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16 Sep 2014, 01:15
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16 Sep 2014, 01:15
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Official Solution:
Is \(x^2*y^3*z > 0\)?
For the inequality \(x^2*y^3*z > 0\) to hold true, the following conditions must be met:
1. Both \(y\) and \(z\) must either be positive or negative, meaning they must share the same sign. This would ensure that \(y^3*z\) is positive;
AND
2. \(x\) cannot be zero, to ensure that \(x^2\) is positive.
(1) \(yz > 0\).
The above implies that \(y\) and \(z\) are either both positive or both negative, which satisfies the first condition. However, information about \(x\) (the second condition) is lacking: if \(x = 0\), \(x^2*y^3*z\) would be 0, not more than 0. Not sufficient.
(2) \(xz < 0\).
The above implies that \(x \ne 0\), thus satisfying the second condition. But we don't have information about the signs of \(y\) and \(z\) (the first condition). This too, is insufficient.
(1)+(2) When combined, both conditions are met. Therefore, it is sufficient.
Answer: C
Is \(x^2*y^3*z > 0\)?
For the inequality \(x^2*y^3*z > 0\) to hold true, the following conditions must be met:
1. Both \(y\) and \(z\) must either be positive or negative, meaning they must share the same sign. This would ensure that \(y^3*z\) is positive;
AND
2. \(x\) cannot be zero, to ensure that \(x^2\) is positive.
(1) \(yz > 0\).
The above implies that \(y\) and \(z\) are either both positive or both negative, which satisfies the first condition. However, information about \(x\) (the second condition) is lacking: if \(x = 0\), \(x^2*y^3*z\) would be 0, not more than 0. Not sufficient.
(2) \(xz < 0\).
The above implies that \(x \ne 0\), thus satisfying the second condition. But we don't have information about the signs of \(y\) and \(z\) (the first condition). This too, is insufficient.
(1)+(2) When combined, both conditions are met. Therefore, it is sufficient.
Answer: C
General Discussion
shasadou
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
Own Kudos:
Given Kudos: 1,475
Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
12 Feb 2016, 01:34
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great question
