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

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Senior Manager
Senior Manager
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G
Joined: 26 Dec 2015
Posts: 257

Kudos [?]: 58 [0], given: 1

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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New post 28 Oct 2017, 12:09
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Difficulty:

  65% (hard)

Question Stats:

49% (01:21) correct 51% (01:20) wrong based on 59 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
[Reveal] Spoiler: OA

Kudos [?]: 58 [0], given: 1

Director
Director
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P
Joined: 25 Feb 2013
Posts: 619

Kudos [?]: 304 [0], given: 39

Location: India
GPA: 3.82
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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, 12:27
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

Kudos [?]: 304 [0], given: 39

if xy>0 and xz<0, which of the following must be true?   [#permalink] 28 Oct 2017, 12:27
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if xy>0 and xz<0, which of the following must be true?

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