-zero.
(1) \(xy >0\).
This implies that \(x\) and \(y\) have the same sign. If all variables are positive, then the answer is YES. However, if all variables are negative, then the answer is NO. Not sufficient.
(2) \(xz > 0\).
This implies that \(x\) and \(z\) have the same sign. If all variables are positive, then the answer is YES. However, if all variables are negative, then the answer is NO. Not sufficient.<
(1)+(2) The same logic applies: if all variables are positive, the answer is YES. However, if all variables are negative, the answer is NO. Not sufficient.
Essentially, while we know that \(y\) and \(z\) are non-zero, the sign of \(x\) remains undetermined, preventing us from conclusively answering the question.
Answer: E
Is \(x^3*y^2*z^2 > 0\)?
For \(x^3*y^2*z^2 > 0\) to be true, \(x\) must be positive, while \(y\) and \(z\) must be non-zero.
(1) \(xy >0\).
This implies that \(x\) and \(y\) have the same sign. If all variables are positive, then the answer is YES. However, if all variables are negative, then the answer is NO. Not sufficient.
(2) \(xz > 0\).
This implies that \(x\) and \(z\) have the same sign. If all variables are positive, then the answer is YES. However, if all variables are negative, then the answer is NO. Not sufficient.<
(1)+(2) The same logic applies: if all variables are positive, the answer is YES. However, if all variables are negative, the answer is NO. Not sufficient.
Essentially, while we know that \(y\) and \(z\) are non-zero, the sign of \(x\) remains undetermined, preventing us from conclusively answering the question.
Answer: E
05 Apr 2016, 02:55
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Hi Bunuel, could i also look at it this way, statement 1-does not mention anything about "z" and statement 2- did not mention anything about "Y". If you put them together, its still insufficient because it fails to consider Z*Y>0. is my line of thinking correct?
