DestinyChild wrote:

If XYZ>0 is X>0

XY > 0

XZ > 0

Obviously the answer is Yes or No;

Get your kudos for reasoning out why the answer is C and keep an eye on time too

Triple kudos for someone suggesting quicker technique for DS stems with triple variables...!

Certainly each statement is not sufficient alone (the logic is identical for each: for S1, x and y can both be negative or both positive, and for S2, x and z can both be negative or both positive). You might notice that S1 tells us z is positive, and S2 tells us y is positive, but that's not what we're looking for.

Now, together, the inequality xy > 0 means 'x and y have the same sign'. So from the two statements we know x and y have the same sign, and x and z have the same sign, so x, y and z all have the same sign. If xyz > 0, they must all be positive, and the answer is C.

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