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

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

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New post 28 Oct 2017, 11:09
2
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A
B
C
D
E

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
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Joined: 25 Feb 2013
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if xy>0 and xz<0, which of the following must be true?  [#permalink]

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

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New post 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
GMAT Club Bot
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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if xy>0 and xz<0, which of the following must be true?

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