Question 1202898: If xy>0 and xz<0, which of the following statements must be true?
I. x+y+z>0
II. xyz<0
III. xy+xz+yz>0
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) None of the above
Answer by ikleyn(52779)   (Show Source):
You can put this solution on YOUR website! .
If xy > 0 and xz < 0, which of the following statements must be true?
I. x + y + z > 0
II. xyz < 0
III. xy + xz + yz > 0
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) None of the above
~~~~~~~~~~~~~~~~~
The answer is (E).
To prove it, it is enough to provide couner-examples to cases (I), (II) and (III) separately.
Counter-example to (I) : x= -1, y= -1, z= 1.
Counter-example to (II) : x= -1, y= -1, z= 1.
Counter-example to (III): x= -1, y= -1, z= 1.
Solved, with explanations.
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