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# If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1321
Location: Malaysia
If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0  [#permalink]

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09 Mar 2017, 22:36
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77% (01:15) correct 23% (00:55) wrong based on 128 sessions

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If $$wx>0$$, $$xy>0$$, and $$yz<0$$, is $$w^3*z^2<0$$ ?

1) $$z>0$$

2) $$x<0$$

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Intern
Joined: 26 Aug 2016
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GMAT 1: 650 Q47 V33
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Re: If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0  [#permalink]

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09 Mar 2017, 22:40
x, y and w should be of same sign. So both of statements are sufficient. Hence D.

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Joined: 05 Jan 2017
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Location: India
Re: If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0  [#permalink]

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10 Mar 2017, 01:43
wx>0, xy>0 and yz<0. This condition holds true if w,x,y are of same sign and z is of opposite sign
There fore in order to answer the question, we need the sign of atleast one variable.

St 1: z is negative. that means w,x,y are positive. therefore w^3 will be positive and z^2 will be positive and hence w^3.z^2 will be positive. ANSWER
St 2: x is negative. that means w and y are negative and z is positive. hence w^3 is negative and z^2 is positive. Hence w^3.z^2 will be negative. ANSWER

Option D
Intern
Joined: 18 Aug 2017
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Re: If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0  [#permalink]

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24 Aug 2017, 06:53
Because $$z^2$$ is always positive, therefore the question is really asking if w<0. And wx>0 so if we know the sign of x we can answer the question.

1- z is positive => y negative => x is negative, we know the sign, SUFF
2- x<0, we know the sign, SUFF

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Re: If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0  [#permalink]

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14 Sep 2017, 14:12
My approach - marked it wrong initially, but then realized why it is D:
1) z > 0
--> y * z < 0 means y is -ve and z is +ve
--> indicates only case of -x *-y>0 and - w*-x>0
--> therefore z sq*w cube <0

2) x<0
--> only case of -x*-y >0
--> -x*-w> 0 (only case possible)
--> -y*z< 0 (carrying over the sign for y)
--therefore w cube * z sq < 0 suff

Ans is D
Re: If wx>0, xy>0, and yz<0, is w^3*z^2<0? 1) z>0 2) x<0 &nbs [#permalink] 14 Sep 2017, 14:12
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