If x y z, which of the following may be true?

Question

If x > y > z, which of the following  may be  true?

I. |x| > |y| > |z|
II. |z| > |y| > |x|
III. |y| > |x| > |z|

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Source: Experts Global

niks18 · Answer

If  x  is positive then Statement I will be true

and if x is negative then Statement II will be true. (When  x  is negative  z  will be the lowest value but it's magnitude will be highest for eg. if x=-1,y=-2 & z=-3 then |z|>|y|>|x|)

Option  C

Cbirole · Answer

Case 1:Let's consider x=3, y=2, z=1(all positive)- I follows
Case 2: Let's consider x= -3, y=-4, z=-5(all negative)- II follows 
Hence answer is C

KarishmaB · Answer

Let's also see why statement III is not possible. 
If x > y but |y| > |x|, what does this imply? It implies that y is negative. 
If y > z, it means z is also negative and more negative i.e. with higher absolute value. So |z| must be greater than |y|.
But as per stmnt III, |y| > |z| which is not possible.

rak08 · Answer

Can you please explain more as to how to eliminate E
I was confused between C & E

How do i assess things better in such questions.

laflem · Answer

Curious how we know we have to input all positives or all negatives?

I was under the assumption any digits can work as long as the results are one of the answers. I, II and III can all be disproven with a combination of positive and negative digits for x, y and z.

Thanks

Bunuel · Answer

Notice that the question asks which of the options  may  be true, not  must  be true. So if an option works for even one set of values, it's valid.

As for which numbers to try, the options involve absolute values, so a good strategy is to plug in real numbers that satisfy x > y > z. We test all positive and then all negative values because with positives, the order of absolute values stays the same, while with negatives, it reverses.

If x > y > z, which of the following may be true?

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