I think in MUST BE question it’s risky to check with only one set of numbers since we have to be assured that condition works for all the numbers. Below is how I solved this question:

First, looking at the number line we can infer that since it is evenly spaced set absolute value of x is equal to the absolute value of y, or in other words y=-x, where x<0. For example, if x=-3, then y= -(-3)=3.

Now, let’s analyze the options.

I. xyz<0 - Must be true, since x is negative, while others are positive.

II. x+z=y - to be sure for this one, I’ve checked two sets: -1,1,2 and -2,2,4. Both yields true. So, it must be true

III. z(y−x)>0- here both multiples (z and (y-x)) must be positive or negative. Now, since z is positive, (y-x) must be positive. Since y is positive and x is negative, the answer must be positive i.e. 2- (-1)=3>0.

Hence, all of them MUST be true. Answer is E.

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