Question 1202898
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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
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The answer is &nbsp;(E).


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To prove it, &nbsp;it is enough to provide couner-examples to cases &nbsp;(I), &nbsp;(II) &nbsp;and &nbsp;(III) &nbsp;separately.



<pre>
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.
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Solved, &nbsp;with explanations.