Hi,
As xyz>0 we have two options:
1. All of the three are positive.
2. 2 are negative and one is positive.
(1) xy>0 gives us the options that either x and y are both positive or both negative. Either way, z has to be positive.
(2) xz>0 gives us the options that either x and z are both positive or both negative. Either way, y has to be positive.
Combining the two statements we know that z and y are positive. Therefore, x is bound to be positive as well.
Therefore, C
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