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If xy^2z < 0 , then which one of the following statements must also be

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If xy^2z < 0 , then which one of the following statements must also be  [#permalink]

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New post Updated on: 06 Jul 2019, 05:26
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Question Stats:

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Originally posted by Bunuel on 09 Apr 2019, 03:37.
Last edited by SajjadAhmad on 06 Jul 2019, 05:26, edited 1 time in total.
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Re: If xy^2z < 0 , then which one of the following statements must also be  [#permalink]

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New post 09 Apr 2019, 03:42
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Bunuel wrote:
If \(xy^2z < 0\), then which one of the following statements must also be true?

I. xz < 0
II. z < 0
III. xyz < 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III


for \(xy^2z < 0\)
either of x,z has to be -ve and y may or may not be -ve
so
out of given options xz < 0 is always true
IMO B
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Re: If xy^2z < 0 , then which one of the following statements must also be  [#permalink]

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New post 09 Apr 2019, 04:08
xy^2z<0. y^2>0. So xz<0. Either x positive and y negative. Or x negative and y positive. 1. xz<0 (true as established) 2. Z<0 (cant say as x could be <0). 3. xyz<0. xz<0 but y could be positive or negative. Just because y^2 is positive doesn't mean y is positive. So xyz is negative if y is positive and xyz is positive if y is negative. Only 1 can be established. Ans B

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Re: If xy^2z < 0 , then which one of the following statements must also be  [#permalink]

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New post 09 Apr 2019, 04:32
Bunuel wrote:
If \(xy^2z < 0\), then which one of the following statements must also be true?

I. xz < 0
II. z < 0
III. xyz < 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III


Given,

\(xy^2z < 0\)

\(y^2 >0\)

So, xz<0. It indicates that either x or z is negative.

y could be negative or positive.

xyz<0. not always true. it is true only if y is positive.

Thus, B is the correct answer.
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Re: If xy^2z < 0 , then which one of the following statements must also be   [#permalink] 09 Apr 2019, 04:32
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