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# Is x^2 * y^5 * z>0 ?

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Is x^2 * y^5 * z>0 ? [#permalink]  31 Jul 2010, 20:41
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57% (02:06) correct 43% (01:26) wrong based on 120 sessions
Is x^2 * y^5 * z>0 ?

(1) xz/y>0
(2) y/z<0
[Reveal] Spoiler: OA
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Re: qs [#permalink]  31 Jul 2010, 20:47
Hi,

To have expression > 0 , there are two cases -
1) both y and z is positive or
2) both y and z is negative ( because x2 is alwasy positive, irrespecitve of sign of x )

Option 1 is not sufficient .

Option 2 is sufficient as it tells that y and z is of opposite sign. So expression is less than zero.
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Re: qs [#permalink]  01 Aug 2010, 06:08
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: qs [#permalink]  01 Aug 2010, 07:51
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: qs [#permalink]  02 Aug 2010, 23:06
what if X=0? Why are we not considering that?
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Re: qs [#permalink]  03 Aug 2010, 04:56
@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: qs [#permalink]  03 Sep 2010, 05:03
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: qs [#permalink]  09 Sep 2010, 20:58
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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.

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.
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Re: Is x^2 * y^5 * z>0 ? [#permalink]  04 Sep 2013, 02:46
Expert's post
Bumping for review and further discussion.
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Re: Is x^2 * y^5 * z>0 ? [#permalink]  01 Nov 2014, 13:50
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Re: Is x^2 * y^5 * z>0 ?   [#permalink] 01 Nov 2014, 13:50
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