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07 Aug 2019, 00:43
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:51) correct
41%
(01:59)
wrong
based on 407
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
07 Aug 2019, 01:16
Kudos
Bookmarks
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.
Posted from my mobile device
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.
Posted from my mobile device
07 Aug 2019, 02:02
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Bunuel
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
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.
