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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: 277
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, 12:09
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Difficulty:

65% (hard)

Question Stats:

53% (01:13) correct 47% (01:23) wrong based on 74 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
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Joined: 25 Feb 2013
Posts: 1183
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, 12:27
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
if xy>0 and xz<0, which of the following must be true? &nbs [#permalink] 28 Oct 2017, 12:27
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