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Updated on: 20 Oct 2013, 11:56
Originally posted by TheGmatTutor on 10 Jun 2010, 12:52.
Last edited by Bunuel on 20 Oct 2013, 11:56, edited 2 times in total.
Last edited by Bunuel on 20 Oct 2013, 11:56, edited 2 times in total.
Edited the question and added the OA
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Is (x^7)(y^2)(z^3) > 0 ?
(1) yz < 0
(2) xz > 0
(m25#34)
(1) yz < 0
(2) xz > 0
S1 is insufficient because we need the sign of x.
S2 is SUFFICIENT, because x^7*z^3 will always be positive, and y^2 will be positive, so the whole product (x^7)(y^2)(z^3) will be positive. Answer: B.
S2 is SUFFICIENT, because x^7*z^3 will always be positive, and y^2 will be positive, so the whole product (x^7)(y^2)(z^3) will be positive. Answer: B.
(m25#34)
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10 Jun 2010, 14:22
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TheGmatTutor
No, not correct. \(y^2\) is not always positive, it's never negative: \(y^2\geq{0}\).
Inequality \(x^7*y^2*z^3>0\) to be true \(x\) and \(z\) must be either both positive or both negative (note that both positive or both negative excludes the possibility of either of them to be zero) AND \(y\) must not be zero. Because if \(y=0\), then \(x^7*y^2*z^3=0\).
10 Jun 2010, 13:22
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Is \(x^7y^2z^3 > 0\) ?
In order for \(x^7y^2z^3 > 0\) to be true, the following conditions must be met:
1. \(y\) cannot be zero. If \(y = 0\), then \(x^7y^2z^3 \) will equal 0, not greater than it.
AND
2. \(x\) and \(z\) must be either both positive or both negative. If \(x\) and \(z\) have different signs (or if either of them is 0), then \(x^7z^3 \) will be negative (or 0), not positive as required.
(1) \(yz < 0\).
This statement implies that \(y \neq 0\), so the first condition is satisfied. However, we don't have information about the signs of \(x\) and \(z\). Not sufficient.
(2) \(xz > 0\).
This statement implies that \(x\) and \(z\) are either both positive or both negative. So, the second condition is met. However, we don't have information about \(y\); if \(y=0\), then the expression is not positive, but equal to 0. Not sufficient.
(1)+(2) Both conditions, \(y\) not being 0 and \(x\) and \(z\) having the same sign, are satisfied. Therefore, \(x^7y^2z^3 > 0\). Sufficient.
Answer: C
Hope it helps.
In order for \(x^7y^2z^3 > 0\) to be true, the following conditions must be met:
1. \(y\) cannot be zero. If \(y = 0\), then \(x^7y^2z^3 \) will equal 0, not greater than it.
AND
2. \(x\) and \(z\) must be either both positive or both negative. If \(x\) and \(z\) have different signs (or if either of them is 0), then \(x^7z^3 \) will be negative (or 0), not positive as required.
(1) \(yz < 0\).
This statement implies that \(y \neq 0\), so the first condition is satisfied. However, we don't have information about the signs of \(x\) and \(z\). Not sufficient.
(2) \(xz > 0\).
This statement implies that \(x\) and \(z\) are either both positive or both negative. So, the second condition is met. However, we don't have information about \(y\); if \(y=0\), then the expression is not positive, but equal to 0. Not sufficient.
(1)+(2) Both conditions, \(y\) not being 0 and \(x\) and \(z\) having the same sign, are satisfied. Therefore, \(x^7y^2z^3 > 0\). Sufficient.
Answer: C
Hope it helps.
