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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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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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Question Stats:

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

1) \(z>0\)

2) \(x<0\)
[Reveal] Spoiler: OA

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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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New post 09 Mar 2017, 21:40
x, y and w should be of same sign. So both of statements are sufficient. Hence D.

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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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New post 10 Mar 2017, 00:43
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

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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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New post 24 Aug 2017, 05:53
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

Answer is D.

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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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New post 14 Sep 2017, 13:12
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

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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] 14 Sep 2017, 13:12
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