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

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Joined: 02 Sep 2009
Posts: 58401
If xy^2z < 0 , then which one of the following statements must also be  [#permalink]

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Updated on: 06 Jul 2019, 05:26
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:48) correct 22% (01:01) wrong based on 37 sessions

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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

Source: Nova GMAT
Difficulty Level: 600

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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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09 Apr 2019, 03:42
1
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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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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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.
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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