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

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Senior Manager
Joined: 26 Dec 2015
Posts: 256
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
if xy>0 and xz<0, which of the following must be true?  [#permalink]

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28 Oct 2017, 11:09
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00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:02) correct 41% (01:57) wrong based on 106 sessions

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

I. $$\frac{y}{z}$$ < 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
Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
if xy>0 and xz<0, which of the following must be true?  [#permalink]

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28 Oct 2017, 11:27
1
LakerFan24 wrote:
if xy > 0 and xz < 0, which of the following must be true?

I. $$\frac{y}{z}$$ < 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

$$xy>0$$ & $$xz<0$$ implies

$$x>0$$, $$y>0$$ & $$z<0$$ ----------(1) $$OR$$

$$x<0$$, $$y<0$$ & $$z>0$$ ----------(2)

I) as is clear from conditions (1) and (2) $$y$$ & $$z$$ will always have opposite signs. hence $$\frac{y}{z}<0$$. True

II) from condition (1) we have $$xyz<0$$ and from condition (2) we have $$xyz>0$$. Hence not always true

III) $$xy>0$$ & $$xz<0$$ or $$-xz>0$$. add both to get $$xy-xz>0$$. True

Option D
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Joined: 06 Apr 2018
Posts: 10
Re: if xy>0 and xz<0, which of the following must be true?  [#permalink]

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08 Aug 2018, 12:06
if xy > 0 and xz < 0, which of the following must be true?

I. y/z< 0 either y and x are both positive or both x and y are negative. either x or z is negative. Combining those equation means that one of z and y MUST be negative = product has to be negative

II. xyz < 0 possible scenario: x= negative, y=negative, z=positve , product will be positive!

III. xy - xz > 0 we know xy is positive, and we know xz is negative, subtract a negative number from a positive MUST produce a positive number

kudos if it helped :D
Re: if xy>0 and xz<0, which of the following must be true? &nbs [#permalink] 08 Aug 2018, 12:06
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