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If zy < xy < 0, is |x - z | + |x| = |z|?

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Joined: 10 Apr 2018
Posts: 181
Re: If zy < xy < 0, is |x - z | + |x| = |z|?  [#permalink]

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New post 17 Sep 2018, 10:41
Hi,

here are my two cents for this question
we are given that
zy<xy<0


Just imagine a number line we will have two cases

Lets see the easiest case first

case 1 because if y>0 then x and z are <0 and definitely x>z here because when we multiply positive y to z and x we should have value of zy<xy
-------z-------x------0-------y

case 2 because if y<0 then x and z are >0 and definitely z>x here because when we multiply negative y to z and x we should have value of zy<xy
------y------0-------x---------z

what are we asked IS the absolute vale of (z-x)+ absolute value of x (x-0) equal to absolute value of z which is (z-0)

Now look at the number lines and see which region would (z-x) , (x-0 and (z-0) be

what do we see in both cases x is between 0 and z . then definitely we can say yes it possible for what is asked. Now had this been which of the following must be true you should pick up this as answer choice.
But in our case we don't need any information to answer our question. However, both the statements point towards Case 1 discussed above. So each is sufficient.


Probus
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Re: If zy < xy < 0, is |x - z | + |x| = |z|? &nbs [#permalink] 17 Sep 2018, 10:41

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