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

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.

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