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If xy > 0 and xz < 0, which of the following must be true?

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If xy > 0 and xz < 0, which of the following must be true?  [#permalink]

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New post 07 Aug 2019, 00:43
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (01:25) correct 46% (01:55) wrong based on 55 sessions

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Re: If xy > 0 and xz < 0, which of the following must be true?  [#permalink]

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New post 07 Aug 2019, 01:16
1
xy>0 and xz<0
xy>0 means either x>0 and y>0 or x<0 and y<0
xz<0 means that when x and z have opposite signs. When x>0 then z<0 and when x<0 then y>0
I.y/z<0 must be true because y and x have the same sign. x and z have opposite signs and by extension y and z have opposite signs. Hence yz<0 and y/z<0.
II. xyz<0. Not necessarily true all the time because when x and y who have the same sign are negative, z>0 and xyz>0. II. is however true when x and y are positive and z<0 then xyz<0.

III. xy-xz>0. always true. When x and y are positive then z<0, then xy>0 and xz<0, xy-xz>0 is true. If x<0 and y<0 then z>0 meaning xz<0. Hence xy-xz>0. Hence always true.

Answer is therefore D.

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Re: If xy > 0 and xz < 0, which of the following must be true?  [#permalink]

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New post 07 Aug 2019, 02:02
Bunuel wrote:
If xy > 0 and xz < 0, which of the following must be true?

I. y/z < 0
II. xyz < 0
III. xy - xz > 0

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III



xy>0 and xz<0

2 cases here :

If x>0:

y>0

z<0

If x<0:

y<0

z>0.

Scan the answer choices :

I. y/z < 0.......true . y and z are always in opposite direction.

II. xyz < 0. could be true.

III. xy - xz > 0.......xy>xz...........True.......Given, xy>0 and xz<0.

D is the correct answer.
GMAT Club Bot
Re: If xy > 0 and xz < 0, which of the following must be true?   [#permalink] 07 Aug 2019, 02:02
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If xy > 0 and xz < 0, which of the following must be true?

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