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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
bibha wrote:
Is x^2 * y^5 * z>0 ?
1.xz/y>0
2.y/z<0


s1: --> x,y, z not = 0.
---> if y = -ve, then xz must be -ve so either x or z is -ve.
if y = +ve, then xz must be +ve x and z must be same sign.

consider y = -ve and x=-ve and z = +ve , evaluate question, answer is false.
consider y= -ve and x=+ve and z = -ve, evaluation question, answer is true.

Therefore: s1 not sufficient.

s2: --> either y=-ve and z=+ve OR y=+ve and z=-ve

Ignore x=+ve or x=-ve since there is a x^2 in question
consider y=-ve and z=+ve, evaluation question, answer is false.
consider y=+ve and z=-ve, evaluation question, answer is false.

s2 alone sufficient.

How to quickly see s1 is insufficient?
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
1. xz/y>0
we need y & z to have similar signs.
but we can't be sure from the first statement, z>0, y<0, x<0, the statement is true
z>0, y>0, x>0, true
z<0, y>0, x>0 true.
Thus, 1) unsuff.
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
what if X=0? Why are we not considering that?
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
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@Bibha

We are not concidering X = 0 because 2) makes it clear that x^2 * y^5 * z <= 0

< because y & z have different signs

= When X = 0. ( also Y & Z cannot be zero as per statement 2 )
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
My approach to see St:1 is insufficient is
xz/y>0 mean both are of same sign.
x^2*y^5*z => x*((x*z)*y^5) here ((x*z)*y^5) is positive since y^5 does not change y sign and xz is same so both give positive, here we dont know remaining x therefore insufficient.
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
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Bumping for review and further discussion.
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Bunuel wrote:
bibha wrote:
Is x^2 * y^5 * z>0 ?
(1) xz/y>0
(2) y/z<0


For \(x^2*y^5*z>0\) to hold true:
1. \(x\) must not be zero;
and
2. \(y\) and \(z\) must be either both positive or both negative.

(1) \(\frac{xz}{y}>0\) --> first condition is satisfied: \(x\neq{0}\), but we don't know aout the second one: \(\frac{xz}{y}>0\) means that either all of them are positive (answer YES) or ANY two are negative and the third one is positive, so it's possible \(y\) and \(z\) to have opposite signs (answer NO). Not sufficient.

(2) \(\frac{y}{z}<0\) --> \(y\) and \(z\) have opposite signs --> second condition is already violated, so the answer to the question is NO. Sufficient.

Answer: B.

Side note for (2): \(\frac{y}{z}<0\) does not mean that \(x^2*y^5*z<0\), it means that \(x^2*y^5*z\leq{0}\) because it's possible \(x\) to be equal to zero and in this case \(x^2*y^5*z=0\). But in any case \(x^2*y^5*z\) is not MORE than zero, so we can answer NO to the question.

Hoe it's clear.


Bunuel shouldn't it be

1) x, y, and z must ≠ 0 AND (why only x ≠ 0?)
2) y and z must be both positive or both negative
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
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Hoozan wrote:
Bunuel wrote:
bibha wrote:
Is x^2 * y^5 * z>0 ?
(1) xz/y>0
(2) y/z<0


For \(x^2*y^5*z>0\) to hold true:
1. \(x\) must not be zero;
and
2. \(y\) and \(z\) must be either both positive or both negative.

(1) \(\frac{xz}{y}>0\) --> first condition is satisfied: \(x\neq{0}\), but we don't know aout the second one: \(\frac{xz}{y}>0\) means that either all of them are positive (answer YES) or ANY two are negative and the third one is positive, so it's possible \(y\) and \(z\) to have opposite signs (answer NO). Not sufficient.

(2) \(\frac{y}{z}<0\) --> \(y\) and \(z\) have opposite signs --> second condition is already violated, so the answer to the question is NO. Sufficient.

Answer: B.

Side note for (2): \(\frac{y}{z}<0\) does not mean that \(x^2*y^5*z<0\), it means that \(x^2*y^5*z\leq{0}\) because it's possible \(x\) to be equal to zero and in this case \(x^2*y^5*z=0\). But in any case \(x^2*y^5*z\) is not MORE than zero, so we can answer NO to the question.

Hoe it's clear.


Bunuel shouldn't it be

1) x, y, and z must ≠ 0 AND (why only x ≠ 0?)
2) y and z must be both positive or both negative


If either of the unknowns is 0, then x^2*y^5*z = 0, and not > 0. The fact that y and z should not be 0 included in the second point: if y and z are both positive or both negative than neither of them is 0.
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
Quote:
If either of the unknowns is 0, then x^2*y^5*z = 0, and not > 0. The fact that y and z should not be 0 included in the second point: if y and z are both positive or both negative than neither of them is 0.


Ahh missed that one. Thank you :)
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
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Re: Is x^2*y^5*z > 0 ? (1) xz/y > 0 (2) y/z < 0 [#permalink]
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