Is z < 0?

(1) xy > 0 which means

either x > 0 and y > 0

or x < 0 and y < 0

So either y > 0 or y < 0

If y > 0 and yz < 0 then z < 0

but if y < 0 and yz < 0 then z > 0

Hence Statement (1) is Not Sufficient

(2) x > 0

This statement by itself gives no information about z, so this is Not Sufficient

(1) & (2)

xy > 0 and yz < 0 and x > 0

if we take xy > 0 and x > 0 then y > 0

We also have yz < 0, as y > 0, so z < 0

So (1) & (2) together is Sufficient. Hence answer is C

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